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06 Jun, 2024 | What are Diffusion Models?
06 Jun, 2024
Diffusion models are a powerful class of generative models that have gained prominence in the field of machine learning and artificial intelligence. They offer a unique approach to generating data by simulating the diffusion process, which is inspired by physical processes such as heat diffusion. This article delves into the diffusion model, exploring its architecture, working principles, applications, and advantages.
Table of Content
Understanding Diffusion ModelsKey Components of Diffusion ModelsArchitecture of Diffusion ModelsWorking Principle of Diffusion ModelsTraining Diffusion ModelsApplications of Diffusion ModelsAdvantages of Diffusion ModelsLimitations of Diffusion ModelsConclusionUnderstanding Diffusion ModelsDiffusion models are generative models that learn to reverse a diffusion process to generate data. The diffusion process involves gradually adding noise to data until it becomes pure noise. Through this process, a simple distribution is transformed into a complex data distribution in a series of small, incremental steps. Essentially, these models operate as a reverse diffusion phenomenon, where noise is introduced to the data in a forward manner and removed in a reverse manner to generate new data samples. By learning to reverse this process, diffusion models start from noise and gradually denoise it to produce data that closely resembles the training examples.
Key Components of Diffusion ModelsForward Diffusion Process: This process involves adding noise to the data in a series of small steps. Each step slightly increases the noise, making the data progressively more random until it resembles pure noise.Reverse Diffusion Process: The model learns to reverse the noise-adding steps. Starting from pure noise, the model iteratively removes the noise, generating data that matches the training distribution.Score Function: This function estimates the gradient of the data distribution concerning the noise. It helps guide the reverse diffusion process to produce realistic samples.Architecture of Diffusion ModelsThe architecture of diffusion models typically involves two main components:
Forward Diffusion ProcessIn this process, noise is incrementally added to the data over a series of steps. This is akin to a Markov chain where each step slightly degrades the data by adding Gaussian noise.
Mathematically, this can be represented as:
q(x_t | x_{t-1}) = \mathcal{N}(x_t; \sqrt{\alpha_t} x_{t-1}, (1 - \alpha_t)I)
where,
x_t is the noisy data at step t,\alpha_t controls the amount of noise added.Reverse Diffusion ProcessThe reverse process aims to reconstruct the original data by denoising the noisy data in a series of steps, reversing the forward diffusion.
This is typically modelled using a neural network that predicts the noise added at each step:
p_\theta(x_{t-1} | x_t) = \mathcal{N}(x_{t-1}; \mu_\theta(x_t, t), \sigma_\theta(x_t, t))
where,
\mu_\theta and \sigma_\theta are learned parameters.Working Principle of Diffusion ModelsThe core idea behind diffusion models is to train a neural network to reverse the diffusion process. During training, the model learns to predict the noise added at each step of the forward process. This is done by minimizing a loss function that measures the difference between the predicted and actual noise.
Forward Process (Diffusion)The forward process involves gradually corrupting the data x_0 with Gaussian noise over a sequence of time steps. Let x_t represent the noisy data at time step t. The process is defined as:
x_t = \sqrt{1 - \beta_t} x_{t-1} + \sqrt{\beta_t} \epsilon
where:
\beta_t is the noise schedule, a small positive number that controls the amount of noise added at each step.\epsilon is is Gaussian noise. As t increases, x_t becomes more noisy until it approximates a Gaussian distribution.
Reverse Process (Denoising)The reverse process aims to reconstruct the original data x_0 from the noisy data x_T at the final time step T. This process is modelled using a neural network to approximate the conditional probability p_\theta(x_{t-1} | x_t). The reverse process can be formulated as:
x_{t-1} = \frac{1}{\sqrt{1 - \beta_t}} \left( x_t - \frac{\beta_t}{\sqrt{1 - \beta_t}} \epsilon_\theta(x_t, t) \right)
where,
\epsilon_\theta is a neural network parameterized by \theta that predicts the noise.Training Diffusion ModelsThe training objective for diffusion models involves minimizing the difference between the true noise \epsilon added in the forward process and the noise predicted by the neural network \epsilon_\theta. The score function, which estimates the gradient of the data distribution concerning the noise, plays a crucial role in guiding the reverse process. The loss function is typically the mean squared error (MSE) between these two quantities:
L(\theta) = \mathbb{E}_{x_0, \epsilon, t} \left[ \| \epsilon - \epsilon_\theta(x_t, t) \|^2 \right]
This encourages the model to accurately predict the noise and, consequently, to denoise effectively during the reverse process.
Applications of Diffusion ModelsDiffusion models have shown great promise in various applications, particularly in generative tasks. Some notable applications include:
Image Generation: Diffusion models can generate high-quality, realistic images from random noise. They have been used to create diverse datasets for training other machine learning models.Speech Synthesis: These models can generate human-like speech by modelling the distribution of audio signals.Data Augmentation: Diffusion models can be used to augment existing datasets with new, synthetic samples, improving the performance of machine learning models.Anomaly Detection: By modelling the normal data distribution, diffusion models can help identify anomalies that deviate from this distribution.Advantages of Diffusion ModelsFlexibility: They can model complex data distributions without requiring explicit likelihood estimation.High-Quality Generation: Diffusion models generate high-quality samples, often surpassing other generative models like GANs.Stable Training: Unlike GANs, diffusion models avoid issues like mode collapse and unstable training dynamics.Theoretical Foundations: Based on well-understood principles from stochastic processes and statistical mechanics.Scalability: Can be effectively scaled to high-dimensional data and large datasets.Robustness: More robust to hyperparameter changes compared to GANs.Limitations of Diffusion ModelsComputationally Intensive: Requires significant computational resources due to the large number of iterative steps.Slow Sampling: Generating samples can be slow because of the many steps needed for the reverse diffusion process.Complexity: The architecture and training process can be complex, making them challenging to implement and understand.Memory Usage: High memory consumption during training due to the need to store multiple intermediate steps.Fine-Tuning: Requires careful tuning of noise schedules and other hyperparameters to achieve optimal performance.Resource Demand: High demand for GPUs or TPUs, making them less accessible for small-scale research or applications with limited resources.ConclusionDiffusion models represent a significant advancement in the field of generative modelling. Their ability to generate high-quality data through a well-defined, stable process makes them a valuable tool for various applications. As research in this area continues to evolve, diffusion models are expected to play an increasingly important role in the development of sophisticated AI systems. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models? | https://www.geeksforgeeks.org/what-are-diffusion-models/?ref=lbp | NLP | What are Diffusion Models? | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Agents in Artificial Intelligence, What are Diffusion Models?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding? | GeeksforGeeks | [-0.0253891367, -0.0231480692, -0.0223094746, 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08 Oct, 2024 | ML | Common Loss Functions
08 Oct, 2024
Loss functions are a fundamental aspect of machine learning algorithms, serving as the bridge between model predictions and the actual outcomes. They quantify how well or poorly a model is performing by calculating the difference between predicted values and actual values. This difference, or “loss,” guides the optimization process to improve model accuracy. In this article, we will explore various common loss functions used in machine learning, categorized into regression and classification tasks.
Table of Content
Importance of Loss Functions in Machine LearningCategories of Loss FunctionsRegression Loss Functions in Machine LearningClassification Loss Functions in Machine LearningChoosing the Right Loss FunctionImportance of Loss Functions in Machine LearningLoss functions are integral to the training process of machine learning models. They provide a measure of how well the model’s predictions align with the actual data. By minimizing this loss, models learn to make more accurate predictions.
The choice of a loss function can significantly affect the performance of a model, making it crucial to select an appropriate one based on the specific task at hand.
Categories of Loss FunctionsThe loss function estimates how well a particular algorithm models the provided data. Loss functions are classified into two classes based on the type of learning task
Regression Models: predict continuous values.Classification Models: predict the output from a set of finite categorical values.By selecting the right loss function, you optimize the model to meet the task’s specific needs, whether it’s a regression or classification problem.
Regression Loss Functions in Machine LearningRegression tasks involve predicting continuous values, such as house prices or temperatures. Here are some commonly used loss functions for regression:
1. Mean Squared Error (MSE) It is the Mean of Square of Residuals for all the datapoints in the dataset. Residuals is the difference between the actual and the predicted prediction by the model.
In machine learning, squaring the residuals is crucial to handle both positive and negative errors effectively. Since normal errors can be either positive or negative, summing them up might result in a net error of zero, misleading the model to believe it is performing well, even when it is not. To avoid this, we square the residuals, converting all values to positive, which gives a true representation of the model’s performance.
Squaring also has the added benefit of assigning more weight to larger errors, meaning that when the cost function is far from its minimal value, the model is penalized more heavily for larger mistakes, helping it converge to the minimal value faster.
The Mean Squared Error (MSE) is a common loss function in machine learning where the mean of the squared residuals is taken rather than just the sum. This ensures that the loss function is independent of the number of data points in the training set, making the metric more reliable across datasets of varying sizes. However, MSE is sensitive to outliers, as large errors have a disproportionately large impact on the final result.
This squaring process is essential for most regression loss functions, ensuring that models can minimize error and improve performance. The formula is:
[Tex]\begin{equation} M S E=\frac{\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}}{n} \end{equation}[/Tex]
Python implementation:
Python
import numpy as np
# Mean Squared Error
def mse( y, y_pred ) :
return np.sum( ( y - y_pred ) ** 2 ) / np.size( y )
where,
i – ith training sample in a datasetn – number of training samplesy(i) – Actual output of ith training sampley-hat(i) – Predicted value of ith training sample2. Mean Absolute Error (MAE) / La LossThe Mean Absolute Error (MAE) is a commonly used loss function in machine learning that calculates the mean of the absolute values of the residuals for all datapoints in the dataset.
The absolute value of the residuals is taken to convert any negative differences into positive values, ensuring that all errors are treated equally.Taking the mean makes the loss function independent of the number of datapoints in the training set, allowing it to provide a consistent measure of error across datasets of different sizes.One key advantage of MAE is that it is robust to outliers, meaning that extreme values do not disproportionately affect the overall error calculation. However, despite this robustness, MAE is often less preferred than Mean Squared Error (MSE) in practice. This is because it is harder to calculate the derivative of the absolute function, as it is not differentiable at the minima. This makes MSE a more common choice when working with optimization algorithms that rely on gradient-based methods.
This loss function example illustrates how the choice of a loss function can significantly impact model performance and training efficiency.
Source: WikipediaThe formula:
[Tex]\begin{equation} M A E=\frac{\sum_{i=1}^{n}\left|y_{i}-\hat{y}_{i}\right|}{n} \end{equation}[/Tex]
Python implementation:
Python
# Mean Absolute Error
def mae( y, y_pred ) :
return np.sum( np.abs( y - y_pred ) ) / np.size( y )
3. Mean Bias ErrorIt is similar to Mean Squared Error (MSE) but provides less accuracy. However, it can help in determining whether the model has a positive bias or negative bias. By analyzing the loss function results, you can assess whether the model consistently overestimates or underestimates the actual values. This insight allows for further refinement of the machine learning model to improve prediction accuracy. Such loss function examples are useful in understanding model performance and identifying areas for optimization, making them an essential part of the machine learning process.
The formula:
[Tex]\begin{equation} M B E=\frac{\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)}{n} \end{equation}[/Tex]
Python implementation:
Python
# Mean Bias Error
def mbe( y, y_pred ) :
return np.sum( y - y_pred ) / np.size( y )
4. Huber Loss / Smooth Mean Absolute ErrorThe Huber loss function is a combination of Mean Squared Error (MSE) and Mean Absolute Error (MAE), designed to take advantage of the best properties of both loss functions. It is commonly used in machine learning when training models because it is less sensitive to outliers than MSE and is still differentiable at its minimum, unlike MAE.
When the error is small, the MSE component of the Huber loss is applied, making the model more sensitive to small errors. Conversely, when the error is large, the MAE part of the loss function is utilized, reducing the impact of outliers.A new hyper-parameter, typically called “delta,” is introduced to determine the threshold where the Huber loss switches from MSE to MAE. This delta value allows the loss function to balance the transition between the two. Additional terms involving this hyper-parameter are also incorporated to smooth the shift between MSE and MAE, ensuring a seamless transition within the loss function.
This is a powerful loss function example that demonstrates the flexibility and effectiveness of loss functions in machine learning, especially when dealing with datasets containing outliers.
Loss FunctionsThe formula:
[Tex]\begin{equation} \text { Loss }= \begin{cases}\frac{1}{2} *(x-y)^{2} & \text { if }(|x-y| \leq \delta) \\ \delta *|x-y|-\frac{1}{2} * \delta^{2} & \text { otherwise }\end{cases} \end{equation}[/Tex]
Python implementation:
Python
def Huber(y, y_pred, delta):
condition = np.abs(y - y_pred) < delta
l = np.where(condition, 0.5 * (y - y_pred) ** 2,
delta * (np.abs(y - y_pred) - 0.5 * delta))
return np.sum(l) / np.size(y)
Classification Loss Functions in Machine Learning1. Cross-Entropy LossCross-Entropy Loss, also known as Negative Log Likelihood, is a commonly used loss function in machine learning for classification tasks. This loss function measures how well the predicted probabilities match the actual labels.
The cross-entropy loss increases as the predicted probability diverges from the true label. In simpler terms, the farther the model’s prediction is from the actual class, the higher the loss. This makes cross-entropy loss an essential tool for improving the accuracy of classification models by minimizing the difference between the predicted and actual labels.
A loss function example using cross-entropy would involve comparing the predicted probabilities for each class against the actual class label, adjusting the model to reduce this error during training.
Python implementation:
Python
# Binary Loss
def cross_entropy(y, y_pred):
return - np.sum(y * np.log(y_pred) + (1 - y) * np.log(1 - y_pred)) / np.size(y)
The formula:
[Tex]\begin{equation} \text { CrossEntropyLoss }=-\left(y_{i} \log \left(\hat{y}_{i}\right)+\left(1-y_{i}\right) \log \left(1-\hat{y}_{i}\right)\right) \end{equation}[/Tex]
2. Hinge LossHinge Loss, also known as Multi-class SVM Loss, is a type of loss function used for maximum-margin classification tasks, most commonly applied in support vector machines (SVMs). This loss function in machine learning is particularly effective in ensuring that the decision boundary is as far away as possible from any data points. Hinge Loss is a convex function, making it suitable for optimization using a convex optimizer.
This type of loss function is widely used in classification tasks as it encourages models to achieve a larger margin between different classes, leading to better generalization. A common loss function example involving Hinge Loss can be seen in SVM models.
The formula:
[Tex]\begin{equation} \text { SVMLoss }=\sum_{j \neq y_{i}} \max \left(0, s_{j}-s_{y_{i}}+1\right) \end{equation}[/Tex]
Python implementation:
Python
# Hinge Loss
def hinge(y, y_pred):
l = 0
size = np.size(y)
for i in range(size):
l = l + max(0, 1 - y[i] * y_pred[i])
return l / size
3. Kullback-Leibler Divergence (KL Divergence)Kullback-Leibler Divergence (KL Divergence) is a widely used loss function in machine learning that measures how one probability distribution differs from a reference probability distribution. This divergence quantifies the “distance” between the two distributions, making it a crucial tool when comparing them.
In machine learning, especially in models involving neural networks, KL Divergence is often applied in tasks where the model outputs are probabilities, such as in classification tasks using the softmax function. By minimizing KL Divergence, the model ensures that its predicted probability distribution closely aligns with the true distribution, making it a valuable loss function example for applications requiring precise probabilistic outputs.
The KL divergence formula:
[Tex]D_{\text{KL}}(P \parallel Q) = \sum_{i} P(i) \log\left(\frac{P(i)}{Q(i)}\right)
[/Tex]
Python Implementation:
Python
import numpy as np
def kl_divergence(P, Q):
"""
Calculate the Kullback-Leibler (KL) Divergence between two distributions P and Q.
Parameters:
P (array-like): The true probability distribution.
Q (array-like): The estimated probability distribution.
Returns:
float: The KL divergence between P and Q.
"""
# Ensure P and Q are numpy arrays
P = np.asarray(P, dtype=np.float32)
Q = np.asarray(Q, dtype=np.float32)
# Add a small epsilon to avoid division by zero or log of zero
epsilon = 1e-10
P = np.clip(P, epsilon, 1)
Q = np.clip(Q, epsilon, 1)
return np.sum(P * np.log(P / Q))
Choosing the Right Loss FunctionThe choice of a loss function in machine learning is influenced by several key factors:
Nature of the Task: Determine whether you are dealing with regression or classification problems.Presence of Outliers: Consider how outliers in your dataset may impact your decision; some loss functions (e.g., Mean Absolute Error (MAE) and Huber loss) are more robust to outliers than others.Model Complexity: Simpler models may benefit from more straightforward loss functions, such as Mean Squared Error (MSE) or Cross-Entropy.Interpretability: Some loss functions provide more intuitive explanations than others, making them easier to understand in practice.ConclusionUnderstanding and selecting the appropriate loss function is critical for building effective machine learning models. Whether you are handling regression or classification tasks, each type of loss function has its strengths and weaknesses, making it suitable for specific scenarios. By carefully considering these factors, practitioners can optimize their models’ performance and achieve better predictive accuracy, ensuring the success of their machine learning endeavors.
Loss Functions in Machine Learning – FAQsHow can I implement custom loss functions in machine learning frameworks?Most machine learning frameworks (like TensorFlow and PyTorch) allow you to define and implement custom loss functions by creating a function that calculates the loss based on the model’s predictions and the actual values. You can then integrate this custom function into your training loop as you would with standard loss functions.
Are there loss functions for imbalanced datasets?Yes, specific loss functions are designed to handle imbalanced datasets. For example, Focal Loss is an adaptation of Cross-Entropy Loss that puts more focus on hard-to-classify examples, making it effective for cases where some classes are significantly underrepresented.
Can loss functions affect model training speed?Yes, the choice of a loss function can influence the training speed of a model. Some loss functions may provide smoother gradients, which can lead to faster convergence during optimization, while others may present challenges like local minima that slow down the training process. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions | https://www.geeksforgeeks.org/ml-common-loss-functions/ | NLP | ML | Common Loss Functions | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Agents in Artificial Intelligence, What are Diffusion Models?, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require 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18 Dec, 2024 | Loss Functions in Deep Learning
18 Dec, 2024
Deep learning has revolutionized fields ranging from computer vision to natural language processing, largely due to the sophisticated architectures and algorithms that power these technologies. At the heart of most deep learning models is the concept of the loss function. This article aims to demystify loss functions, exploring their types, roles, and significance in training deep learning models.Table of ContentWhat is a Loss Function?How Loss Functions Work?Types of Loss FunctionsHow to Choose the Right Loss Function?What is a Loss Function?A loss function is a mathematical function that measures how well a model's predictions match the true outcomes. It provides a quantitative metric for the accuracy of the model's predictions, which can be used to guide the model's training process. The goal of a loss function is to guide optimization algorithms in adjusting model parameters to reduce this loss over time.Why are Loss Functions Important?Loss functions are crucial because they:Guide Model Training: The loss function is the basis for the optimization process. During training, algorithms such as Gradient Descent use the loss function to adjust the model's parameters, aiming to reduce the error and improve the model’s predictions.Measure Performance: By quantifying the difference between predicted and actual values, the loss function provides a benchmark for evaluating the model's performance. Lower loss values generally indicate better performance.Influence Learning Dynamics: The choice of loss function affects the learning dynamics, including how fast the model learns and what kind of errors are penalized more heavily. Different loss functions can lead to different learning behaviors and results.How Loss Functions Work?Prediction vs. True Value:The model produces a prediction based on its current parameters.The loss function computes the error between the prediction and the actual value.Error Measurement:The error is quantified by the loss function as a real number representing the "cost" or "penalty" for incorrect predictions.This error can then be used to adjust the model's parameters in a way that reduces the error in future predictions.Optimization:Gradient Descent: Most models use gradient descent or its variants to minimize the loss function. The algorithm calculates the gradient of the loss function with respect to the model parameters and updates the parameters in the opposite direction of the gradient.Objective Function: The loss function is a key component of the objective function that algorithms aim to minimize.Types of Loss FunctionsLoss functions come in various forms, each suited to different types of problems. Here are some common categories and examples:1. Regression Loss FunctionsIn machine learning, loss functions are critical components used to evaluate how well a model's predictions match the actual data. For regression tasks, where the goal is to predict a continuous value, several loss functions are commonly used. Each has its own characteristics and is suitable for different scenarios. Here, we will discuss four popular regression loss functions: Mean Squared Error (MSE) Loss, Mean Absolute Error (MAE) Loss, Huber Loss, and Log-Cosh Loss.1. Mean Squared Error (MSE) LossThe Mean Squared Error (MSE) Loss is one of the most widely used loss functions for regression tasks. It calculates the average of the squared differences between the predicted values and the actual values.\text{MSE} =\frac{1}{n}\sum_{i=1}^{n}(y_i−\widehat{y}_i)^2Advantages:Simple to compute and understand.Differentiable, making it suitable for gradient-based optimization algorithms.Disadvantages:Sensitive to outliers because the errors are squared, which can disproportionately affect the loss.2. Mean Absolute Error (MAE) LossThe Mean Absolute Error (MAE) Loss is another commonly used loss function for regression. It calculates the average of the absolute differences between the predicted values and the actual values.\text{MAE}= \frac{1}{n}\sum_{i=1}^{n} ∣y_i − \widehat{y_i}∣Advantages:Less sensitive to outliers compared to MSE.Simple to compute and interpret.Disadvantages:Not differentiable at zero, which can pose issues for some optimization algorithms.3. Huber LossHuber Loss combines the advantages of MSE and MAE. It is less sensitive to outliers than MSE and differentiable everywhere, unlike MAE. Huber Loss is defined as:\begin{cases}\frac{1}{2} (y_i - \hat{y}_i)^2 & \quad \text{for } |y_i - \hat{y}_i| \leq \delta \\\delta |y_i - \hat{y}_i| - \frac{1}{2} \delta^2 & \quad \text{for } |y_i - \hat{y}_i| > \delta\end{cases}Advantages: Robust to outliers, providing a balance between MSE and MAE. Differentiable, facilitating gradient-based optimization. Disadvantages: Requires tuning of the parameter \delta.4. Log-Cosh Loss Log-Cosh Loss is another smooth loss function for regression, defined as the logarithm of the hyperbolic cosine of the prediction error. It is given by: \text{Log-Cosh} = \sum_{i=1}^{n} \log (\cosh (\hat{y}_i - y_i)) where \cosh(x) = \frac{e^x + e^{-x}}{2}Advantages:Combines the benefits of MSE and MAE. Smooth and differentiable everywhere, making it suitable for gradient-based optimization. Disadvantages:More complex to compute compared to MSE and MAE.2. Classification Loss FunctionsClassification loss functions are essential for evaluating how well a classification model's predictions match the actual class labels. Different loss functions cater to various classification tasks, including binary, multiclass, and imbalanced datasets. Here, we will discuss several widely used classification loss functions: Binary Cross-Entropy Loss (Log Loss), Categorical Cross-Entropy Loss, Sparse Categorical Cross-Entropy Loss, Kullback-Leibler Divergence Loss (KL Divergence), Hinge Loss, Squared Hinge Loss, and Focal Loss.1. Binary Cross-Entropy Loss (Log Loss)Binary Cross-Entropy Loss, also known as Log Loss, is used for binary classification problems. It measures the performance of a classification model whose output is a probability value between 0 and 1.\text{Binary Cross-Entropy} = - \frac{1}{n} \sum_{i=1}^{n} [y_i \log(\hat{y}_i) + (1 - y_i) \log(1 - \hat{y}_i)]where n is the number of data points, y_i is the actual binary label (0 or 1), and \hat{y}_i is the predicted probability.Advantages:Suitable for binary classification.Differentiable, making it useful for gradient-based optimization.Disadvantages:Can be sensitive to imbalanced datasets.2. Categorical Cross-Entropy LossCategorical Cross-Entropy Loss is used for multiclass classification problems. It measures the performance of a classification model whose output is a probability distribution over multiple classes.\text{Categorical Cross-Entropy} = - \sum_{i=1}^{n} \sum_{j=1}^{k} y_{ij} \log(\hat{y}_{ij})where n is the number of data points, k is the number of classes, y_{ij} is the binary indicator (0 or 1) if class label j is the correct classification for data point i, and \hat{y}_{ij} is the predicted probability for class j.Advantages:Suitable for multiclass classification.Differentiable and widely used in neural networks.Disadvantages:Not suitable for sparse targets.3. Sparse Categorical Cross-Entropy LossSparse Categorical Cross-Entropy Loss is similar to Categorical Cross-Entropy Loss but is used when the target labels are integers instead of one-hot encoded vectors.\text{Sparse Categorical Cross-Entropy} = - \sum_{i=1}^{n} \log(\hat{y}_{i, y_i})where y_i is the integer representing the correct class for data point iii.Advantages:Efficient for large datasets with many classes.Reduces memory usage by using integer labels instead of one-hot encoded vectors.Disadvantages:Requires integer labels.4. Kullback-Leibler Divergence Loss (KL Divergence)KL Divergence measures how one probability distribution diverges from a second, expected probability distribution. It is often used in probabilistic models.\text{KL Divergence} = \sum_{i=1}^{n} \sum_{j=1}^{k} y_{ij} \log\left(\frac{y_{ij}}{\hat{y}_{ij}}\right)Advantages:Useful for measuring divergence between distributions.Applicable in various probabilistic modeling tasks.Disadvantages:Sensitive to small differences in probability distributions.5. Hinge LossHinge Loss is used for training classifiers, especially for support vector machines (SVMs). It is suitable for binary classification tasks.\text{Hinge Loss} = \frac{1}{n} \sum_{i=1}^{n} \max(0, 1 - y_i \cdot \hat{y}_i)where y_i is the actual label (-1 or 1), and \hat{y}_i is the predicted value.Advantages:Effective for SVMs.Encourages correct classification with a margin.Disadvantages:Not differentiable at zero, posing challenges for some optimization methods.6. Squared Hinge LossSquared Hinge Loss is a variation of Hinge Loss that squares the hinge loss term, making it more sensitive to misclassifications.\text{Squared Hinge Loss} = \frac{1}{n} \sum_{i=1}^{n} \max(0, 1 - y_i \cdot \hat{y}_i)^2Advantages:Penalizes misclassifications more heavily.Encourages larger margins.Disadvantages:Similar challenges as Hinge Loss regarding differentiability at zero.7. Focal LossFocal Loss is designed to address class imbalance by focusing more on hard-to-classify examples. It introduces a modulating factor to the standard cross-entropy loss.\text{Focal Loss} = - \frac{1}{n} \sum_{i=1}^{n} (1 - \hat{y}_i)^\gamma \log(\hat{y}_i)where γ\gammaγ is a focusing parameter.Advantages:Effective for addressing class imbalance.Focuses on hard-to-classify examples.Disadvantages:Requires tuning of the focusing parameter γ\gammaγ.3. Ranking Loss FunctionsRanking loss functions are used to evaluate models that predict the relative order of items. These are commonly used in tasks such as recommendation systems and information retrieval.1. Contrastive LossContrastive Loss is used to learn embeddings such that similar items are closer in the embedding space, while dissimilar items are farther apart. It is often used in Siamese networks.\text{Contrastive Loss} = \frac{1}{2N} \sum_{i=1}^{N} \left( y_i \cdot d_i^2 + (1 - y_i) \cdot \max(0, m - d_i)^2 \right)where d_i is the distance between a pair of embeddings, y_i is 1 for similar pairs and 0 for dissimilar pairs, and mmm is a margin.2. Triplet LossTriplet Loss is used to learn embeddings by comparing the relative distances between triplets: an anchor, a positive example, and a negative example.\text{Triplet Loss} = \frac{1}{N} \sum_{i=1}^{N} \left[ \|f(x_i^a) - f(x_i^p)\|_2^2 - \|f(x_i^a) - f(x_i^n)\|_2^2 + \alpha \right]_+where f(x) is the embedding function, x_i^a is the anchor, x_i^p is the positive example,x_i^n is the negative example, and \alpha is a margin.3. Margin Ranking LossMargin Ranking Loss measures the relative distances between pairs of items and ensures that the correct ordering is maintained with a specified margin.\text{Margin Ranking Loss} = \frac{1}{N} \sum_{i=1}^{N} \max(0, -y_i \cdot (s_i^+ - s_i^-) + \text{margin})where s_i^+ and s_i^- are the scores for the positive and negative samples, respectively, and y_i is the label indicating the correct ordering.4. Image and Reconstruction Loss FunctionsThese loss functions are used to evaluate models that generate or reconstruct images, ensuring that the output is as close as possible to the target images.1. Pixel-wise Cross-Entropy LossPixel-wise Cross-Entropy Loss is used for image segmentation tasks, where each pixel is classified independently.\text{Pixel-wise Cross-Entropy} = - \frac{1}{N} \sum_{i=1}^{N} \sum_{c=1}^{C} y_{i,c} \log(\hat{y}_{i,c})where N is the number of pixels, C is the number of classes, y_{i,c} is the binary indicator for the correct class of pixel i, and\hat{y}_{i,c} is the predicted probability for class c.2. Dice LossDice Loss is used for image segmentation tasks and is particularly effective for imbalanced datasets. It measures the overlap between the predicted segmentation and the ground truth.\text{Dice Loss} = 1 - \frac{2 \sum_{i=1}^{N} y_i \hat{y}_i}{\sum_{i=1}^{N} y_i + \sum_{i=1}^{N} \hat{y}_i}where y_i is the ground truth label and \hat{y}_i is the predicted label.3. Jaccard Loss (Intersection over Union, IoU)Jaccard Loss, also known as IoU Loss, measures the intersection over union of the predicted segmentation and the ground truth.\text{Jaccard Loss} = 1 - \frac{\sum_{i=1}^{N} y_i \hat{y}_i}{\sum_{i=1}^{N} y_i + \sum_{i=1}^{N} \hat{y}_i - \sum_{i=1}^{N} y_i \hat{y}_i}4. Perceptual LossPerceptual Loss measures the difference between high-level features of images rather than pixel-wise differences. It is often used in image generation tasks.\text{Perceptual Loss} = \sum_{i=1}^{N} \| \phi_j(y_i) - \phi_j(\hat{y}_i) \|_2^2where \phi_j is a layer in a pre-trained network, and y_i and \hat{y}_i are the ground truth and predicted images, respectively.5. Total Variation LossTotal Variation Loss encourages spatial smoothness in images by penalizing differences between adjacent pixels.\text{Total Variation Loss} = \sum_{i,j} \left( (y_{i,j+1} - y_{i,j})^2 + (y_{i+1,j} - y_{i,j})^2 \right)5. Adversarial Loss FunctionsAdversarial loss functions are used in generative adversarial networks (GANs) to train the generator and discriminator networks.1. Adversarial Loss (GAN Loss)The standard GAN loss function involves a minimax game between the generator and the discriminator.\min_G \max_D \mathbb{E}_{x \sim p_{data}(x)} [\log D(x)] + \mathbb{E}_{z \sim p_z(z)} [\log (1 - D(G(z)))]2. Least Squares GAN LossLeast Squares GAN Loss aims to provide more stable training by minimizing the Pearson χ2\chi^2χ2 divergence.\min_D \frac{1}{2} \mathbb{E}_{x \sim p_{data}(x)} [(D(x) - 1)^2] + \frac{1}{2} \mathbb{E}_{z \sim p_z(z)} [D(G(z))^2]\min_G \frac{1}{2} \mathbb{E}_{z \sim p_z(z)} [(D(G(z)) - 1)^2]minG21Ez∼pz(z)[(D(G(z))−1)2]6. Specialized Loss FunctionsSpecialized loss functions cater to specific tasks such as sequence prediction, count data, and cosine similarity.1. CTC Loss (Connectionist Temporal Classification)CTC Loss is used for sequence prediction tasks where the alignment between input and output sequences is unknown.\text{CTC Loss} = - \log(p(y | x))where p(y∣x) is the probability of the correct output sequence given the input sequence.2. Poisson LossPoisson Loss is used for count data, modeling the distribution of the predicted values as a Poisson distribution.\text{Poisson Loss} = \sum_{i=1}^{N} (\hat{y}_i - y_i \log(\hat{y}_i))3. Cosine Proximity LossCosine Proximity Loss measures the cosine similarity between the predicted and target vectors, encouraging them to point in the same direction.\text{Cosine Proximity Loss} = - \frac{1}{N} \sum_{i=1}^{N} \frac{y_i \cdot \hat{y}_i}{\|y_i\| \|\hat{y}_i\|}4. Log LossLog Loss, or logistic loss, is used for binary classification tasks. It measures the performance of a classification model whose output is a probability value between 0 and 1.\text{Log Loss} = - \frac{1}{N} \sum_{i=1}^{N} [y_i \log(\hat{y}_i) + (1 - y_i) \log(1 - \hat{y}_i)]5. Earth Mover's Distance (Wasserstein Loss)Earth Mover's Distance measures the distance between two probability distributions and is often used in Wasserstein GANs.\text{Wasserstein Loss} = \mathbb{E}_{x \sim p_r} [D(x)] - \mathbb{E}_{z \sim p_z} [D(G(z))]How to Choose the Right Loss Function?Choosing the right loss function is crucial for the success of your deep learning model. Here are some guidelines to help you make the right choice:1. Understand the Task at HandRegression Tasks: If your task is to predict continuous values, you generally use loss functions like Mean Squared Error (MSE) or Mean Absolute Error (MAE).Classification Tasks: If your task involves predicting discrete labels, you typically use loss functions like Binary Cross-Entropy for binary classification or Categorical Cross-Entropy for multi-class classification.Ranking Tasks: If your task involves ranking items (e.g., recommendation systems), loss functions like Contrastive Loss or Triplet Loss are appropriate.Segmentation Tasks: For image segmentation, Dice Loss or Jaccard Loss are often used to handle class imbalances.2. Consider the Output TypeContinuous Outputs: Use regression loss functions (e.g., MSE, MAE).Discrete Outputs: Use classification loss functions (e.g., Cross-Entropy, Focal Loss).Sequence Outputs: For tasks like speech recognition or handwriting recognition, use CTC Loss.3. Handle Imbalanced DataIf your dataset is imbalanced (e.g., rare events), consider loss functions that focus on difficult examples, like Focal Loss for classification tasks.4. Robustness to OutliersIf your data contains outliers, consider using loss functions that are robust to them, such as Huber Loss for regression tasks.5. Performance and ConvergenceChoose loss functions that help your model converge faster and perform better. For example, using Hinge Loss for SVMs can sometimes lead to better performance than Cross-Entropy for classification.ConclusionLoss functions are fundamental to the training and evaluation of deep learning models. They serve as the metric for error measurement and the foundation for optimization algorithms. Understanding the different types of loss functions and their applications is crucial for designing effective deep learning models and achieving high performance on your tasks. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning | https://www.geeksforgeeks.org/loss-functions-in-deep-learning/?ref=ml_lbp | NLP | Loss Functions in Deep Learning | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Loss Functions in Deep Learning, Agents in Artificial Intelligence, What are Diffusion Models?, 30+ Best Artificial Intelligence Project Ideas with 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27 Dec, 2023 | Kaiming Initialization in Deep Learning
27 Dec, 2023
Kaiming Initialization is a weight initialization technique in deep learning that adjusts the initial weights of neural network layers to facilitate efficient training by addressing the vanishing or exploding gradient problem. The article aims to explore the fundamentals of Kaiming initialization and it's implementation.
What is Kaiming Initialization?The Kaiming initialization method, also known as Kaiming He initialization or He normal initialization, is a technique for initializing the weights of artificial neural networks. This method was introduced in the paper titled "Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification" by Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.
The motivation behind Kaiming initialization is to address the vanishing or exploding gradient problem that can occur during the training of deep neural networks. In deep networks, especially those using rectified linear unit (ReLU) activation functions, traditional weight initialization methods such as random normal or Xavier initialization may lead to gradients that vanish or explode as they are propagated through the layers during backpropagation.
The Kaiming initialization method is calculated as a random number with a Gaussian probability distribution (G) with a mean of 0.0 and a standard deviation of sqrt(2/n), where n is the number of inputs to the node.
W \rightarrow\Nu(0,\frac{2}{n})
The factor of 2 in the variance is specific to the ReLU activation function. For other activation functions, such as sigmoid or hyperbolic tangent, different initialization strategies might be more appropriate.
Derivation of Kaiming InitializationWe will use the below assumption to derive kaiming initialization.
The output of neural network at any layer is given as y = Wx + b. Here W is the weight matrixX is the inputb is the biasAll elements in W share the same distribution and are independent of each other. All elements in X are mutually independent and share the same distribution.We assume Weight in each layer has zero mean.Independence of Weights and Inputs: The initialization assumes that the weights and inputs are independent of each other.Bias Initialization: The derivation does not explicitly consider biases. In practice, biases are often initialized to zero or small constant values separately from the weight.We will use the below properties of variance.
Var(XY) = Var(X)Var(Y) + (E[X])^2Var(Y) + (E[Y])^2Var(X)
Var(X) = E(X^2) - [E(X)]^2
Let us consider two layers 'k-1'and 'k'. The output of the 'k-1' layer is being feed into layer 'k'. Now the output of ith neuron in layer k can be written as
y_i = ∑W_{ij}X_{j} + b_i
Here
Xj is the jth input to the neuron in layer k from the k-1 layer. The summation is over the length of the neuron in k-1 layerWij represents the weight associated with the ith row and jth column in the Weight matrix. The row matrix has size 1*(number of neurons in the k-1 layer)Now we can write.
Var(y_i) = Var(∑W_{ij}X_j)
Since we are assuming that each element in weight and input are independent and coming from the same distribution and also weight and inputs are independent of each other, we can simplify the above equation as
Var(y_i) = n* Var(W_{ij}X_j)
where we assume n is the number of neurons in layer k-1:
Using the first property,
Var(y_i) = n *(Var(W_{ij})Var(X_j) + (E[W_{ij}])^2Var(X_j) + Var(W_{ij})(E[X_j])^2)
Assuming zero mean for weight,
Var(y_i) = n *(Var(W_{ij})Var(X_j) + 0*Var(X_j) + Var(W_{ij})(E[X_j])^2)
Var(y_i) = n *Var(W_{ij}) *(Var(X_j) +(E[X_j])^2)
Using property 2, we get,
Var(y_i) = n *Var(W_{ij}) * E[X_j^2] \; ...(1)
Now for a continuous variable, the expected value is the sum of the product of all the possible values of the variable and its probability.
E[X^2] = ∫_{-\infty}^\infty x^2p(x)dx
Since the input to the current layer is equal to the Relu of the output of the previous layer(yl-1) i.e x = max(0,yl-1)
E[X^2] = ∫_0^\infty y_{l-1}^2p(y_{l-1})dy_{l-1}
(here we are taking integration from 0 instead of -inf as y gets activated only for positive values)
E[X^2] = 0.5*∫_{-\infty}^\infty y_{l-1}^2p(y_{l-1})dy_{l-1}
E[X^2] = 0.5 * Var(y_{l-1})
Substituting this value in Eq (1)
Var(y_i) = 0.5 * n * Var(w_{ij}) * Var*(y_{l-1})
We drop the index and write the above equation for a particular layer as each element in the weight matrix and input is independent and comes from same distribution as per our assumption.
Var(y^l) = 0.5 * n * Var(W^l) * Var*(y^{l-1})
Now considering L (1 to L) layers we can write this as
Var(y^L) = Var(y^1)\Pi_{l=2}^{L} 0.5*n^lVar(w^l)
This product is the key to the initialization design. A proper initialization method should avoid reducing or magnifying the magnitudes of input signals exponentially. So, we expect the above product to take a proper scalar (e.g., 1). A sufficient condition is:
\frac{n}{2}Var(W^l) = 1
This gives us
W \rightarrow\Nu(0,\frac{2}{n})
Note that:
We derived the initialization solely through the forward pass. The same outcomes can be achieved when employing the backpropagation process.The formula holds exclusively in the case of employing ReLU as the activation function in each layer. Should a different activation function be employed, the initialization can be derived by incorporating the specific activation function into the integral of the term E[X2]Advantages Through a meticulous analysis of the properties of ReLU and the challenges posed by vanishing and exploding gradients, Kaiming He and his colleagues devised an initialization method that has become a cornerstone for initializing weights in deep neural networks. The advantages of Kaiming initialization technique are:
Mitigation of Vanishing and Exploding Gradients: Kaiming He initialization helps mitigate the vanishing and exploding gradient problems that can impede the training of deep networks. Preservation of Variance: The initialization method is designed to preserve the variance of weights, particularly during the forward pass. This helps maintain an appropriate scale of activations across layers, preventing issues like overly small or large values.Efficient Training of Deeper Networks: Kaiming He initialization has been shown to contribute to more efficient training of deeper networks. Deep neural networks with many layers can benefit from this initialization method to ensure that information and gradients are propagated effectively through the network.Adaptability to ReLU Activation: Kaiming He initialization is tailored for ReLU activation functions, which are widely used in deep learning. It takes into account the characteristics of ReLU, such as non-saturation for positive inputs, to set appropriate initial weights.Empirical Success Across Tasks: Empirical studies have consistently demonstrated the effectiveness of Kaiming He initialization across various computer vision and natural language processing tasks. It has become a go-to initialization strategy for practitioners working with deep neural networks.Implementation torch.nn.init.kaiming_uniform_ is a PyTorch initialization method designed for initializing weights in a neural network. It follows the Kaiming He initialization strategy, which is specifically tailored for the rectified linear unit (ReLU) activation functions.
Python3
import torch
import torch.nn.init as init
weight_tensor = torch.empty(3, 3) # Example weight tensor
init.kaiming_uniform_(weight_tensor, mode='fan_in', nonlinearity='relu')
Parameters:
tensor: The PyTorch tensor represents the weights to be initialized.mode: Specifies the mode for computing the fan. It can be 'fan_in' or 'fan_out'.'fan_in':Choosing 'fan_in' as the mode for computing the fan in weight initialization means that the scaling factor is based on the number of input units (fan-in) to a neuron in the current layer.This choice preserves the magnitude of the variance of the weights during the forward pass. In other words, it ensures that the variance of the weights entering a neuron in the current layer is maintained.'fan_out':Choosing 'fan_out' as the mode means that the scaling factor is based on the number of output units (fan out) from a neuron in the current layer.This choice is motivated by the desire to preserve the magnitudes during the backward pass, specifically during backpropagation. It helps in maintaining the variance of the gradients as they are propagated backward through the network.nonlinearity: Specifies the nonlinearity function. For ReLU, it should be set to 'relu'.ConclusionThe core principle behind Kaiming initialization is to set the initial weights in a way that facilitates stable and efficient training. In this article we saw the mathematical details behind the initialization technique, its advantages and how it can be implemented in python. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning | https://www.geeksforgeeks.org/kaiming-initialization-in-deep-learning/?ref=ml_lbp | NLP | Kaiming Initialization in Deep Learning | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Loss Functions in Deep Learning, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep 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10 Jan, 2024 | Swift - Initialization
10 Jan, 2024
Swift also supports object-oriented programming language. A class is a blueprint and an object is nothing but it is defined as an instance of a class. A class can be defined in the class using the class keyword in Swift. We can initialize the values for the stored properties or the data members in the particular class. The keyword to create initialization for the data members and properties of a particular class is init(). This article focuses on discussing initialization in Swift.
INIT () For Stored Data MembersThe init() responsibility is to initialize the instance of a class that is an object. The initialization in Swift is used for assigning the values for the stored properties. The other feature of Swift is that it provides the deinitializer that takes the functionality of memory management after the deallocation of the particular class instances. The main important thing that the initializer is used for the classes is
The init() is used to create a default value for the stored properties that are present in the class and structures.The init() is also used to assign the default value for the property.The init() can have parameters or it can be created without the parameters.To initialize an instance the init() is used.Role of INIT() in a ClassSyntax:
class class_name { init() { // initialization of the members }}
Example 1:
Program to initialize the data members by passing the parameters in the init() in a class:
Swift
// Program to initialize the data members
// by passing the parameters in the init()
class Geeks
{
// Members in the class
var name : String
var roll : Int
// Initializer in the class
init(name : String , roll : Int)
{
self.name = name
self.roll = roll
}
}
// Created an instance of type Geeks named gfg
var gfg = Geeks(name : "Geek",roll : 404)
print(gfg.name,gfg.roll,separator:" ",terminator:".")
OutputGeek 404.Explanations:
In this first we create a class named Geeks and with the data members name and rollno.In the class, we create the init() function with the parameters passed so that we can assign the values to the data members in the class.we created an instance for the class named Geeks with the variable named gfg and passed a string and int.we printed the name and roll no that were assigned by us.Another important thing is that we use self which is nothing but the reference of that particular instance.Example 2:
Program to initialize the data member without passing the parameters in the init:
Swift
// Program to initialize the data member
// without passing the parameters in the init
class Student
{
// Data Members
var name : String
var roll : Int
// No parameters are passed here in the init
init()
{
name = "Prateek"
roll = 66
}
}
// The instance of class student with the name 'instance'
var instance = Student()
// Printing the name and roll for the object named instance
print(instance.name,instance.roll,separator : " ",terminator : ".")
OutputPrateek 66.Explanation:
In the above program, we have first created a class with the name Student and with the data members' name and roll no.In this, we initialized the init() with no parameters passed in it and so we have assigned the default values in the init() with the values prateek and 66 After that, we created a variable with the name instance of the type Student class.Now we have printed the data members' values with the help of the created variable of type student.Role of INIT() in the StructureExample 1:
Program to initialize the data members in the structure by using the init() along with the parameters and without using the init():
Swift
// Structure Without having the init function
struct Area
{
// DATA MEMBERS by having the default values
// in the structure
var length = 4
var breadth = 5
}
// Another structure by having the init function
struct Area_Rect
{
var length : Int
var breadth : Int
// DATA MEMBERS
init()
{
// Assigning the values with the help of
// the init() function
length = 2
breadth = 3
}
}
var obj1 = Area()
var obj2 = Area_Rect()
print("Without init function the values ", obj1.length,
obj1.breadth, separator:" ", terminator:"\n")
print("With Passing the init function the values ", obj2.length,
obj2.breadth, separator : " ", terminator: ".")
OutputWithout init function the values 4 5
With Passing the init function the values 2 3.Explanation:
First, we created two structures in the above program one with the name Area and one with the name Area_Rect both structures contain the members named length and breadth.In the structure Area there is no init() function initialized we have passed the default values for the member's length and breadth.In the structure Area_Rect we have created an init() function and we have not passed the values in the init() we will assign the values for length and breadth.Then we have to print the values of the data members present in both the structures. This program is similar to the above program.Example 2:
Program to initialize the variables in the structure by passing the parameters into the init function:
Swift
// Program to initialize the variables in the
// structure by passing the parameters into the init function
struct Car
{
// DataMembers of the class
var speed : Double
var name : String
// Assigning the values from the init
init(speed : Double , name : String)
{
self.speed = speed
self.name = name
}
}
// Instance named 'type' of type Car
var type = Car(speed : 223.45,name : "Ferrari")
print("The car speed is \(type.speed) KMPH.",
"The car name is \(type.name)",
separator: "\n", terminator: ".")
OutputThe car speed is 223.45 KMPH.
The car name is Ferrari. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization | https://www.geeksforgeeks.org/swift-initialization/?ref=ml_lbp | NLP | Swift - Initialization | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Loss Functions in Deep Learning, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require 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12 Sep, 2022 | Swift – If Statement
12 Sep, 2022
Just like other programming languages in Swift language also if statement is used to execute the program based on the evaluation of one or more conditions or in other words if statement is used to run a piece of code only when the given condition is true. There are also known as branch statement. For example, let us consider a case where you’re going to go to the market, and your father tells you, “if they have the plastic container on sale, buy 2 containers”. This is a conditional statement states that you’ll perform some action, i.e., “buy 2 containers” only if the given condition, i.e., “they have the plastic container on sale” is true. Such type of statement is very useful in programming because they allow programmers to implement conditional behavior into their programs.
Syntax:
if (condition) {
// body of if statement
}
The if statement evaluates the condition inside the parenthesis() and the code inside curly braces{ } is the body of the if statement. Here,
If the condition is fulfilled i.e. evaluated to true, then the code present in the body of the if statement is executed.
If the condition is not fulfilled i.e. evaluated to false, the code present in the body of the if statement is skipped and the control moves to the next statement present after the if statement.
It can be better understood via visual diagram as follows :
Example 1:
// Swift program of if statement
let val = 30
// Checking if number is greater than zero
if (val > 0)
{
// Code i.e. body of if statement
print(“The given number is positive.”)
}
// Statement just after if statement
// (This statement is always executed)
print(“Learning if statement in Swift.”)
Output:
The given number is positive.
Learning if statement in Swift.
Explanation: In the above example, we have declared a variable named “val”. Observe the test condition, “val > 0”. Here, 30 > 0 which means the condition is true so the control flow of the program enters inside the body of the if statement and executes code/statements written inside it, i.e., “The given number is positive.”. Now if we set val = -20 and run the above program then the output will be “Learning if statement in Swift”. This happens because the value of a val variable is less than 0 so the condition is false. Hence, the body of if block is skipped and the control flow of the program executes code/statements written outside/after the if statement.
Example 2:
// Swift program of if statement
let number = 30
// Checking if number is greater than equal to 18
if (number >= 18)
{
// Code i.e. body of if statement
print(“This person is eligible for voting”)
}
// Statement just after if statement
// (This statement is always executed)
print(“Only 18+ peoples are eligible for voting”)
Output :
This person is eligible for voting
Only 18+ peoples are eligible for voting
Example 3: Lot of you might have a question like can we use multiple if statements instead of if-else statements. Here is an answer for you!
// Swift Program to use Multiple If Statementslet number = 9// When the condition is True then it will print the statement else it will skip the condition// 1st if statementif(number%2 == 0){ print(“\(number) is an even number”)}// 2nd if statementif(number%2 != 0){ print(“\(number) is an odd number”)}// 3rd if statementif(number == 9){ print(“Given number \(number) is equal to the given condition number”)}
Output:
9 is a odd number
Given number 9 is equal to the given condition number | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement | https://www.geeksforgeeks.org/swift-if-statement/?ref=ml_lbp | NLP | Swift – If Statement | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Loss Functions in Deep Learning, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 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23 Sep, 2024 | 6 Best iOS Project Ideas For Beginners
23 Sep, 2024
If you have decided to start working on some fascinating project ideas then you need to think first before getting started. However, it’s not an easy task to find new project ideas for learning and improving any new programming language. Those who are trying their hands-on experience with an iOS app development can go with certain programming languages such as React Native, Flutter, Swift, Objective C, and so on. However, Apple adopted Swift as their official language for developing iOS apps for different platforms (Mac, iPhone, etc.) and swift is heavily used among developers throughout the world.
In the past few years, we’ve witnessed the enormous growth of the digitized market, especially in app development and the way people have accepted it with wide arms is quite extinguishing. Be it business (from small to medium), healthcare, or education, in fact, we’re surrounded by this trend all across the Internet. Interestingly, recently, as per a survey, iOS is moving every year with a growth of 6% (above 25% as of now) in India, and that’s the main reason why the company has started rolling out affordable iPhones.
In this field of opportunities, now is the best time to enter into the World of iOS app development and that’s why we thought to bring up something to uplift your skills. In this article, we are going to discuss some of the Best iOS Project Ideas that you can start right away.
6 Project Ideas for iOS app Development:
1. Doctor Appointment App
This app can allow patients to connect with their doctors over the platform. This has been the best solution so for to get a consultation in this digital world and will also enable patients to connect as per their suitable timing. This iOS app is an efficient way of overseeing the arrangements more adequately. It will generally consist of two major units i.e. patient and doctor. On one side, the patient will open the application and with a few clicks, s/he can schedule an appointment without making any inquiry calls or waiting. Whereas on the other hand, doctors will also save a lot of time which usually takes (like filing up basic details, time slots, staff management) and so on. However, this could be a game-changing project idea for you to give a kickstart in the iOS development and you’ll have to consider some of the below pointers will starting this project:
As per a survey, there are billions of active individuals that are using health-related services and at this pace, it is expected to increase somewhere around $230 Billion in the next couple of years.
This app will not only save time but will also focus on eliminating human errors
It becomes easy to manage and track records, especially when data is stored in the central DB
For Example: Practo
2. Money Management App
The next one on this list is a budgeting app that can help users to manage the flow of money in their day-to-day lives. You can categorize users into two large segments, where one is those who are money-minded people and always takes a path towards saving whereas the other one is the spenders who want to control their expenditures and have no control over their expenses. This app can be a life safer and can teach its users how they can control their expenditures. Recently, a report suggested that 20% of Americans exhausted their wallet during the pandemic and that it all happened due to mismanagement of the budget. On the other hand, there are countries like London, where people seek help with money management tools (under the age of 30) for spending wisely. Thus, this app can work like a charm and it will easily track all the user’s expenditures by pulling out all the necessary details from the bank and other sources of investments and will keep them parallel to maintain the graph. Besides this, there are certain things to consider for you as a developer before hopping into this project idea:
This app idea can also be helpful in tracking and updating real-time transactions.
The money management app will provide full insight and will also provide various options for investments.
The opportunities are huge in fintech in 2022 and it is expected to be somewhere between $310 Billion at a CAGR of 25%
For Example: Mint
3. Compare – Car App
With the advancement of technology, today people have become so reliable with technology that they want everything under their thumb. Earlier like people used to visit showrooms, but with the change of time and pandemics, most things are now becoming digital. Just like “Car”, Yes, today people are eager to look into every specification before stepping out of their house. This app can be built in such a way that users would be able to select 2 cars and an automatic report will pop up right in front of them by which they can compare all of the specifications on a single screen. However, this app can have solidified other functions too that you can consider if you’re planning to get started with this iOS application:
If the user will request a detailed report, a brief report will be generated along with all the information and can be sent to the user’s mail address.
It can be helpful in saving customers’ time.
An admin panel will be created by which user accounts can be handled and any unauthorized activity or comment will be monitored and will be removed from the admin’s end.
For Example: CarDekho
4. Sleep Tracking App
As we are moving forward and surrounded by technology, people are becoming more and more tech-friendly and they are trying to do everything they can which is tech-built. However, today users have been curious about maintaining and analyzing the data of their sleep records to check for any irregularities. This has never been an easy task but machine learning and artificial intelligence and advancement in hardware capabilities have made it possible in today’s time. The requirement arises when a survey was conducted where it was observed that people do face challenges in their sleep patterns. This app will help in collecting data on wake-up time, sleep duration, and any unusual distraction. Besides this, users would be getting an option to customize their tracking requirements. This can be a challenging and a perfect project idea for iOS app development, however, you need to focus on a few things before processing ahead:
For creating this app, all entries are required to be stored over the server that can be called anytime whenever the user asks for
The signup feature can be added to social accounts so that it can sound more appealing
This project can be implemented using React
For Example: SleepCycle
5. Notebook
This is one of the best apps to work on for those who are trying to brush up their skills. It’s a basic app that you can create for writing, editing, and saving notes. This also allows users to share those notes across the platform and they will also have the facility to modify the contents whenever required. Besides this, being a developer, you can do some modifications to UI, add cool color contrasts, and add themes so that it can look beyond simple. You can also design in two patterns either in a short notepad with a word limit of up to 900-1000 words or the notepad can be crafted beyond these limits. However, being a clean and simple app, there are certain things to consider while working on this project:
This app is light weighted and can easily run with minimum requirements
Data can be centralized and can easily share with anyone as per the requirement
Suitable for beginners to get hands-on experience
For Example: Notebook-Notes
6. Online Store – Furniture
Following the trend, online stores have now become a game-changer in business for attracting customers. That’s why we bought the last iOS project as an online store for furniture apps. This app will enable opportunities and will open doors to showcase their business on a broad platform. However, online stores are not new in the trend but creating something for any specific industry can make a real impact. Not just this, if you’ll see the graph, the figures for online furniture stores have been booming from $509 Billion (2020) to $607 Billion (2025) *worldwide. So, you see the figures and opportunities that can be looked into beforehand, right? Now there are a few pointers to see before you actually try your hands-on:
Since furniture is considered a premium product so it is a must to have a nice and intuitive UI & UX for a rich experience.
AR can also be implemented for more clarity before buying
The app will be divided into 3 major divisions, first one would be the user panel, then the store owner, and at last admin panel.
For Example: UrbanLadder
The app development market is vast and with the growing pace and advancement iOS has become a pioneer. Even if you’re at an early stage, this article will definitely provide you with some additional guidance to enhance your development skills. However, the projects do not end here but we have carefully picked the 6 best iOS project ideas for you to enter into the development field. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners | https://www.geeksforgeeks.org/6-best-ios-project-ideas-for-beginners/?ref=lbp | NLP | 6 Best iOS Project Ideas For Beginners | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, 6 Best iOS Project Ideas For Beginners, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Loss Functions in Deep Learning, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Swift - Initialization, Swift – If Statement | GeeksforGeeks | [-0.0499666594, 0.0262507144, -0.0115332054, 0.0118579725, 0.0326034836, 0.0235733632, -0.00568343047, 0.0046695224, 0.00269517372, -0.00495468406, 0.0217673406, -0.0399226323, 0.0456892364, -0.00557649462, -0.0128481174, -0.000727261242, 0.0116203381, -0.0219732895, -0.0179493427, -0.0259338692, 0.000670327921, -0.0345996134, -0.0356452093, -0.0244288482, 0.0147333527, 0.0134105189, 0.00564778503, 0.00899843499, -0.016095791, 0.0249674879, 0.0353917293, 0.00354471779, 0.0206108503, -0.0256170221, -0.0263140835, 0.0100836335, -0.0284211114, -0.0162383728, 0.00482002413, 0.0072518196, 0.0410315953, -0.00142382807, -0.00227337214, 0.0297677089, 0.00912517309, 0.0112480437, 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19 Sep, 2023 | Swift Programming Language
19 Sep, 2023
Swift is a general-purpose, multi-paradigm, object-oriented, functional, imperative, and block-structured language. Swift is the result of the latest research on programming languages and is built using a modern approach to safety, and software design patterns by Apple Inc. for iOS applications, macOS applications, watchOS applications, tvOS applications.
Swift is easy to learn, easy to implement, safe, fast, and expressive. Developing Swift in the open has its exciting aspects as it is now free to be ported across a wide range of platforms, devices, and use cases.
The features of Swift are designed to work together to create a powerful language. Additional features of Swift include:
Closures (similar to lambda functions in other languages) unified with function pointers
Tuples and multiple return values
Concise and fast iteration over a range or collection
Structs and Classes that support methods, extensions, and protocols
Functional programming patterns, e.g., map and filter
Powerful error handling built-in
Advanced control flow with do, guard, defer, and repeat keywords
Optionals and force-unwrap
Type Inference and type annotation
Memory Management: Automatic reference counting is a system which tracks the number of references to an object in memory. When an object is no longer needed in the future , ARC automatically deallocates the memory used by that object. This helps to prevent memory leaks, which can occur when an object is no longer needed but its memory is not released, and can help to improve the performance of the program.Swift is managed as a collection of projects, each with its repositories. The current list of projects include:
The Swift compiler command-line tool
The Standard library bundled as part of the language
Core libraries that provide higher-level functionality
The Swift REPL included LLDB debugger
Xcode playground support to enable playgrounds in Xcode.
The Swift package manager for distributing and building Swift source code
Example:
Swift
// Basic Swift Program
import Foundation // This functionality provides basic functionality to apps
var str1 = "Hello geeks!"
let str2 = "How are you?"
print (str1)
print (str2)
Output:
Hello geeks!
How are you?
Run: Code can be tested on Online IDE for Swift
Note: Import statement is used to import any objective-C framework or library directly into Swift program. var keyword is used for variable and let keyword is used for constant. There is no need for”;” for termination, in case the programmer uses it compiler won’t show an error.
Advantages –
Swift is open-sourced and easy to learn as it has a very simple and easy syntax
Swift is approachable and familiar. It is Interoperable with objective-C as well which means that developers can use Swift and Objective-C together in the same project, and can even call Swift code from Objective-C and vice versa
Swift is a statically typed language, which means that the type of each variable is checked at compile-time rather than at runtime. This can help to improve the performance of Swift code, as the compiler can optimize the code more effectively. Additionally, Swift uses modern optimization techniques, such as automatic reference counting and protocol-oriented programming, to help improve the efficiency of the code.
Swift is enterprise-ready.
Disadvantages:
The language is still quite young and the talent pool is limited : Swift is considered a “moving target” as it is a new language and the number of swift programmers is few.
Poor interoperability with third-party tools and IDEs : There are very less tools and IDEs that can support Swift and the language is proprietary to Apple and is primarily used on Apple platforms. Example : Xcode
Lack of support for earlier iOS versions : One of the main disadvantages of Swift is that it is not backwards compatible with earlier versions. This means that if you are using an older version of Swift and want to update to a newer version, you may have to rewrite some of your code to make it compatible with the new version.
Steep Learning curve : Despite the fact that Swift has a relatively easier syntax , there are a number of advanced concepts and features that take time to learn. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language | https://www.geeksforgeeks.org/swift-programming-language/ | NLP | Swift Programming Language | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, 6 Best iOS Project Ideas For Beginners, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Loss Functions in Deep Learning, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Swift - Initialization, Swift – If Statement | GeeksforGeeks | [-0.0633854046, 0.0260959622, -0.0086543411, 0.0265346617, -0.012256993, 0.0316661149, 0.0123633444, 0.00523448037, -0.0504371263, -0.0163249318, 0.0325435102, -0.0117717646, 0.00644090353, -0.00301107252, -0.0508891195, 0.0575360768, 0.000780186849, 0.011379594, -0.026734069, -0.0038319719, 0.0121439947, -0.016856689, -0.0660973638, -0.0168699827, 0.010289493, 0.00334674399, 0.0300708432, -0.000427067134, -0.0651933774, -0.0101166721, -0.0195154715, -0.00113330653, -0.0120309964, -0.0121307, 0.00685966201, 0.0291668568, 0.000492290419, -0.019449003, -0.0121772289, 0.0120309964, -0.0176410303, 0.00110754953, 0.0216956753, 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09 Jun, 2022 | Introduction to Visual Programming Language
09 Jun, 2022
Any language that uses the graphics or blocks that are already defined with the code and you just need to use those blocks without worrying about the lines of code is known as a visual programming language. In today’s era majority of the programming languages are text-based i.e. we have to write the lines of code to perform the specific task like in C or C++. programming if you want to print a table of 2 then you have to write the complete text using syntax and functions of that language but in visual programming language this task is replaced by graphics or blocks like components then can be joined logically to perform the task.
Visual Programming language lets the user think in a logical manner unlike in regular programming language the user has to think about that how he/she can explain the program to the computer, to do this let’s take one small analogy like if you have to code multiplication table of 2 then in regular programming language what you will do is you will take the loop and with the help of it you can print the multiplication table but in the visual basic language you just have to add the block which has the inbuilt code in it of loop and you just specify the value and you just have to think logically and your work is done without worrying about the semicolon, syntax, functions, etc.
Examples of Visual Programming Language:
There are n numbers of visual programming languages and the few which are in the top list is given below
Scratch: With the help of this language users can create, stories, games, and animations without writing any lines of code in this you just have to create the logic and assemble the blocks.
Blockly: Used to create block-based programming language and editors, and also to generate code from blocks to javascript lua dart python and PHP, etc.
mBlock language: It is used in programming robots.
Bubble language: It is used to create web applications.
Minibloq language: It is used as a graphical programming environment for Arduino.
Examples of Visual Programming Language Interface:
You just have to choose/create and join the blocks and your applications are ready without writing any lines of code and also in all the visual programming languages, one thing is common that it will have the graphic blocks like in the given image below.
Figure: Example of the interface of Scratch visual programming language
Figure: Example of Blockly language used by kodular to create apps
Applications of Visual Programming language:
VPL can be used in multiple domains like multimedia, educational purpose, video games, automation. Let’s see them in brief:
Multimedia:- VPL helps users create multimedia without worrying about the real code or other complex features. It narrows down to specific functions and with the help of those functions, multimedia is created.
Educational Purpose:-Scratch VPL, etc are used to help students in their projects and make them familiar with the coding.
VideoGames:-VPL helps to create the videogames without writing lines of codes Ex- Scratch VPL is used to make videogames.
Advantages of visual programming language:
Easy to convert ideas into reality for example you don’t know how to code so you can start with VPL(Visual Programming Language). and then switch to actual coding.
Visuals are easy to grasp i.e. to develop something in visual programming language requires less efforts.
It includes a variety of built in objects that are required while creating something using VPL.
It is a beginner-friendly also anyone will be able to derive the logic without worrying about writing lines of code.
Adding a user-specific code is also available and simple as it allows to create of blocks as per the convenience of the user.
Disadvantages of visual programming language:
These languages require more memory as they use graphics, as a result, their execution is also slow and a large amount of memory is occupied by them.
They can only work in an operating system like windows, mac, or any other operating system which supports graphics.
As the inbuilt functions are not sufficient so you have to add your custom code as a result it is cumbersome.
Only limited functions are present in these languages.
Adding our custom code as a block requires coding knowledge or else you have to work with limited functions which are provided with the language.
As a computer engineer, it is not a good idea to use VPL as most of the tech giants like FAANG or other tech companies work on textual languages like JAVA, HTML, etc, rather than VPL.
For the long run VPL might not be that much useful as in a regular language you can explore more in it but in VPL at one point you will get bored by using the same it.
Difference between regular programming languages and visual programming languages:
Sr. No
Regular Languages
Visual Programming Language
1.
It is a programming language that only uses text.
It is a programming language that uses graphics or blocks in place of text.
2.
It is not beginner-friendly language
It is a beginner-friendly language
3.
Customization and flexible applications can be created using regular languages
There are not that much customizable as the blocks or graphics that contain the codes are limited and after that, we need to add our custom code as a block.
4.
These are quite fast and efficient
This is not fast and efficient as every block has some code with it so it takes time and also it has graphics with it.
5.
The interface is not good i.e. only text and syntax of language we have to get familiar with it.
The interface is great as the user has to just join the blocks and frame the logic without writing the code
6
requires time to learn as the user has to get familiar with the language syntax then code in it
any school student will be able to grasp the VPL and create the applications
7.
Requires lot of efforts as a beginner to start with the language
Doesn’t require a lot of effort and also the main targeted user of VPL is school level students so that they can love the coding
8.
These are quite fast as compared to VPL as they don’t have graphics.
These are slow as compared to regular languages as it has graphics.
9.
These require less memory as compared to VPL
This requires more memory as it has graphics so to store them more memory is used.
10.
Examples: Javascript, C, C++, Java, Python Etc.
Examples: Mblock, Blockly, Scratch Etc.
Although both Regular and Visual Programming Language is in the trend in their respective categories the only difference that lies between them is that regular languages are written first and with the help of visual programming languages the parts of regular language are taken in according to its functions and the blocks and with the help of block programming is made simpler. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language | https://www.geeksforgeeks.org/introduction-to-visual-programming-language/?ref=ml_lbp | NLP | Introduction to Visual Programming Language | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, 6 Best iOS Project Ideas For Beginners, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Loss Functions in Deep Learning, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Swift - Initialization, Introduction to Visual Programming Language, Swift – If Statement | GeeksforGeeks | [-0.0188673139, 0.0128671806, -0.0253657531, 0.0207649674, 0.00933809206, 0.0232633166, -0.0112903537, -0.00655646, -0.00976131, -0.0106213968, 0.0378711522, 0.0024386209, -0.0270176679, -0.0557282045, -0.0436869822, 0.0330382809, 0.0166010521, 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30 Jul, 2024 | What is D Programming Language: Usage and Applications
30 Jul, 2024
The D programming language is another powerful high-performance language designed for effective programming of system-level and application software. Combining the efficiency of C++ with the simplicity of modern languages like Python, D attempts to provide a productive experience without applying any kind of optimization wizardry. This article elaborates to the length of the detail on the different aspects of D: features, syntax, benefits, and real-world applications.Table of ContentHistory and Development of D Programming LanguageKey Features of D Programming LanguageSyntax and Basics of D Programming LanguageAdvantages of Using D Programming LanguageReal-World Applications of D Programming LanguageGetting Started with D Programming Language1. Installation2. Writing Your First ProgramHistory and Development of D Programming LanguageThe D programming language was designed by Walter Bright, creator of Digital Mars, in 2001. The language aimed to eliminate many of the C++ limitations while being endowed with all of the powerful features of that language. After that, D added many crucial features in such a way that turned it into a modern language of the community. Indeed, features such as garbage collection, contract programming, and multi-paradigm support have led D to become a general-purpose, multiparadigm language: quite versatile and robust.Key Features of D Programming Language 1. High performanceD has competitive performance to that of C and C++, and, at the same time, offers much higher-level abstractions. All that makes it fit for not only system-level programming but also for performance-critical applications. The D compiler, DMD, creates mean, lean, and highly optimized machine code.2. Clarity and ReadabilityD's design and syntax are supposed to carry out a lot of readability, minimizing lots of the complexity associated with languages such as C++. This philosophy of design emphasizes minimalism and lucidity, making the language accessible to both beginners and experienced software developers.3. Memory SafetyD offers memory safety features, like garbage collection, which ensures that common programming mistakes regarding memory fail to occur, whereby common classes of memory bugs like memory leaks and buffer overflows are avoided. For those cases in which manual memory management must be done for parts of programs that negatively affect performance, developers are free to control garbage collection.4. MetaprogrammingD supports strong metaprogramming, which allows developers to easily write code that writes other code, to maximize output while minimizing verbosity. This is done using templates and mixins, as well as CTFE(Compile Time Function Evaluation).5. ConcurrencyD is endowed with support for concurrent programming, thereby making inclusion in a multi-threaded application easy to program. Built-in support features like fibers, message-passing, and shared data are good ways to manage the concurrency.6. CompatibilityD is compatible with C and C++ code very extensively; this interoperability stretches from linking with C libraries to using C++ classes and templates.Syntax and Basics of D Programming Language1. Variables and Data TypesBecause D is strongly typed, it natively supports data types of a wide degree, going from plain primitives—like int, float, char—to more compound ones, including arrays and structures. The type system of D is designed to be strong while still being extremely flexible for advanced manipulations of the types within the program.int a = 10;float b = 20.5;char c = 'D';string s = "Hello, D!";2. Control StructuresD includes the standard control structures if-else, loops (for, while, do-while) and switch statements. These control structures have been enhanced further by facilities such as scope guards and labels, among others, for more controlled structures of managing flow.for (int i = 0; i < 10; i++) { writeln(i);}if (a > b) { writeln("a is greater than b");} else { writeln("a is not greater than b");}3. FunctionsFunctions are defined using the void keyword, in case a function does not return a value, or the return type for those that do. D supports function overloading and provides means for default and named arguments, through which more meaning can be encoded in—interfaces.void greet() { writeln("Hello, D!");}int add(int x, int y) { return x + y;}4. Object-Oriented ProgrammingIt supports object-oriented principles like classes and polymorphism through inheritance and, additionally, multiple inheritance and interfaces together make it quite a powerful way to design large-scale software. It also supports other object-oriented characteristics, such as interfaces, abstract classes, and provides power for multiple inheritance, although not through the class, through the interfaces.class Animal { void makeSound() { writeln("Some sound"); }}class Dog : Animal { override void makeSound() { writeln("Bark"); }}Advantages of Using D Programming Language1. Performance and EfficiencyD's high performance makes it a very good language with which to do system-level programming and game development, as well as several other performance-critical applications. Its ability to produce highly optimized machine code ensures that applications run efficiently.2. Contemporary FeaturesFurthermore, D has all the other features that garbage collection, type inference, and metaprogramming—common to many new programming languages—have. These features altogether tend to make D coding very intuitive, as opposed to coding with old languages like C++.3. Easy to LearnWith its syntax simple and actually quite usual for those acquainted with C or C++, this language is relatively easy to grasp. At the same time, the language is based on readability and simplicity, which helps new developers acquire the basics rather swiftly.4. Strong Community and EcosystemD is strongly community-based and vibrant, offering a lot of libraries, tools, and frameworks for support during development. This kind of community development will make sure the language grows to meet the needs of users.5. Platform Compatibility Being cross-platform, D can be used on Windows, Linux, and macOS, which makes it flexible for different development environments. More so, it ensures that D application developments can easily run across several systems with minor modifications.Real-World Applications of D Programming Language1. System ProgrammingD's ability to produce more efficient and high-performing code makes it suitable for developing operating systems, drivers, and, in general, low-level coding in the system. It provides compatibility with C to leverage existing system libraries.2. Game DevelopmentIt being high in performance makes D ideal for game development, where most demands are on speed and efficiency. Game engines, as well as performance-critical game logic, can be effectively implemented in D.3. Computing in ScienceD's high-performance computing and numerical analysis libraries make it suitable for scientific applications. Equally, D provides lengthy numerical computation and data manipulation libraries.4. Web DevelopmentD can be used for the development of any kind of web with frameworks like Vibe.d while offering great performance for server-side applications. Vibe.d enables asynchronous I/O and as such is well suited for high-concurrency web services.5. ScriptingThis compact and readable mainstream language means that D can also serve well in scripting and automation operations. Compiling scripts down to native code gives a speed advantage over interpreted scripting languages.Getting Started with D Programming Language1. InstallationFirst of all, to program in D, you need to install the D compiler. The most used are DMD, which stands for D Digital Mars D.a) Installation on Windows:choco install dmdb) Installation on Linux:sudo apt-get install dmd2. Writing Your First Programa) Create a file named hello.d with the following content:import std.stdio;void main() { writeln("Hello, D!");}b) Compile and run the program:dmd hello.d./helloConclusionThe D programming language unifies together functionality with high performance and modern features in a way that it becomes versatile and competent for diverse applications: concerns of writing system-level software, games of high performance, complex scientific calculations, and generally everything else. D gives you the tools and power you need to succeed, and growing strong communities with growing ecosystems allow D to be available from more and more different places.Also Read:Top Programming Languages For Competitive Programming Top 10 Fastest Programming Languages 10 Best Coding Games to Advance Your Programming Skills What is D Programming Language: Usage and Applications - FAQsWhat is the D programming language and why is it important?D is a high-performance system programming and application language. It is kind of important since it possesses the ability to combine qualities of C++ efficiency with the modern ease of a language needed to be important in writing efficient and buildable software.How can I structure my D project for better maintainability?Structuring a D project involves properly keeping the code files into a clear and logical directory structure. Use a separate folder for each component, module, and utility. Consistent naming and absolute imports may be another technique for maintainingWhat are the best practices for creating reusable components in D? D offers reusability of components by keeping the size of the components very small and thematically focused, templating for generic programming, and not hardcoding the components. The individual component would be made up of separate modules where, inside each of them, documentation is necessary to do.What is the role of metaprogramming in D? Metaprogramming in D is the ability for developers to use the language to write code that can write code. Developers can write a code generator, which allows them to decrease redundancy and thus improve the efficiency of the code. Rather importantly, it is key for template programming and for. Can I use C and C++ libraries in D?Sure, D can interact with C and C++ code. This actually implies a compatible use with an already developed library or codebase, making transitioning to D—in this regard—rather easy. What are some popular frameworks and libraries in D?Some of the common frameworks and libraries for D include Vibe.d for web development, Mir for scientific computing, and GtkD for GUI applications. These libraries enhance functionalities for easy programming in the respective areas of their application general. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications | https://www.geeksforgeeks.org/what-is-d-programming-language/?ref=ml_lbp | NLP | What is D Programming Language: Usage and Applications | Artificial Intelligence – Boon or Bane, Natural Language Processing (NLP) Tutorial, ML | Common Loss Functions, 6 Best iOS Project Ideas For Beginners, AI ML DS - Projects, Artificial Intelligence Examples, NLP, Loss Functions in Deep Learning, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion Models?, What is D Programming Language: Usage and Applications, Kaiming Initialization in Deep Learning, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Does Artificial Intelligence Require Coding?, Swift - Initialization, Introduction to Visual Programming Language, Swift – If Statement | GeeksforGeeks | [-0.0272592064, -0.0110936845, -0.0257882196, 0.0295729451, 0.0237043239, 0.0419537425, -0.00728214579, -0.0165792368, -0.0101743182, 0.0634362623, 0.0201341193, 0.0115457065, 0.0141199315, -0.0435473099, -0.0177744124, 0.0481747873, 0.00385367638, 0.015529626, -0.0122045856, 0.00783759635, 0.00704464316, 0.0316874869, -0.0443747379, 0.0132312113, 0.0115840137, 0.0251599867, 0.00688375393, -0.00868801, -0.0307221524, 0.00193545723, 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22 Jul, 2024 | Best Programming Languages for Data Science in 2024
22 Jul, 2024
In today’s data-rich world, data science plays a crucial role in unlocking valuable insights from vast amounts of data. With an exponential increase in data production, the need for skilled data scientists proficient in programming languages tailored for data analysis and machine learning has never been more critical.
This article compiles the top programming languages essential for data science, offering a comprehensive overview of their features and applications. Whether you’re an aspiring data scientist or a seasoned professional looking to expand your skill set, understanding these languages is key to thriving in the data-driven landscape.
Table of Content
What is Data Science?
Best Programming Languages for Data Science
1. Python
2. R
3. SQL
4. MATLAB
5. Java
6. Scala
7. Julia
8. Perl
What is Data Science?
Data science is a field that involves using scientific methods, algorithms, and systems to extract insights and knowledge from structured and unstructured data. It combines various disciplines such as statistics, machine learning, data analysis, and programming to analyze and interpret complex data sets. The goal of data science is to uncover patterns, trends, and relationships in data that can be used to make informed decisions and predictions.
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Best Programming Languages for Data Science
Now, let’s explore the top and best-suited programming languages for data science, essential for mastering this dynamic field. These languages are carefully curated to provide a comprehensive understanding of data analysis, statistical modeling, machine learning, and data visualization. Each language offers unique advantages, empowering data scientists to tackle diverse challenges and unlock the full potential of data-driven insights. Whether you’re a beginner seeking a solid foundation or an experienced professional aiming to enhance your skills, mastering these Best Programming Languages for Data Science is crucial for success in the rapidly evolving field of data science.
1. Python
Python is one of the best programming languages for data science because of its capacity for statistical analysis, data modeling, and easy readability. Another reason for this huge success of Python in Data Science is its extensive library support for data science and analytics. There are many Python libraries that contain a host of functions, tools, and methods to manage and analyze data. Each of these libraries has a particular focus with some libraries managing image and textual data, data mining, neural networks, data visualization, and so on. For example, Pandas is a free Python software library for data analysis and data handling, NumPy for numerical computing, SciPy for scientific computing, Matplotlib for data visualization, etc.
2. R
When talking about Data Science, it is impossible not to talk about R. In fact, it can be said that R is one of the best languages for Data Science as it was developed by statisticians for statisticians! It is also very popular (despite getting stiff competition from Python!) with an active community and many cutting edge libraries currently available. In fact, there are many R libraries that contain a host of functions, tools, and methods to manage and analyze data. Each of these libraries has a particular focus with some libraries managing image and textual data, data manipulation, data visualization, web crawling, machine learning, and so on. For example, dplyr is a very popular data manipulation library, ggplot2 is a data visualization library, etc.
3. SQL
SQL or Structured Query Language is a language specifically created for managing and retrieving the data stored in a relational database management system. This language is extremely important for data science as it deals primarily with data. The main role of data scientists is to convert the data into actionable insights and so they need SQL to retrieve the data to and from the database when required. There are many popular SQL databases that data scientists can use such as SQLite, MySQL, Postgres, Oracledb, and Microsoft SQL Server. BigQuery, in particular, is a data warehouse that can manage data analysis over petabytes of data and enable super fats SQL queries.
4. MATLAB
MATLAB is a very popular programming language for mathematical operations which automatically makes it important for Data Science. And that’s because Data Science also deals a lot in math. MATLAB is so popular because it allows mathematical modeling, image processing, and data analysis. It also has a lot of mathematical functions that are useful in data science for linear algebra, statistics, optimization, Fourier analysis, filtering, differential equations, numerical integration, etc. In addition to all these, MATLAB also has built-in graphics that can be used for creating data visualizations with a variety of plots.
5. Java
Java is one of the oldest programming languages and it is pretty important in data science as well. Most of the big data and data science tools are written in Java such as Hive, Spark, and Hadoop. Since Hadoop runs on the Java virtual machine, it is important to fully understand Java for using Hadoop. Moreover, there are many Data science libraries and tools that are also in Java such as Weka, MLlib, Java-ML, Deeplearning4j, etc.
6. Scala
Scala is a programming language that is an extension of Java as it was originally built on the Java Virtual Machine (JVM). So it can easily integrate with Java. However, the real reason that Scala is so useful for Data Science is that it can be used along with Apache Spark to manage large amounts of data. So when it comes to big data, Scala is the go-to language. Many of the data science frameworks that are created on top of Hadoop actually use Scala or Java or are written in these languages. However, one downside of Scala is that it is difficult to learn and there are not as many online community support groups as it is a niche language.
7. Julia
Julia is an extremely fast programming language and it can work with data even faster than Python, R, MATLAB, or JavaScript. Julia is also great for numerical analysis which makes it an optimal language for data science. Julia has mathematical libraries and data manipulation tools that are a great asset for data analytics but it also has packages for general-purpose computing. All in all, Julia has a total of 1900 packages available. It is also able to integrate with other programming languages like R, Python, Matlab, C, C++ Java, Fortran, etc. either directly or through packages.
8. Perl
Perl can handle data queries very efficiently as compared to some other programming languages as it uses lightweight arrays that don’t need a high level of focus from the programmer. It is also quite similar to Python and so is a useful programming language in Data Science. In fact, Perl 6 is touted as the ‘big-data lite’ with many big companies such as Boeing, Siemens, etc. experimenting with it for Data Science. Perl is also very useful in quantitative fields such as finance, bioinformatics, statistical analysis, etc.
Conclusion
Now that you know the top programming languages for data science, its time to go ahead and practice them! Each of these programming languages has its own importance and there is no such language that can be called a “correct language” for Data Science. For example, you may use Python for data analytics and also SQL data management. So, it is upon you to make the correct choice of language on the basis of your objectives and preferences for each individual project. And always remember, whatever your choice, it will only expand your skillset and help you grow as a Data Scientist!
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Best Programming Languages for Data Science in 2024 – FAQs
Why are programming languages important in data science?
Programming languages are essential in data science for data manipulation, analysis, visualization, and machine learning model implementation.
Which programming languages are best for data science?
Python, R, SQL, MATLAB, Java, Scala, Julia, and Perl are among the top programming languages for data science, each offering unique strengths and applications in data analysis and machine learning.
Can I use multiple programming languages for data science projects?
Yes, it’s common to use multiple programming languages in data science projects based on the specific requirements and strengths of each language for different tasks.
What skills are essential for a career in data science?
A career in data science requires a combination of technical skills such as programming, statistics, and machine learning, as well as soft skills like problem-solving, critical thinking, and effective communication. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024 | https://www.geeksforgeeks.org/programming-languages-for-data-science/?ref=ml_lbp | NLP | Best Programming Languages for Data Science in 2024 | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0219449401, 0.0142420931, -0.0137997326, 0.0455054604, 0.0134246871, -0.027272502, -0.026926307, 0.00527467113, 0.0168289412, 0.0210794527, 0.0120399063, -0.0409279875, 0.0387931168, -0.0131746577, -0.018261807, 0.0154345436, 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11 May, 2022 | 5 Best Languages for Competitive Programming
11 May, 2022
Needless to say, Competitive Programming is one of the most crucial and popular aspects of a programmer’s journey. Though, all the programmers are strongly recommended to participate in such coding challenges to enhance their coding skills and to get various ravishing prizes, rewards, and other career opportunities. Meanwhile, there’s a question that often comes to the mind of individuals before getting into the Competitive Programming world — Which is the best programming language for Competitive Programming? And truly, as there are numerous preferred programming languages available, it becomes quite difficult to find out the relevant and worthwhile one!!
Before moving further, let’s take a brief introduction to Competitive Programming. Competitive Programming concerns with the coding competitions or challenges where you’re required to showcase your programming skills under different specified constraints such as minimum time, reduced complexity, etc. Indeed, Competitive Programming is the best way to analyze your programming skills through competing with the various other profound programmers across the world & gain the utmost exposure to real-time programming. Moreover, there are numerous renowned platforms that organize various coding challenges for competitive programming such as TopCoder, CodeChef, and many more.
https://www.youtube.com/watch?v=deaQG10LWR8
Now, let’s get back to the main concern — how to figure out the best language for Competitive Programming? Here, in this article, we’ll let you know about these 5 most recommended programming languages that you can consider to start your Competitive Programming journey:
1. C++
Indeed, C++ is one of the most recommended and widely used programming languages for Competitive Programming. C++, developed by Bjarne Stroustrup, is a relatively faster programming language in comparison to various other renowned languages. Meanwhile, as the execution time plays a crucial role in Competitive Programming, hence C++ is the most preferred language by the programmers. The general-purpose programming language consists of a rich library known as Standard Template Library that makes it easier for the programmers to do efficient & effective programming. The Standard Template Library includes C++ template classes that offer various data structures such as lists, trees, stacks, graphs, arrays, etc. Moreover, the language supports OOPS (Object-Oriented Programming) features as well to help you out while solving real-time problems in coding challenges.
2. JAVA
Here comes another most recommended programming language for Competitive Programming — JAVA. The object-oriented language, developed in 1995, works on Write Once, Run Anywhere concept which implies that the compiled Java code can be executed on any platform, that supports Java, without recompilation. Meanwhile, JAVA comes up with a rich library set such as BigInteger class used for calculation based on large integers or Regular Expressions, Geometry Library to handle geometrical problems, and many more. Furthermore, various other worthwhile features supported by JAVA such as better exception handling, Java Containers, etc. make it one of the most preferred languages for Competitive Programming. Moreover, the language is easy to learn and you can start to learn JAVA from various online & offline resources.
3. Python
Python gives you numerous reasons to pick it up for your next Competitive Programming contest. The high-level programming language is quite easy to learn and implement with having a very simple syntax. Moreover, the language has an extensive library & function support which somehow increases the efficiency of programmers in coding competitions. Furthermore, the language has several other worthwhile features as well such as no limit on the integer value, functions can return more than one value, code indentation, robust input statements, flexible number of arguments to a function, etc. makes Python a suitable language for Competitive Programming. Also, the language has wide use in various trending domains such as Machine Learning, Artificial Intelligence, Data Science, and many more.
4. Ruby
Ruby is also one of the most sought-after programming languages in the competitive programming world. It is an object-oriented programming language that is very user-friendly, flexible, and easy to learn. Meanwhile, Ruby is a dynamic programming language and is based on several other programming languages such as Perl, Smalltalk, Lisp, Ada, Smalltalk, and Eiffel. Though, Ruby is an interpreted scripting language so it is quite slow in comparison to other compiled languages and this aspect gives the upper hand to other languages while considering the best programming language for competitive language. Moreover, apart from competitive programming, Ruby is also used in a wide range of domains such as Web Applications, Database Solutions, Data Science, and many more.
5. Kotlin
Last but not least — Kotlin. Kotlin, introduced in 2011, is a general-purpose programming language that supports object-oriented programming paradigms along with functional programming features. The language is easy to learn and provides access to a rich library including various data structures, collections, etc. Moreover, while programming in Kotlin, you can use existing Java Frameworks & Libraries as well. The languages offer various crucial features that can be beneficial during competitive programming such as Type Inference, Smart Casts, avoids the Null Pointer Exception, and many more. Furthermore, as Kotlin emphasizes more readable syntax, so it makes it easier to review the code, and also you can easily learn and understand the language efficiently through various online and offline resources.
So, these are several best programming languages for competitive programming that can be taken into consideration. Although, apart from opting for a relevant & worthwhile programming language, you’re required to emphasize more on Algorithm building and Data Structures as well. Though, you can easily get command over Data Structures & Algorithms through various prominent online resources such as GeeksforGeeks, etc. Now, what are you waiting for? Choose a relevant programming language, prepare yourself, and participate in the upcoming prestigious Coding Challenges!! | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming | https://www.geeksforgeeks.org/5-best-languages-for-competitive-programming/?ref=ml_lbp | NLP | 5 Best Languages for Competitive Programming | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [0.00161008071, -0.0187961496, -0.0136869894, 0.0187683441, 0.0223829895, 0.0243293364, 0.00503269676, 0.0108439326, -0.0105936881, 0.0205061547, -0.00893234182, -0.0245378725, 0.0284305662, -0.0324205793, -0.000583035173, 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14 Feb, 2025 | MEX (Minimum Excluded) in Competitive Programming
14 Feb, 2025
MEX of a sequence or an array is the smallest non-negative integer that is not present in the sequence.Note: The MEX of an array of size N cannot be greater than N since the MEX of an array is the smallest non-negative integer not present in the array and array having size N can only cover integers from 0 to N-1. Therefore, the MEX of an array with N elements cannot be greater than N itself.ExamplesInput: S[] = {1, 2, 0, 4, 5}Output: 3Explanation: The given sequence contains 0, 1, 2, 4, and 5. The smallest non-negative integer missing from the sequence is 3, as all numbers before it are present.Input: S[] = {2, 0, 3, 10}Output: 1Explanation: The given sequence contains 0, 2, 3, and 10. The smallest non-negative integer missing from the sequence is 1, as 0 is present but 1 is not.Input: S[] = {1, 2, 3, 4, 5}Output: 0Explanation: The given sequence contains 1, 2, 3, 4, and 5, but 0 is missing. Since 0 is the smallest non-negative integer not present in the sequence, it is the MEX.How to Find MEX of an array (Without Updates) ?The idea is to use a map to store frequency of each element of an array. Then, iterate through non-negative integers from 0 to N, and return the first integer with a frequency of 0 in the map. This integer represents the smallest non-negative integer not present in the array, which is the MEX.
C++
#include <bits/stdc++.h>
using namespace std;
// Function to find the MEX of the array
int mex(vector<int>& arr, int N)
{
// Create a map to store the frequency of each element
map<int, int> mp;
for (int i = 0; i < N; i++) {
mp[arr[i]]++;
}
// Initialize MEX to 0
int mex = 0;
// Iterate through non-negative integers from 0 to N
for (int i = 0; i <= N; i++) {
// Find the first integer with a frequency of 0 in the map
if (mp[i] == 0) {
mex = i;
break;
}
}
// Return MEX as the answer
return mex;
}
int main()
{
// Example array
vector<int> arr = { 1, 0, 2, 4 };
int N = arr.size();
// Call the mex function and print the result
cout << "MEX of the array: " << mex(arr, N) << endl;
return 0;
}
Java
import java.util.HashMap;
public class MinimumExcludedValue {
// Function to find the MEX of the array
static int mex(int[] arr, int N) {
// Create a map to store the frequency of each element
HashMap<Integer, Integer> mp = new HashMap<>();
for (int i = 0; i < N; i++) {
mp.put(arr[i], mp.getOrDefault(arr[i], 0) + 1);
}
// Initialize MEX to 0
int mex = 0;
// Iterate through non-negative integers from 0 to N
for (int i = 0; i <= N; i++) {
// Find the first integer with a frequency of 0 in the map
if (!mp.containsKey(i)) {
mex = i;
break;
}
}
// Return MEX as the answer
return mex;
}
public static void main(String[] args) {
// Example array
int[] arr = {1, 0, 2, 4};
int N = arr.length;
// Call the mex function and print the result
System.out.println("MEX of the array: " + mex(arr, N));
}
}
Python
# Function to find the MEX of the array
def mex(arr):
# Create a dictionary to store the frequency of each element
freq_map = {}
for num in arr:
freq_map[num] = freq_map.get(num, 0) + 1
# Initialize MEX to 0
mex_val = 0
# Iterate through non-negative integers from 0 to N
N = len(arr)
for i in range(N + 1):
# Find the first integer with a frequency of 0 in the dictionary
if i not in freq_map:
mex_val = i
break
# Return MEX as the answer
return mex_val
# Main function
if __name__ == "__main__":
# Example array
arr = [1, 0, 2, 4]
# Call the mex function and print the result
print("MEX of the array:", mex(arr))
C#
using System;
using System.Collections.Generic;
using System.Linq;
class MexAlgorithm
{
static int Mex(int[] arr, int N)
{
Dictionary<int, int> freqMap = new Dictionary<int, int>();
// Store the frequency of each element in the array
for (int i = 0; i < N; i++)
{
if (freqMap.ContainsKey(arr[i]))
{
freqMap[arr[i]]++;
}
else
{
freqMap[arr[i]] = 1;
}
}
int mex = 0;
// Iterate through non-negative integers from 0 to N
for (int i = 0; i <= N; i++)
{
// Find the first integer with a frequency of 0 in the dictionary
if (!freqMap.ContainsKey(i) || freqMap[i] == 0)
{
mex = i;
break;
}
}
return mex;
}
static void Main()
{
// Example array
int[] arr = { 1, 0, 2, 4 };
int N = arr.Length;
// Call the Mex function and print the result
Console.WriteLine("MEX of the array: " + Mex(arr, N));
}
}
JavaScript
// Function to find the MEX of the array
function mex(arr, N) {
// Create a map to store the frequency of each element
const mp = new Map();
for (let i = 0; i < N; i++) {
if (mp.has(arr[i])) {
mp.set(arr[i], mp.get(arr[i]) + 1);
} else {
mp.set(arr[i], 1);
}
}
// Initialize MEX to 0
let mex = 0;
// Iterate through non-negative integers from 0 to N
for (let i = 0; i <= N; i++) {
// Find the first integer with a frequency of 0 in the map
if (!mp.has(i) || mp.get(i) === 0) {
mex = i;
break;
}
}
// Return MEX as the answer
return mex;
}
// Main function
function main() {
// Example array
const arr = [1, 0, 2, 4];
const N = arr.length;
// Call the mex function and print the result
console.log("MEX of the array:", mex(arr, N));
}
// Call the main function
main();
OutputMEX of the array: 3Time Complexity: O(N log N) due to insertions in the map and an additional O(N) iteration for finding the MEX, making it effectively O(N log N).Auxiliary Space : O(N) for storing the frequency map.Further Optimization: We can use a Set instead of map to optimize the space used. However time and space complexity remain the same.How to Find MEX of an array (With Updates) ?Given an array arr of size N, and q queries. In each query you are given two numbers (idx, val), you have to update the element at index idx with value val. The task is to determine the MEX of the array after each query.Approach:The idea is to use a map to store frequency of each element of an array. Then insert all the numbers in the set from 0 to N which are not present in the array. For each query, update the array and maintain the map and set accordingly. The MEX for each query is determined by selecting the smallest element from the set and added to the result. Step-by-step approach:Create a map to store the frequency of array elements and a set to store the elements(from 0 to N) which are not present in the array. For each query.Decrement the frequency of the element which is being replaced. If the frequency becomes 0, that element is added to set since it is not present in the array.Increment the frequency of the updated element. Remove the updated element from the set if the set contains it, since the updated element will be present in the set. The MEX for each query is determined by selecting the smallest element from the set and added to the result. Below is the implementation of above approach:
C++
#include <bits/stdc++.h>
using namespace std;
// Function to calculate the MEX of an array after a series
// of queries
vector<int> mex(vector<int>& arr, int N,
vector<vector<int> > queries, int q)
{
// Initialize a map to store element frequencies
map<int, int> mp;
// Initialize a set to store non-present elements
set<int> st;
// Populate the map for the initial array
for (int i = 0; i < N; i++) {
mp[arr[i]]++;
}
// Add the elements to set which are not present in the
// array.
for (int i = 0; i <= N; i++) {
if (mp[i] == 0)
st.insert(i);
}
// Initialize a vector to store MEX values after each
// query
vector<int> mex;
// Process each query
for (int i = 0; i < q; i++) {
int idx = queries[i][0];
int val = queries[i][1];
// Update the frequency of element which being
// replaced.
mp[arr[idx]]--;
// If the frequency of element which is being
// replaced becomes 0, add it to set.
if (mp[arr[idx]] == 0) {
st.insert(arr[idx]);
}
arr[idx] = val;
mp[arr[idx]]++;
// If the updated element is in the set, remove it
if (st.find(arr[idx]) != st.end())
st.erase(arr[idx]);
// Calculate the MEX and add it to the result vector
int ans = *st.begin();
mex.push_back(ans);
}
return mex;
}
// Driver Code
int main()
{
// Example array
vector<int> arr = { 1, 0, 2, 4, 7 };
int N = arr.size();
// Example queries
vector<vector<int> > queries
= { { 1, 3 }, { 0, 0 }, { 4, 1 }, { 2, 10 } };
int q = queries.size();
// Call the 'mex' function to calculate MEX values after
// each query
vector<int> ans = mex(arr, N, queries, q);
// Print the results
for (int i = 0; i < q; i++) {
cout << "MEX of the array after query " << i + 1
<< " : " << ans[i] << endl;
}
return 0;
}
Java
import java.util.*;
public class Main {
// Function to calculate the MEX of an array after a series
// of queries
static List<Integer> mex(List<Integer> arr, int N,
List<List<Integer>> queries, int q) {
// Initialize a map to store element frequencies
Map<Integer, Integer> mp = new HashMap<>();
// Initialize a set to store non-present elements
TreeSet<Integer> st = new TreeSet<>();
// Populate the map for the initial array
for (int i = 0; i < N; i++) {
mp.put(arr.get(i), mp.getOrDefault(arr.get(i), 0) + 1);
}
// Add the elements to set which are not present in the array
for (int i = 0; i <= N; i++) {
if (!mp.containsKey(i))
st.add(i);
}
// Initialize a list to store MEX values after each query
List<Integer> mex = new ArrayList<>();
// Process each query
for (int i = 0; i < q; i++) {
int idx = queries.get(i).get(0);
int val = queries.get(i).get(1);
// Update the frequency of element which is being replaced
mp.put(arr.get(idx), mp.get(arr.get(idx)) - 1);
// If the frequency of the element which is being replaced becomes 0, add it to set
if (mp.get(arr.get(idx)) == 0) {
st.add(arr.get(idx));
}
arr.set(idx, val);
mp.put(val, mp.getOrDefault(val, 0) + 1);
// If the updated element is in the set, remove it
if (st.contains(arr.get(idx)))
st.remove(arr.get(idx));
// Calculate the MEX and add it to the result list
int ans = st.first();
mex.add(ans);
}
return mex;
}
// Driver Code
public static void main(String[] args) {
// Example array
List<Integer> arr = new ArrayList<>(Arrays.asList(1, 0, 2, 4, 7));
int N = arr.size();
// Example queries
List<List<Integer>> queries = new ArrayList<>(
Arrays.asList(
Arrays.asList(1, 3),
Arrays.asList(0, 0),
Arrays.asList(4, 1),
Arrays.asList(2, 10)
)
);
int q = queries.size();
// Call the 'mex' function to calculate MEX values after each query
List<Integer> ans = mex(arr, N, queries, q);
// Print the results
for (int i = 0; i < q; i++) {
System.out.println("MEX of the array after query " + (i + 1) + " : " + ans.get(i));
}
}
}
Python
def mex(arr, N, queries, q):
# Initialize a dictionary to store element frequencies
mp = {}
# Initialize a set to store non-present elements
st = set()
# Populate the dictionary for the initial array
for num in arr:
mp[num] = mp.get(num, 0) + 1
# Add the elements to set which are not present in the array.
for i in range(N + 1):
if i not in mp:
st.add(i)
mex = [] # Initialize a list to store MEX values after each query
# Process each query
for i in range(q):
idx, val = queries[i]
# Update the frequency of the element being replaced.
mp[arr[idx]] -= 1
# If the frequency of the element being replaced becomes 0, add it to the set.
if mp[arr[idx]] == 0:
st.add(arr[idx])
arr[idx] = val
# Update the frequency of the new element.
mp[val] = mp.get(val, 0) + 1
# If the updated element is in the set, remove it.
if arr[idx] in st:
st.remove(arr[idx])
# Calculate the MEX and add it to the result list
ans = min(st)
mex.append(ans)
return mex
# Example array
arr = [1, 0, 2, 4, 7]
N = len(arr)
# Example queries
queries = [
[1, 3],
[0, 0],
[4, 1],
[2, 10]
]
q = len(queries)
# Call the 'mex' function to calculate MEX values after each query
ans = mex(arr, N, queries, q)
# Print the results
for i in range(q):
print(f"MEX of the array after query {i + 1}: {ans[i]}")
C#
using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
// Function to calculate the MEX of an array after a series
// of queries
static List<int> Mex(List<int> arr, int N, List<List<int>> queries, int q)
{
// Initialize a dictionary to store element frequencies
Dictionary<int, int> mp = new Dictionary<int, int>();
// Initialize a HashSet to store non-present elements
HashSet<int> st = new HashSet<int>();
// Populate the dictionary for the initial array
foreach (int num in arr)
{
if (mp.ContainsKey(num))
mp[num]++;
else
mp[num] = 1;
}
// Add the elements to set which are not present in the array.
for (int i = 0; i <= N; i++)
{
if (!mp.ContainsKey(i))
st.Add(i);
}
// Initialize a list to store MEX values after each query
List<int> mex = new List<int>();
// Process each query
foreach (List<int> query in queries)
{
int idx = query[0];
int val = query[1];
// Update the frequency of element which is being replaced.
mp[arr[idx]]--;
// If the frequency of element which is being replaced becomes 0, add it to set.
if (mp[arr[idx]] == 0)
st.Add(arr[idx]);
arr[idx] = val;
if (mp.ContainsKey(val))
mp[val]++;
else
mp[val] = 1;
// If the updated element is in the set, remove it
if (st.Contains(val))
st.Remove(val);
// Calculate the MEX and add it to the result list
int ans = st.Min();
mex.Add(ans);
}
return mex;
}
// Driver Code
static void Main(string[] args)
{
// Example array
List<int> arr = new List<int> { 1, 0, 2, 4, 7 };
int N = arr.Count;
// Example queries
List<List<int>> queries = new List<List<int>>
{
new List<int> { 1, 3 },
new List<int> { 0, 0 },
new List<int> { 4, 1 },
new List<int> { 2, 10 }
};
int q = queries.Count;
// Call the 'Mex' function to calculate MEX values after each query
List<int> ans = Mex(arr, N, queries, q);
// Print the results
for (int i = 0; i < q; i++)
{
Console.WriteLine($"MEX of the array after query {i + 1} : {ans[i]}");
}
}
}
JavaScript
function calculateMex(arr, N, queries, q) {
// Initialize a dictionary to store element frequencies
let mp = new Map();
// Initialize a Set to store non-present elements
let st = new Set();
// Populate the dictionary for the initial array
arr.forEach((num) => {
mp.set(num, (mp.get(num) || 0) + 1);
});
// Add the elements to set which are not present in the array
for (let i = 0; i <= N; i++) {
if (!mp.has(i)) {
st.add(i);
}
}
// Initialize a list to store MEX values after each query
let mex = [];
// Process each query
for (let i = 0; i < q; i++) {
let idx = queries[i][0];
let val = queries[i][1];
// Update the frequency of element which is being replaced
mp.set(arr[idx], mp.get(arr[idx]) - 1);
// If the frequency of element which is being replaced becomes 0, add it to set
if (mp.get(arr[idx]) === 0) {
st.add(arr[idx]);
}
arr[idx] = val;
if (mp.has(val)) {
mp.set(val, mp.get(val) + 1);
} else {
mp.set(val, 1);
}
// If the updated element is in the set, remove it
if (st.has(val)) {
st.delete(val);
}
// Calculate the MEX and add it to the result list
let ans = Math.min(...Array.from(st));
mex.push(ans);
}
return mex;
}
// Example array
let arr = [1, 0, 2, 4, 7];
let N = arr.length;
// Example queries
let queries = [
[1, 3],
[0, 0],
[4, 1],
[2, 10]
];
let q = queries.length;
// Call the 'calculateMex' function to calculate MEX values after each query
let ans = calculateMex(arr, N, queries, q);
// Print the results
for (let i = 0; i < q; i++) {
console.log(`MEX of the array after query ${i + 1} : ${ans[i]}`);
}
OutputMEX of the array after query 1 : 0
MEX of the array after query 2 : 1
MEX of the array after query 3 : 5
MEX of the array after query 4 : 2Time Complexity: O(N + Q log N), O(N) for initialization, O(log N) for each query due to set operations.Auxiliary Space: O(N), for the frequency map and set.How to solve MEX related problems in Competitive Programming ?MEX Related tasks usually involves finding MEX of the array while updating its elements. Some of the common characteristics of MEX related tasks include:Array Updates - In general we are generally given queries in which we have either add, remove or update the values of array and the task involves finding the MEX after each such query.Data Structures- To optimally compute MEX after each query, set and maps are generally used because both provide fast lookup time for the elements (log n), also they keep elements sorted making it easier to find the minimum non-present element (MEX).Let us consider few problems involving MEX:Problem 1: Given an empty array arr[] and a integer m. You are given q queries. In ith query you add a element yi to the array. After each query you can perform the following operation any number of times: Choose an element arrj and set arrj to arrj +m or arrj -m. The task is maximize the value of MEX of array arr after each query. The problem can be solved in following way:Observation: We need to firstly observe that after applying the operation: arrj +m or arrj -m on an element arrj, its modulo with m still remains the same after the operation.Keep the track of Frequency: We keep track of frequency of remainders when divided by m, i.e., for each number [0,m-1] keep track of its frequency with each query. Let freq0 , freq1 ,......, freqm-1 be the frequency of remainders 0, 1, ..... m-1.Query Updates: During each query, we update the frequency of the remainder, by keeping the set sorted based on frequency and remainder. For example, if the query adds an element y, we calculate y % m to determine its remainder when divided by m and then update its frequency.MEX Calculation: In each query after updating the frequency of remainder we will find the minimum of {freq0 , freq1 ,......, freqm-1 }. If frqj is remainder with minimum frequency the maximum MEX will be equal to: j*frqj + j.For example:- Suppose m=5 and frequency of remainders 0, 1, 2, 3, 4 are 3, 4, 4, 2 ,5 respectively. The minimum frequency is of remainder 3 with frequency 2. Since frequency of remainder 3 is 2, elements 3 and 8 will be present in the array by performing the operations. So the MEX will be 13 (2*10+3) in this case.Problem 2: Given an array of n integers each integer lies in range [0,N]. The task is to make the array exactly {0, 1, 2,... , N-1} in almost 2*n operations. In one operation you can pick any element of the array and replace it with MEX of the array.The problem can be solved in following way:Observation: MEX of the array after each operation will lie between [0,N] and in the final array for each index i, arri = i. Let cnt be the number of indexes such that arri is not equal to i. Thus the cnt represents number of indexes for which we have to change the value of that index to its correct value.Perform the Operations: In each operation we will firstly find the MEX of the array. Now we have 2 cases:Case 1: When Mex of the array is between [0,N-1]: In this case we will simply put the MEX of the array in its correct index, i.e., if min_exc represents the MEX of the array then we will put min_exc in the index min_exc, this will decrease the value of cnt by 1.Case 2: When Mex of the array is N: In this case, we will put the MEX of the array in any of the index for which arri is not equal to i. The value of cnt will remain the same.Correctness: The above approach will convert array arr to {0,1,2, .... , N-1} in almost 2*N operations. The maximum value of cnt can be N, and the above approach decreases the value of cnt will by 1 in almost 2 operations because each time we encounter Case 2(MEX of the array is N), next time we perform the operation, we will get Case 1(MEX of the array is not N) since N was inserted in the array in last operation so MEX will not be N. Thus, we will Case 1 in which value of cnt will be decreased by 1. Hence, it takes almost 2*N operations to make the value of cnt 0.Practice Problems on MEX:Minimum operations to make all Array elements 0 by MEX replacement Minimum operations to make the MEX of the given set equal to x Find the Prefix-MEX Array for given Array Rearrange array elements to maximize the sum of MEX of all prefix arrays Maximum number of elements that can be removed such that MEX of the given array remains unchanged Maximum MEX from all subarrays of length K Minimum operations for same MEX Maximize MEX by adding or subtracting K from Array elements MEX of generated sequence of N+1 integers where ith integer is XOR of (i-1) and K Maximize sum of MEX values of each node in an N-ary Tree Find MEX of every subtree in given Tree Minimum size of the array with MEX as A and XOR of the array elements as B Rearrange Array to maximize sum of MEX of all Subarrays starting from first index | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming | https://www.geeksforgeeks.org/mex-minimum-excluded-in-competitive-programming/?ref=lbp | NLP | MEX (Minimum Excluded) in Competitive Programming | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0148914279, 0.0127436975, -0.0243609641, 0.0297978744, 0.0289267674, 0.0410021171, -0.0101153571, 0.00949206483, 0.0038749252, 0.0164459031, -0.00168777024, -0.0249016508, 0.017542297, -0.0208464973, -0.0122030107, 0.0134571046, -0.00899643451, 0.0153044527, -0.0270193424, -0.0234147608, -0.0422336832, -0.00767100044, -0.0219729282, 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09 Nov, 2023 | Minimum operations to make the MEX of the given set equal to x
09 Nov, 2023
Given a set of n integers, perform minimum number of operations (you can insert/delete elements into/from the set) to make the MEX of the set equal to x (that is given).
Note:- The MEX of a set of integers is the minimum non-negative integer that doesn’t exist in it. For example, the MEX of the set {0, 2, 4} is 1 and the MEX of the set {1, 2, 3} is 0.
Examples :
Input : n = 5, x = 3 0 4 5 6 7Output : 2The MEX of the set {0, 4, 5, 6, 7} is 1 which is not equal to 3. So, we should add 1 and 2 to theset. After adding 1 and 2, the set becomes {0, 1, 2, 4, 5, 6, 7} and 3 is the minimumnon-negative integer that doesn't exist in it.So, the MEX of this set is 3 which is equal tox i.e. 3. So, the output of this example is 2 as we inserted 1 and 2 in the set.Input : n = 1, x = 0 1Output : 0In this example, the MEX of the given set {1}is already 0. So, we do not need to perform any operation. So, the output is 0.
Approach: The approach is to see that in the final set all the elements less than x should exist, x shouldn’t exist and any element greater than x doesn’t matter. So, we will count the number of elements less than x that don’t exist in the initial set and add this to the answer. If x exists we will add 1 to the answer because x should be removed.
Below is the implementation of above approach:
C++
// CPP program to perform minimal number
// of operations to make the MEX of the
// set equal to the given number x.
#include <bits/stdc++.h>
using namespace std;
// function to find minimum number of
// operations required
int minOpeartions(int arr[], int n, int x)
{
int k = x, i = 0;
while (n--) {
// if the element is less than x.
if (arr[n] < x)
k--;
// if the element equals to x.
if (arr[n] == x)
k++;
}
return k;
}
// driver function
int main()
{
int arr[] = { 0, 4, 5, 6, 7 };
int n = sizeof(arr) / sizeof(arr[0]);
int x = 3;
// output
cout << minOpeartions(arr, n, x) << endl;
}
Java
// Java program to perform minimal number
// of operations to make the MEX of the
// set equal to the given number x.
import java.io.*;
class GFG {
// function to find minimum number of
// operations required
static int minOpeartions(int arr[], int n, int x)
{
int k = x, i = 0;
n--;
while (n > -1) {
// if the element is less than x.
if (arr[n] < x)
k--;
// if the element equals to x.
if (arr[n] == x)
k++;
n--;
}
return k;
}
// driver function
public static void main(String args[])
{
int arr[] = { 0, 4, 5, 6, 7 };
int n = arr.length;
int x = 3;
// output
System.out.println(minOpeartions(arr, n, x));
}
}
/* This code is contributed by Nikita Tiwari.*/
Python
# Python 3 program to perform minimal number
# of operations to make the MEX of the
# set equal to the given number x.
# function to find minimum number of
# operations required
def minOpeartions(arr, n, x) :
k = x
i = 0
n = n-1
while (n>-1) :
# if the element is less than x.
if (arr[n] < x) :
k = k - 1
# if the element equals to x.
if (arr[n] == x) :
k = k + 1
n = n - 1
return k
# driver function
arr = [ 0, 4, 5, 6, 7 ]
n = len(arr)
x = 3
# output
print( minOpeartions(arr, n, x))
# This code is contributed by Nikita Tiwari.
C#
// C# program to perform minimal number
// of operations to make the MEX of the
// set equal to the given number x.
using System;
class GFG {
// function to find minimum number
// of operations required
static int minOpeartions(int[] arr,
int n, int x)
{
int k = x;
n--;
while (n > -1) {
// if the element is less
// than x.
if (arr[n] < x)
k--;
// if the element equals
// to x.
if (arr[n] == x)
k++;
n--;
}
return k;
}
// driver function
public static void Main()
{
int[] arr = { 0, 4, 5, 6, 7 };
int n = arr.Length;
int x = 3;
// output
Console.WriteLine(
minOpeartions(arr, n, x));
}
}
// This code is contributed by vt_m.
Javascript
<script>
// Javascript program to perform minimal number
// of operations to make the MEX of the
// set equal to the given number x.
// function to find minimum number of
// operations required
function minOpeartions(arr, n, x)
{
let k = x, i = 0;
while (n-- > 0) {
// if the element is less than x.
if (arr[n] < x)
k--;
// if the element equals to x.
if (arr[n] == x)
k++;
}
return k;
}
let arr = [ 0, 4, 5, 6, 7 ];
let n = arr.length;
let x = 3;
// output
document.write(minOpeartions(arr, n, x));
</script>
PHP
<?php
// PHP program to perform minimal
// number of operations to make
// the MEX of the set equal to
// the given number x.
// function to find minimum number
// of operations required
function minOpeartions( $arr, $n, $x)
{
$k = $x; $i = 0;
while ($n--)
{
// if the element is
// less than x.
if ($arr[$n] < $x)
$k--;
// if the element equals to x.
if ($arr[$n] == $x)
$k++;
}
return $k;
}
// Driver Code
$arr = array(0, 4, 5, 6, 7);
$n = count($arr);
$x = 3;
echo minOpeartions($arr, $n, $x) ;
// This code is contributed by anuj_67.
?>
Output
2
Time Complexity: O(n)Auxiliary Space: O(1) | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Minimum operations to make the MEX of the given set equal to x | https://www.geeksforgeeks.org/minimum-operations-to-make-the-mex-of-the-given-set-equal-to-x/?ref=lbp | NLP | Minimum operations to make the MEX of the given set equal to x | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Minimum operations to make the MEX of the given set equal to x, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0112342127, 0.0156192658, -0.00926027726, 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31 Oct, 2023 | Rearrange Array to maximize sum of MEX of all Subarrays starting from first index
31 Oct, 2023
Given an array arr[] of N elements ranging from 0 to N-1(both included), the task is to rearrange the array such that the sum of all the MEX from every subarray starting from index 0 is maximum. Duplicates can be present in the array.
MEX of an array is the first non-negative element that is missing from the array.
Examples:
Input: N = 3, arr[] = {2, 1, 0}Output: 6Explanation: Initially for subarray {2} the missing element is 0.For {2, 1} the missing element is 0, and for {2, 1, 0} the missing element is 3. In this way the answer is 0 + 0 + 3 = 3.But if the array is rearranged like {0, 1, 2}, the answer will be 1 + 2 + 3 = 6.
Input: N = 5, arr[] = {0, 0, 0, 0, 0}Output: 5
Approach:
The idea is to put the smaller elements in the beginning of new array to get highest possible missing whole numbers for each subarray, but if we have duplicates then the duplicates would be inserted in the end of the new array.
Follow the steps to solve the problems:
Sort the array.
Initialize 2 variables cur to store the current smallest missing whole number and count to store the number of times the smallest whole number would be smallest for the next subarrays.
If the current element is greater than cur, then for all the next subarrays the smallest whole number would be cur, as the array is sorted. So add the number of remaining subarrays to count and break the loop.
Else if we find the duplicates then increase the count variable to add the value in the end.
Else, for each index update cur and add the values into an ans variable that will contain the final answer.
In the end, if cur is not 0, means there are subarrays that have cur as the smallest whole number and that are not added to ans, so add cur * count to the ans and return it.
Illustration:
Consider N = 6, arr[] = {4, 2, 0, 4, 1, 0}
Initialize, ans = 0, cur = 0, count = 0
Sort the array, so arr[] = {0, 0, 1, 2, 4, 4}
For index 0: => arr[i] = cur, => thus cur would be cur + 1 = 1 => ans would be ans + cur = 0 + 1 = 1
For index 1: => arr[i] = cur – 1 => Means it is a duplicate => Increase the count variable, count = 0 + 1 = 1
For index 2: => arr[i] = cur => cur would be cur + 1 = 2 => ans would be ans + cur = 1 + 2 = 3
For index 3: => arr[i] = cur, => Thus cur would be cur + 1 = 3 => ans would be ans + cur = 3 + 3 = 6
For index 4: => arr[i] > cur => cur would be the same for all the remaining subarrays. => Thus, count = count + 6 – 4 = 1 + 2(remaining subarrays) = 3 and break the loop.
In the end add cur * count to ans, thus ans = 6 + 3 * 3 = 15
Below is the implementation of this approach:
C++
// C++ code to implement above approach
#include <bits/stdc++.h>
using namespace std;
// Function to get maximum sum
int maxSum(vector<int> arr)
{
// Final sum
int ans = 0;
// Sorting the array to get minimum at first
sort(arr.begin(), arr.end());
// Here temp is for checking the number
// which is not present Cou is for
// how many elements will be in the end
int temp = 0, cou = 0;
// Traversing the array
for (int i = 0; i < arr.size(); i++) {
if (arr[i] == temp) {
temp++;
ans += temp;
}
// If found duplicates
else if (temp - 1 == arr[i]) {
cou++;
}
// If found any missing element
else {
if (temp < arr[i]) {
cou += arr.size() - i;
break;
}
}
}
// Adding the missing element for
// all the element which are duplicates or
// the elements which left by break statement.
if (cou != 0)
ans = ans + (cou * temp);
return ans;
}
// Driver Code
int main()
{
int N = 3;
vector<int> arr = { 2, 1, 0 };
// Function call
cout << maxSum(arr) << endl;
return 0;
}
Java
// JAVA code to implement the approach
import java.util.*;
class GFG
{
// Function to get maximum sum
static int maxSum(int[] arr)
{
// Final sum
int ans = 0;
// Sorting the array to get minimum at first
Arrays.sort(arr);
// Here temp is for checking the number
// which is not present Cou is for
// how many elements will be in the end
int temp = 0, cou = 0;
// Traversing the array
for (int i = 0; i < arr.length; i++) {
if (arr[i] == temp) {
temp++;
ans += temp;
}
// If found duplicates
else if (temp - 1 == arr[i]) {
cou++;
}
// If found any missing element
else {
if (temp < arr[i]) {
cou += arr.length - i;
break;
}
}
}
// Adding the missing element for
// all the element which are duplicates or
// the elements which left by break statement.
if (cou != 0)
ans = ans + (cou * temp);
return ans;
}
// Driver Code
public static void main(String[] args)
{
int N = 3;
int[] arr = { 2, 1, 0 };
// Function call
System.out.println(maxSum(arr));
}
}
// This code is contributed by sanjoy_62.
Python3
# python3 implementation of above approach
# Function to get maximum sum
def maxSum(arr) :
# Final sum
ans = 0
# Sorting the array to get minimum at first
arr.sort()
# Here temp is for checking the number
# which is not present Cou is for
# how many elements will be in the end
temp = 0
cou = 0
# Traversing the array
for i in range(0, len(arr)) :
if (arr[i] == temp) :
temp += 1
ans += temp
# If found duplicates
elif (temp - 1 == arr[i]) :
cou += 1
# If found any missing element
else :
if (temp < arr[i]) :
cou += len(arr) - i
break
# Adding the missing element for
# all the element which are duplicates or
# the elements which left by break statement.
if (cou != 0) :
ans = ans + (cou * temp)
return ans
# Driver Code
if __name__ == "__main__":
N = 3
arr = [ 2, 1, 0 ]
# Function call
print(maxSum(arr))
C#
// C# code to implement the approach
using System;
class GFG
{
// Function to get maximum sum
static int maxSum(int[] arr)
{
// Final sum
int ans = 0;
// Sorting the array to get minimum at first
Array.Sort(arr);
// Here temp is for checking the number
// which is not present Cou is for
// how many elements will be in the end
int temp = 0, cou = 0;
// Traversing the array
for (int i = 0; i < arr.Length; i++) {
if (arr[i] == temp) {
temp++;
ans += temp;
}
// If found duplicates
else if (temp - 1 == arr[i]) {
cou++;
}
// If found any missing element
else {
if (temp < arr[i]) {
cou += arr.Length - i;
break;
}
}
}
// Adding the missing element for
// all the element which are duplicates or
// the elements which left by break statement.
if (cou != 0)
ans = ans + (cou * temp);
return ans;
}
// Driver Code
public static void Main(string[] args)
{
int[] arr = { 2, 1, 0 };
// Function call
Console.WriteLine(maxSum(arr));
}
}
// This code is contributed by AnkThon
Javascript
<script>
// Javascript code to implement above approach
// Function to get maximum sum
function maxSum(arr)
{
// Final sum
let ans = 0;
// Sorting the array to get minimum at first
arr.sort(function(a, b) {
return a - b;
});
// Here temp is for checking the number
// which is not present Cou is for
// how many elements will be in the end
let temp = 0, cou = 0;
// Traversing the array
for (let i = 0; i < arr.length; i++) {
if (arr[i] == temp) {
temp++;
ans += temp;
}
// If found duplicates
else if (temp - 1 == arr[i]) {
cou++;
}
// If found any missing element
else {
if (temp < arr[i]) {
cou += arr.length - i;
break;
}
}
}
// Adding the missing element for
// all the element which are duplicates or
// the elements which left by break statement.
if (cou != 0)
ans = ans + (cou * temp);
return ans;
}
// Driver Code
let N = 3;
let arr = [ 2, 1, 0 ];
// Function call
document.write(maxSum(arr));
// This code is contributed by satwik4409.
</script>
Output
6
Time Complexity: O(N * log N)Auxiliary Space: O(1) | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index | https://www.geeksforgeeks.org/rearrange-array-to-maximize-sum-of-mex-of-all-subarrays-starting-from-first-index/ | NLP | Rearrange Array to maximize sum of MEX of all Subarrays starting from first index | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion 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16 Nov, 2022 | Minimize moves to segregate even and odd by swapping adjacent elements
16 Nov, 2022
Given an array arr[] of size N, the task is to find the minimum moves to segregate even and odd numbers by swapping two adjacent elements at a time.
Example:
Input: N = 7, arr = {3, 5, 2, 7, 9, 11, 12}Output: 3Explanation: Swap arr[2] and arr[3] to get arr = {3, 5, 7, 2, 9, 11, 12}.Move 2: Swap arr[3] and arr[4] to get arr = {3, 5, 7, 9, 2, 11, 12}.Move 3: Swap arr[4] and arr[5] to get arr = {3, 5, 7, 9, 11, 2, 12}.All odds are at the beginning from arr[0 . . . 4] and evens at the end from arr[5 . . . 6].
Input: N = 5, arr = {3, 5, 7, 2, 4}Output: 0
Approach:
This problem can be broken down into two sub-problems:
Shifting all odd to the front or
shifting all odd to the end (minimum of which will give us the optimal answer).
So this problem can be solved using the greedy approach, where initially the number of moves to shift odd to the beginning are counted and then the number of moves to shift odd to the end are counted and minimum of both is returned as answer.
To shift any number by consecutive swapping, moves required is abs(j – i) where j is the index of the last number of the opposite parity and i is the index of the current number.
Follow the given steps to solve the problem:
Traverse the array arr from 0 to n-1 (say i).
If arr[i] is odd then add i-j in startMoves and increment j.
Reinitialize j to n-1.
Traverse the array arr from n-1 to 0 (say i).
If arr[i] is odd then add j-i to endMoves and decrement j.
Return minimum of startMoves and endMoves as the final answer.
Below is the implementation of this approach:
C++14
// C++ code to implement the approach
#include <bits/stdc++.h>
using namespace std;
// Function to return minimum number of swaps
// required to segregate evens and odds
int minMovesToSegregate(int* arr, int& n)
{
int startMoves = 0, endMoves = 0, j = 0;
for (int i = 0; i < n; i++) {
if (arr[i] & 1)
startMoves += i - (j++);
}
j = n - 1;
for (int i = n - 1; i >= 0; i--) {
if (arr[i] & 1)
endMoves += (j--) - i;
}
return min(startMoves, endMoves);
}
// Driver code
int main()
{
int arr[] = { 3, 5, 2, 7, 9, 11, 12 };
int N = sizeof(arr) / sizeof(arr[0]);
// Function call
cout << minMovesToSegregate(arr, N);
return 0;
}
Java
/*package whatever //do not write package name here */
import java.io.*;
class GFG
{
// Java code to implement the approach
// Function to return minimum number of swaps
// required to segregate evens and odds
static int minMovesToSegregate(int arr[], int n)
{
int startMoves = 0, endMoves = 0, j = 0;
for (int i = 0; i < n; i++) {
if (arr[i]%2==1)
startMoves += i - (j++);
}
j = n - 1;
for (int i = n - 1; i >= 0; i--) {
if (arr[i]%2==1)
endMoves += (j--) - i;
}
return Math.min(startMoves, endMoves);
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 3, 5, 2, 7, 9, 11, 12 };
int N = arr.length;
// Function call
System.out.println(minMovesToSegregate(arr, N));
}
}
// This code is contributed by satwik4409.
Python3
# Python code for the above approach
# Function to return minimum number of swaps
# required to segregate evens and odds
def minMovesToSegregate(arr, n):
startMoves = 0
endMoves = 0
j = 0
for i in range(0, n, 1):
if (arr[i] % 2 == 1):
startMoves += i - j
j += 1
j = n-1
for i in range(n-1, -1, -1):
if (arr[i] % 2 == 1):
endMoves = endMoves + j-i
j -= 1
return min(startMoves, endMoves)
arr = [3, 5, 2, 7, 9, 11, 12]
N = len(arr)
# Function call
print(minMovesToSegregate(arr, N))
# This code is contributed by lokeshmvs21.
C#
// C# code to implement the approach
using System;
public class GFG
{
// Function to return minimum number of swaps
// required to segregate evens and odds
static int minMovesToSegregate(int []arr, int n)
{
int startMoves = 0, endMoves = 0, j = 0;
for (int i = 0; i < n; i++) {
if (arr[i] % 2 == 1)
startMoves += i - (j++);
}
j = n - 1;
for (int i = n - 1; i >= 0; i--) {
if (arr[i] % 2 == 1)
endMoves += (j--) - i;
}
return Math.Min(startMoves, endMoves);
}
// Driver code
public static void Main(string[] args)
{
int []arr = { 3, 5, 2, 7, 9, 11, 12 };
int N = arr.Length;
// Function call
Console.WriteLine(minMovesToSegregate(arr, N));
}
}
// This code is contributed by AnkThon
Javascript
<script>
// Javascript code to implement the approach
// Function to return minimum number of swaps
// required to segregate evens and odds
function minMovesToSegregate(arr, n)
{
let startMoves = 0, endMoves = 0, j = 0;
for (let i = 0; i < n; i++) {
if (arr[i] & 1)
startMoves += i - (j++);
}
j = n - 1;
for (let i = n - 1; i >= 0; i--) {
if (arr[i] & 1)
endMoves += (j--) - i;
}
return Math.min(startMoves, endMoves);
}
// Driver code
let arr = [ 3, 5, 2, 7, 9, 11, 12 ];
let N = arr.length;
// Function call
document.write(minMovesToSegregate(arr, N));
// This code is contributed by hrithikgarg03188.
</script>
Output
3
Time Complexity: O(N)Auxiliary Space: O(1) | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements | https://www.geeksforgeeks.org/minimize-moves-to-segregate-even-and-odd-by-swapping-adjacent-elements/?ref=next_article | NLP | Minimize moves to segregate even and odd by swapping adjacent elements | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Swift Programming Language, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0239378829, -0.0128538907, -0.0116002122, 0.00855451077, -0.00739670219, 0.0242771134, 0.00990405865, 0.0215190202, -0.0365484096, 0.0346310213, -0.0293655712, -0.0131267495, 0.024218116, 0.0146090398, -0.00705747167, -0.0288641, -0.0255307909, 0.0101105468, -0.00851763785, -0.0346900187, 0.0198228676, -0.027846409, -0.0384068042, 0.0146680372, -0.0386427902, 0.0161650758, 0.0236871466, 0.0232151728, -0.0283626299, 0.0197048746, 0.0255307909, 0.00298486068, 0.00692104222, -0.0252358075, -0.0193656441, -0.000590427197, -0.00667399354, 0.0280234, -0.00667399354, 0.0127801448, -0.0149408961, -0.0167402942, -0.0205603242, -0.00266591017, -0.00260138256, 0.0344245322, 0.016769791, -0.00482297456, 0.00246679643, 0.0128465155, 0.0098524373, 0.0194246396, 0.0173302591, 0.0300587825, 0.00289636571, 0.0160175841, 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15 Apr, 2021 | Minimum elements to be removed such that sum of adjacent elements is always even
15 Apr, 2021
Given an array of N integers. The task is to eliminate the minimum number of elements such that in the resulting array the sum of any two adjacent values is even.
Examples:
Input : arr[] = {1, 2, 3}
Output : 1
Remove 2 from the array.
Input : arr[] = {1, 3, 5, 4, 2}
Output : 2
Remove 4 and 2.
Approach: The sum of 2 numbers is even if either both of them is odd or both of them is even. This means for every pair of consecutive numbers that have the different parity, eliminate one of them.So, to make the adjacent elements sum even, either all elements should be odd or even. So the following greedy algorithm works:
Go through all the elements in order.
Count the odd and even elements in the array.
Return the minimum count.
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find minimum number of eliminations
// such that sum of all adjacent elements is even
int min_elimination(int n, int arr[])
{
int countOdd = 0;
// Stores the new value
for (int i = 0; i < n; i++)
// Count odd numbers
if (arr[i] % 2)
countOdd++;
// Return the minimum of even and
// odd count
return min(countOdd, n - countOdd);
}
// Driver code
int main()
{
int arr[] = { 1, 2, 3, 7, 9 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << min_elimination(n, arr);
return 0;
}
Java
// Java implementation of the above approach
class GFG
{
// Function to find minimum number of
// eliminations such that sum of all
// adjacent elements is even
static int min_elimination(int n, int arr[])
{
int countOdd = 0;
// Stores the new value
for (int i = 0; i < n; i++)
// Count odd numbers
if (arr[i] % 2 == 1)
countOdd++;
// Return the minimum of even
// and odd count
return Math.min(countOdd, n - countOdd);
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 1, 2, 3, 7, 9 };
int n = arr.length;
System.out.println(min_elimination(n, arr));
}
}
// This code is contributed by Code_Mech
Python3
# Python 3 implementation of the
# above approach
# Function to find minimum number of
# eliminations such that sum of all
# adjacent elements is even
def min_elimination(n, arr):
countOdd = 0
# Stores the new value
for i in range(n):
# Count odd numbers
if (arr[i] % 2):
countOdd += 1
# Return the minimum of even and
# odd count
return min(countOdd, n - countOdd)
# Driver code
if __name__ == '__main__':
arr = [1, 2, 3, 7, 9]
n = len(arr)
print(min_elimination(n, arr))
# This code is contributed by
# Surendra_Gangwar
C#
// C# implementation of the above approach
using System;
class GFG
{
// Function to find minimum number of
// eliminations such that sum of all
// adjacent elements is even
static int min_elimination(int n, int[] arr)
{
int countOdd = 0;
// Stores the new value
for (int i = 0; i < n; i++)
// Count odd numbers
if (arr[i] % 2 == 1)
countOdd++;
// Return the minimum of even
// and odd count
return Math.Min(countOdd, n - countOdd);
}
// Driver code
public static void Main()
{
int[] arr = { 1, 2, 3, 7, 9 };
int n = arr.Length;
Console.WriteLine(min_elimination(n, arr));
}
}
// This code is contributed by Code_Mech
PHP
<?php
// PHP implementation of the above approach
// Function to find minimum number of
// eliminations such that sum of all
// adjacent elements is even
function min_elimination($n, $arr)
{
$countOdd = 0;
// Stores the new value
for ($i = 0; $i < $n; $i++)
// Count odd numbers
if ($arr[$i] % 2 == 1)
$countOdd++;
// Return the minimum of even
// and odd count
return min($countOdd, $n - $countOdd);
}
// Driver code
$arr = array(1, 2, 3, 7, 9);
$n = sizeof($arr);
echo(min_elimination($n, $arr));
// This code is contributed by Code_Mech
?>
Javascript
<script>
// Function to find minimum number of eliminations
// such that sum of all adjacent elements is even
function min_elimination(n, arr)
{
let countOdd = 0;
// Stores the new value
for (let i = 0; i < n; i++)
// Count odd numbers
if (arr[i] % 2)
countOdd++;
// Return the minimum of even and
// odd count
return Math.min(countOdd, n - countOdd);
}
// Driver code
let arr= [1, 2, 3, 7, 9];
let n = arr.length;
document.write(min_elimination(n, arr));
</script>
Output:
1
Time Complexity: O(N )
Auxiliary Space: O(1) | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even | https://www.geeksforgeeks.org/minimum-elements-to-be-removed-such-that-sum-of-adjacent-elements-is-always-even/?ref=ml_lbp | NLP | Minimum elements to be removed such that sum of adjacent elements is always even | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.012085353, -0.000344894506, -0.012484869, -5.44540926e-05, -0.0048798, 0.0390098654, 0.0302490536, 0.0151102589, -0.0146037294, 0.0064564608, -0.0388671793, -0.0223158114, 0.0207748227, -0.000478438, -0.0295927059, -0.0135835372, -0.00783336349, -0.0040236949, 0.00635658205, -0.0498824, -0.0103945453, 0.00148213236, -0.0109224766, 0.00186559616, -0.0123921242, 0.0348149501, 0.0262253601, 0.0144967167, -0.0454591922, 0.022743864, 0.000309669354, 0.00445531448, 0.0250981543, -0.00868946873, 0.00174788164, 0.00582151627, 0.0160947796, 0.0378969274, 0.00658844365, 0.0187487062, 0.00311765, -0.00367411855, -0.0311336964, -0.00684884237, 0.00758366613, 0.0224299598, 0.0246272963, 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03 Jun, 2021 | Maximum sum such that exactly half of the elements are selected and no two adjacent
03 Jun, 2021
Given an array A containing N integers. Find the maximum sum possible such that exact floor(N/2) elements are selected and no two selected elements are adjacent to each other. (if N = 5, then exactly 2 elements should be selected as floor(5/2) = 2) For a simpler version of this problem check out this.
Examples:
Input: A = [1, 2, 3, 4, 5, 6] Output: 12 Explanation: Select 2, 4 and 6 making the sum 12.
Input : A = [-1000, -100, -10, 0, 10] Output : 0 Explanation: Select -10 and 10, making the sum 0.
Approach:
We will use the concept of dynamic programming. The following is how the dp states are defined:
dp[i][j] = maximum sum till index i such that j elements are selected
Since no two adjacent elements can be selected :
dp[i][j] = max(a[i] + dp[i-2][j-1], dp[i-1][j])
Below is the implementation of the above approach.
C++
// C++ program to find maximum sum possible
// such that exactly floor(N/2) elements
// are selected and no two selected
// elements are adjacent to each other
#include <bits/stdc++.h>
using namespace std;
// Function return the maximum sum
// possible under given condition
int MaximumSum(int a[], int n)
{
int dp[n + 1][n + 1];
// Intitialising the dp table
for (int i = 0; i < n + 1; i++)
{
for (int j = 0; j < n + 1; j++)
dp[i][j] = INT_MIN;
}
// Base case
for (int i = 0; i < n + 1; i++)
dp[i][0] = 0;
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= i; j++)
{
int val = INT_MIN;
// Condition to select the current
// element
if ((i - 2 >= 0
&& dp[i - 2][j - 1] != INT_MIN)
|| i - 2 < 0)
{
val = a[i - 1] +
(i - 2 >= 0 ?
dp[i - 2][j - 1] : 0);
}
// Condition to not select the
// current element if possible
if (i - 1 >= j)
{
val = max(val, dp[i - 1][j]);
}
dp[i][j] = val;
}
}
return dp[n][n / 2];
}
//Driver code
int main()
{
int A[] = {1, 2, 3, 4, 5, 6};
int N = sizeof(A) / sizeof(A[0]);
cout << MaximumSum(A, N);
return 0;
}
Java
// Java program to find maximum sum possible
// such that exactly Math.floor(N/2) elements
// are selected and no two selected
// elements are adjacent to each other
class GFG{
// Function return the maximum sum
// possible under given condition
static int MaximumSum(int a[], int n)
{
int [][]dp = new int[n + 1][n + 1];
// Intitialising the dp table
for(int i = 0; i < n + 1; i++)
{
for(int j = 0; j < n + 1; j++)
dp[i][j] = Integer.MIN_VALUE;
}
// Base case
for(int i = 0; i < n + 1; i++)
dp[i][0] = 0;
for(int i = 1; i <= n; i++)
{
for(int j = 1; j <= i; j++)
{
int val = Integer.MIN_VALUE;
// Condition to select the current
// element
if ((i - 2 >= 0 &&
dp[i - 2][j - 1] != Integer.MIN_VALUE) ||
i - 2 < 0)
{
val = a[i - 1] + (i - 2 >= 0 ?
dp[i - 2][j - 1] : 0);
}
// Condition to not select the
// current element if possible
if (i - 1 >= j)
{
val = Math.max(val, dp[i - 1][j]);
}
dp[i][j] = val;
}
}
return dp[n][n / 2];
}
// Driver code
public static void main(String[] args)
{
int A[] = { 1, 2, 3, 4, 5, 6 };
int N = A.length;
System.out.print(MaximumSum(A, N));
}
}
// This code is contributed by Rajput-Ji
Python3
# Python3 program to find maximum sum possible
# such that exactly floor(N/2) elements
# are selected and no two selected
# elements are adjacent to each other
import sys
# Function return the maximum sum
# possible under given condition
def MaximumSum(a,n):
dp = [[0 for i in range(n+1)] for j in range(n+1)]
# Intitialising the dp table
for i in range(n + 1):
for j in range(n + 1):
dp[i][j] = -sys.maxsize-1
# Base case
for i in range(n+1):
dp[i][0] = 0
for i in range(1,n+1,1):
for j in range(1,i+1,1):
val = -sys.maxsize-1
# Condition to select the current
# element
if ((i - 2 >= 0 and dp[i - 2][j - 1] != -sys.maxsize-1) or i - 2 < 0):
if (i - 2 >= 0):
val = a[i - 1] + dp[i - 2][j - 1]
else:
val = a[i - 1]
# Condition to not select the
# current element if possible
if (i - 1 >= j):
val = max(val, dp[i - 1][j])
dp[i][j] = val
return dp[n][n // 2]
#Driver code
if __name__ == '__main__':
A = [1, 2, 3, 4, 5, 6]
N = len(A)
print(MaximumSum(A,N))
# This code is contributed by Bhupendra_Singh
C#
// C# program to find maximum sum possible
// such that exactly Math.floor(N/2) elements
// are selected and no two selected
// elements are adjacent to each other
using System;
class GFG{
// Function return the maximum sum
// possible under given condition
static int MaximumSum(int []a, int n)
{
int [,]dp = new int[n + 1, n + 1];
// Intitialising the dp table
for(int i = 0; i < n + 1; i++)
{
for(int j = 0; j < n + 1; j++)
dp[i, j] = Int32.MinValue;
}
// Base case
for(int i = 0; i < n + 1; i++)
dp[i, 0] = 0;
for(int i = 1; i <= n; i++)
{
for(int j = 1; j <= i; j++)
{
int val = Int32.MinValue;
// Condition to select the current
// element
if ((i - 2 >= 0 &&
dp[i - 2, j - 1] != Int32.MinValue) ||
i - 2 < 0)
{
val = a[i - 1] + (i - 2 >= 0 ?
dp[i - 2, j - 1] : 0);
}
// Condition to not select the
// current element if possible
if (i - 1 >= j)
{
val = Math.Max(val, dp[i - 1, j]);
}
dp[i, j] = val;
}
}
return dp[n, n / 2];
}
// Driver code
public static void Main()
{
int []A = { 1, 2, 3, 4, 5, 6 };
int N = A.Length;
Console.Write(MaximumSum(A, N));
}
}
// This code is contributed by Nidhi_biet
Javascript
<script>
// JavaScript program to find maximum sum possible
// such that exactly Math.floor(N/2) elements
// are selected and no two selected
// elements are adjacent to each other
// Function return the maximum sum
// possible under given condition
function MaximumSum(a,n)
{
let dp = [];
for(let i=0;i<n+1;i++) dp.push(Array(n+1));
// Intitialising the dp table
for(let i = 0; i < n + 1; i++)
{
for(let j = 0; j < n + 1; j++)
dp[i][j] = -10000;
}
// Base case
for(let i = 0; i < n + 1; i++)
dp[i][0] = 0;
for(let i = 1; i <= n; i++)
{
for(let j = 1; j <= i; j++)
{
let val = -10000;
// Condition to select the current
// element
if ((i - 2 >= 0 &&
dp[i - 2, j - 1] != -10000) ||
i - 2 < 0)
{
val = a[i - 1] + (i - 2 >= 0 ?
dp[i - 2][j - 1] : 0);
}
// Condition to not select the
// current element if possible
if (i - 1 >= j)
{
val = Math.max(val, dp[i - 1][j]);
}
dp[i][j] = val;
}
}
return dp[n][n / 2]
}
// Driver code
let A = [1, 2, 3, 4, 5, 6];
let N = A.length;
document.write(MaximumSum(A, N));
// This code is contributed by Nidhi_biet
</script>
Output:
12
Time Complexity : O(N2)
Efficient Approach
We will use dynamic programming but with slightly modified states. Storing both the index and is number of elements taken till now are futile since we always need to take exact floor(i/2) elements, so at i’th position for the dp storage we will assume floor(i/2) elements in the subset till now.
The following is the dp table states:
dp[i][1] = maximum sum till i’th index, picking element a[i], with floor(i/2) elements, none adjacent to each other. dp[i][0] = maximum sum till i’th index, not picking element a[i], with floor(i/2) elements, none adjacent to each other.
We have two cases :
When i is odd : If we have to pick a[i], then we can’t pick a[i-1], so the only options left are (i – 2)th and (i – 3) rd state (because floor((i – 2)/2) = floor((i – 3)/2) = floor(i/2) – 1, and since we pick a[i], total picked elements will be floor(i/2) ). If we don’t pick a[i], then a sum will be formed by taking a[i-1] and using states i – 1, i – 2 and i – 3 or a[i – 2] using state i – 3 as these will only give the total of floor(i/2).
dp[i][1] = arr[i] + max({dp[i – 3][1], dp[i – 3][0], dp[i – 2][1], dp[i – 2][0]}) dp[i][0] = max({arr[i – 1] + dp[i – 2][0], arr[i – 1] + dp[i – 3][1], arr[i – 1] + dp[i – 3][0], arr[i – 2] + dp[i – 3][0]})
When i is even : If we pick a[i], then using states i – 1 and i – 2, else picking a[i – 1] and using state i – 2.
dp[i][1] = arr[i] + max({dp[i – 2][1], dp[i – 2][0], dp[i – 1][0]}) dp[i][0] = arr[i – 1] + dp[i – 2][0]
Below is the implementation of the above approach.
C++
// C++ program to find maximum sum possible
// such that exactly floor(N/2) elements
// are selected and no two selected
// elements are adjacent to each other
#include <bits/stdc++.h>
using namespace std;
// Function return the maximum sum
// possible under given condition
int MaximumSum(int a[], int n)
{
int dp[n + 1][2];
// Intitialising the dp table
memset(dp, 0, sizeof(dp));
// Base case
dp[2][1] = a[1];
dp[2][0] = a[0];
for (int i = 3; i < n + 1; i++) {
// When i is odd
if (i & 1) {
int temp = max({ dp[i - 3][1],
dp[i - 3][0],
dp[i - 2][1],
dp[i - 2][0] });
dp[i][1] = a[i - 1] + temp;
dp[i][0] = max({ a[i - 2] + dp[i - 2][0],
a[i - 2] + dp[i - 3][1],
a[i - 2] + dp[i - 3][0],
a[i - 3] + dp[i - 3][0] });
}
// When i is even
else {
dp[i][1] = a[i - 1] + max({ dp[i - 2][1],
dp[i - 2][0],
dp[i - 1][0] });
dp[i][0] = a[i - 2] + dp[i - 2][0];
}
}
// Maximum of if we pick last element or not
return max(dp[n][1], dp[n][0]);
}
// Driver code
int main()
{
int A[] = {1, 2, 3, 4, 5, 6};
int N = sizeof(A) / sizeof(A[0]);
cout << MaximumSum(A, N);
return 0;
}
Java
// Java program to find maximum sum possible
// such that exactly Math.floor(N/2) elements
// are selected and no two selected
// elements are adjacent to each other
import java.util.*;
class GFG{
// Function return the maximum sum
// possible under given condition
static int MaximumSum(int a[], int n)
{
int [][]dp = new int[n + 1][2];
// Base case
dp[2][1] = a[1];
dp[2][0] = a[0];
for(int i = 3; i < n + 1; i++)
{
// When i is odd
if (i % 2 == 1)
{
int temp = Math.max((Math.max(dp[i - 3][1],
dp[i - 3][0])),
Math.max(dp[i - 2][1],
dp[i - 2][0]));
dp[i][1] = a[i - 1] + temp;
dp[i][0] = Math.max((Math.max(a[i - 2] +
dp[i - 2][0],
a[i - 2] +
dp[i - 3][1])),
Math.max(a[i - 2] +
dp[i - 3][0],
a[i - 3] +
dp[i - 3][0]));
}
// When i is even
else
{
dp[i][1] = a[i - 1] + (Math.max((
Math.max(dp[i - 2][1],
dp[i - 2][0])),
dp[i - 1][0]));
dp[i][0] = a[i - 2] + dp[i - 2][0];
}
}
// Maximum of if we pick last element or not
return Math.max(dp[n][1], dp[n][0]);
}
static int max(int []arr)
{
return 1;
}
// Driver code
public static void main(String[] args)
{
int A[] = {1, 2, 3, 4, 5, 6};
int N = A.length;
System.out.print(MaximumSum(A, N));
}
}
// This code is contributed by Rajput-Ji
Python3
# Python3 program to find maximum sum possible
# such that exactly floor(N/2) elements
# are selected and no two selected
# elements are adjacent to each other
# Function return the maximum sum
# possible under given condition
def MaximumSum(a, n):
dp = [[0 for x in range (2)]
for y in range(n + 1)]
# Base case
dp[2][1] = a[1]
dp[2][0] = a[0]
for i in range (3, n + 1):
# When i is odd
if (i & 1):
temp = max([dp[i - 3][1],
dp[i - 3][0],
dp[i - 2][1],
dp[i - 2][0]])
dp[i][1] = a[i - 1] + temp
dp[i][0] = max([a[i - 2] + dp[i - 2][0],
a[i - 2] + dp[i - 3][1],
a[i - 2] + dp[i - 3][0],
a[i - 3] + dp[i - 3][0]])
# When i is even
else:
dp[i][1] = (a[i - 1] + max([dp[i - 2][1],
dp[i - 2][0],
dp[i - 1][0]]))
dp[i][0] = a[i - 2] + dp[i - 2][0]
# Maximum of if we pick last
# element or not
return max(dp[n][1], dp[n][0])
# Driver code
if __name__ == "__main__":
A = [1, 2, 3, 4, 5, 6]
N = len(A)
print(MaximumSum(A, N))
# This code is contributed by Chitranayal
C#
// C# program to find maximum sum possible
// such that exactly Math.Floor(N/2) elements
// are selected and no two selected
// elements are adjacent to each other
using System;
class GFG{
// Function return the maximum sum
// possible under given condition
static int MaximumSum(int []a, int n)
{
int [,]dp = new int[n + 1, 2];
// Base case
dp[2, 1] = a[1];
dp[2, 0] = a[0];
for(int i = 3; i < n + 1; i++)
{
// When i is odd
if (i % 2 == 1)
{
int temp = Math.Max((Math.Max(dp[i - 3, 1],
dp[i - 3, 0])),
Math.Max(dp[i - 2, 1],
dp[i - 2, 0]));
dp[i, 1] = a[i - 1] + temp;
dp[i, 0] = Math.Max((Math.Max(a[i - 2] +
dp[i - 2, 0],
a[i - 2] +
dp[i - 3, 1])),
Math.Max(a[i - 2] +
dp[i - 3, 0],
a[i - 3] +
dp[i - 3, 0]));
}
// When i is even
else
{
dp[i, 1] = a[i - 1] + (Math.Max((
Math.Max(dp[i - 2, 1],
dp[i - 2, 0])),
dp[i - 1, 0]));
dp[i, 0] = a[i - 2] + dp[i - 2, 0];
}
}
// Maximum of if we pick last element or not
return Math.Max(dp[n, 1], dp[n, 0]);
}
static int max(int []arr)
{
return 1;
}
// Driver code
public static void Main(String[] args)
{
int []A = { 1, 2, 3, 4, 5, 6 };
int N = A.Length;
Console.Write(MaximumSum(A, N));
}
}
// This code is contributed by 29AjayKumar
Javascript
<script>
// Javascript program to find maximum sum possible
// such that exactly floor(N/2) elements
// are selected and no two selected
// elements are adjacent to each other
// Function return the maximum sum
// possible under given condition
function MaximumSum(a, n)
{
var dp = Array.from(Array(n+1), ()=>Array(2).fill(0));
// Base case
dp[2][1] = a[1];
dp[2][0] = a[0];
for (var i = 3; i < n + 1; i++) {
// When i is odd
if (i & 1) {
var temp = ([dp[i - 3][1],
dp[i - 3][0],
dp[i - 2][1],
dp[i - 2][0] ].reduce((a,b)=>
Math.max(a,b)));
dp[i][1] = a[i - 1] + temp;
dp[i][0] = ([ a[i - 2] + dp[i - 2][0],
a[i - 2] + dp[i - 3][1],
a[i - 2] + dp[i - 3][0],
a[i - 3] + dp[i - 3][0] ].reduce((a,b)=>
Math.max(a,b)));
}
// When i is even
else {
dp[i][1] = a[i - 1] + ([ dp[i - 2][1],
dp[i - 2][0],
dp[i - 1][0] ].reduce((a,b)=>
Math.max(a,b)));
dp[i][0] = a[i - 2] + dp[i - 2][0];
}
}
// Maximum of if we pick last element or not
return Math.max(dp[n][1], dp[n][0]);
}
// Driver code
var A = [1, 2, 3, 4, 5, 6];
var N = A.length;
document.write( MaximumSum(A, N));
</script>
Output:
12
Time Complexity: O(N) | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent | https://www.geeksforgeeks.org/maximum-sum-such-that-exactly-half-of-the-elements-are-selected-and-no-two-adjacent/?ref=ml_lbp | NLP | Maximum sum such that exactly half of the elements are selected and no two adjacent | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0100907581, 0.00379519654, -0.00791038, 0.0119213825, 0.0126208887, 0.00938381, 0.00573000265, 0.0237981156, -0.0287690777, 0.011936265, -0.0207917243, -0.00393286534, 0.0606933795, -0.0038063589, -0.0289476756, 0.00151156727, -0.0163416695, -0.00346962828, -0.00778387394, -0.051406309, -0.0224586334, 0.00649648346, -0.0212679841, 0.0334274955, 0.000314638542, 0.0173834879, 0.00192364375, 0.00472539198, -0.0297960136, 0.0310164299, 0.000648346089, 0.000143831436, 0.0216995943, -0.0117725506, 0.00484445691, 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02 Jun, 2021 | Maximum length subsequence such that adjacent elements in the subsequence have a common factor
02 Jun, 2021
Given an array arr[], the task is to find the maximum length of a subsequence such that the adjacent elements in the subsequence have a common factor.
Examples:
Input: arr[] = { 13, 2, 8, 6, 3, 1, 9 } Output: 5Max length subsequence with satisfied conditions: { 2, 8, 6, 3, 9 }
Input: arr[] = { 12, 2, 8, 6, 3, 1, 9 } Output: 6Max length subsequence with satisfied conditions: {12, 2, 8, 6, 3, 9 }
Input: arr[] = { 1, 2, 2, 3, 3, 1 } Output: 2
Approach: A naive approach is to consider all subsequences and check every subsequence whether it satisfies the condition. An efficient solution is to use Dynamic programming. Let dp[i] denote the maximum length of subsequence including arr[i]. Then, the following relation holds for every prime p such that p is a prime factor of arr[i]:
dp[i] = max(dp[i], 1 + dp[pos[p]])
where pos[p] gives the index of p in the array
where it last occurred.
Explanation: Traverse the array. For an element arr[i], there are 2 possibilities.
If the prime factors of arr[i] have shown their first appearance in the array, then dp[i] = 1
If the prime factors of arr[i] have already occurred, then this element can be added in the subsequence since there’s a common factor. Hence dp[i] = max(dp[i], 1 + dp[pos[p]]) where p is the common prime factor and pos[p] is the latest index of p in the array.
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach
#include <bits/stdc++.h>
#define N 100005
#define MAX 10000002
using namespace std;
int lpd[MAX];
// Function to compute least
// prime divisor of i
void preCompute()
{
memset(lpd, 0, sizeof(lpd));
lpd[0] = lpd[1] = 1;
for (int i = 2; i * i < MAX; i++)
{
for (int j = i * 2; j < MAX; j += i)
{
if (lpd[j] == 0)
{
lpd[j] = i;
}
}
}
for (int i = 2; i < MAX; i++)
{
if (lpd[i] == 0)
{
lpd[i] = i;
}
}
}
// Function that returns the maximum
// length subsequence such that
// adjacent elements have a common factor.
int maxLengthSubsequence(int arr[], int n)
{
int dp[N];
unordered_map<int, int> pos;
// Initialize dp array with 1.
for (int i = 0; i <= n; i++)
dp[i] = 1;
for (int i = 0; i <= n; i++)
{
while (arr[i] > 1)
{
int p = lpd[arr[i]];
if (pos[p])
{
// p has appeared at least once.
dp[i] = max(dp[i], 1 + dp[pos[p]]);
}
// Update latest occurrence of prime p.
pos[p] = i;
while (arr[i] % p == 0)
arr[i] /= p;
}
}
// Take maximum value as the answer.
int ans = 1;
for (int i = 0; i <= n; i++)
{
ans = max(ans, dp[i]);
}
return ans;
}
// Driver code
int main()
{
int arr[] = { 13, 2, 8, 6, 3, 1, 9 };
int n = sizeof(arr) / sizeof(arr[0]);
preCompute();
cout << maxLengthSubsequence(arr, n);
return 0;
}
Python3
# Python3 implementation of the
# above approach
import math as mt
N = 100005
MAX = 1000002
lpd = [0 for i in range(MAX)]
# to compute least prime divisor of i
def preCompute():
lpd[0], lpd[1] = 1, 1
for i in range(2, mt.ceil(mt.sqrt(MAX))):
for j in range(2 * i, MAX, i):
if (lpd[j] == 0):
lpd[j] = i
for i in range(2, MAX):
if (lpd[i] == 0):
lpd[i] = i
# Function that returns the maximum
# length subsequence such that
# adjacent elements have a common factor.
def maxLengthSubsequence(arr, n):
dp = [1 for i in range(N + 1)]
pos = dict()
# Initialize dp array with 1.
for i in range(0, n):
while (arr[i] > 1):
p = lpd[arr[i]]
if (p in pos.keys()):
# p has appeared at least once.
dp[i] = max(dp[i], 1 + dp[pos[p]])
# Update latest occurrence of prime p.
pos[p] = i
while (arr[i] % p == 0):
arr[i] //= p
# Take maximum value as the answer.
ans = 1
for i in range(0, n + 1):
ans = max(ans, dp[i])
return ans
# Driver code
arr = [13, 2, 8, 6, 3, 1, 9]
n = len(arr)
preCompute()
print(maxLengthSubsequence(arr, n))
# This code is contributed by Mohit Kumar
Java
// Java implementation of the above approach
import java.util.*;
class GfG {
static int N, MAX;
// Check if UpperBound is
// given for all test Cases
// N = 100005 ;
// MAX = 10000002;
static int lpd[];
// Function to compute least prime divisor
// of i upto MAX element of the input array
// it will be space efficient
// if more test cases are there it's
// better to find prime divisor
// upto upperbound of input element
// it will be cost efficient
static void preCompute()
{
lpd = new int[MAX + 1];
lpd[0] = lpd[1] = 1;
for (int i = 2; i * i <= MAX; i++)
{
for (int j = i * 2; j <= MAX; j += i)
{
if (lpd[j] == 0)
{
lpd[j] = i;
}
}
}
for (int i = 2; i <= MAX; i++)
{
if (lpd[i] == 0)
{
lpd[i] = i;
}
}
}
// Function that returns the maximum
// length subsequence such that
// adjacent elements have a common factor.
static int maxLengthSubsequence(Integer arr[], int n)
{
Integer dp[] = new Integer[N];
Map<Integer, Integer> pos
= new HashMap<Integer, Integer>();
// Initialize dp array with 1.
for (int i = 0; i <= n; i++)
dp[i] = 1;
for (int i = 0; i <= n; i++)
{
while (arr[i] > 1) {
int p = lpd[arr[i]];
if (pos.containsKey(p))
{
// p has appeared at least once.
dp[i] = Math.max(dp[i],
1 + dp[pos.get(p)]);
}
// Update latest occurrence of prime p.
pos.put(p, i);
while (arr[i] % p == 0)
arr[i] /= p;
}
}
// Take maximum value as the answer.
int ans = Collections.max(Arrays.asList(dp));
return ans;
}
// Driver code
public static void main(String[] args)
{
Integer arr[] = { 12, 2, 8, 6, 3, 1, 9 };
N = arr.length;
MAX = Collections.max(Arrays.asList(arr));
preCompute();
System.out.println(
maxLengthSubsequence(arr, N - 1));
}
}
// This code is contributed by Prerna Saini.
C#
// C# implementation of the
// above approach
using System;
using System.Collections;
class GFG {
static int N = 100005;
static int MAX = 10000002;
static int[] lpd = new int[MAX];
// to compute least prime divisor of i
static void preCompute()
{
lpd[0] = lpd[1] = 1;
for (int i = 2; i * i < MAX; i++)
{
for (int j = i * 2; j < MAX; j += i)
{
if (lpd[j] == 0)
{
lpd[j] = i;
}
}
}
for (int i = 2; i < MAX; i++)
{
if (lpd[i] == 0)
{
lpd[i] = i;
}
}
}
// Function that returns the maximum
// length subsequence such that
// adjacent elements have a common factor.
static int maxLengthSubsequence(int[] arr, int n)
{
int[] dp = new int[N];
Hashtable pos = new Hashtable();
// Initialize dp array with 1.
for (int i = 0; i <= n; i++)
dp[i] = 1;
for (int i = 0; i <= n; i++)
{
while (arr[i] > 1) {
int p = lpd[arr[i]];
if (pos.ContainsKey(p))
{
// p has appeared at least once.
dp[i] = Math.Max(
dp[i],
1 + dp[Convert.ToInt32(pos[p])]);
}
// Update latest occurrence of prime p.
pos[p] = i;
while (arr[i] % p == 0)
arr[i] /= p;
}
}
// Take maximum value as the answer.
int ans = 1;
for (int i = 0; i <= n; i++)
{
ans = Math.Max(ans, dp[i]);
}
return ans;
}
// Driver code
public static void Main()
{
int[] arr = { 13, 2, 8, 6, 3, 1, 9 };
int n = arr.Length - 1;
preCompute();
Console.WriteLine(maxLengthSubsequence(arr, n));
}
}
// This code is contributed by Ryuga
Javascript
<script>
// JavaScript implementation of the above approach
let N, MAX;
// Check if UpperBound is
// given for all test Cases
// N = 100005 ;
// MAX = 10000002;
let lpd;
// Function to compute least prime divisor
// of i upto MAX element of the input array
// it will be space efficient
// if more test cases are there it's
// better to find prime divisor
// upto upperbound of input element
// it will be cost efficient
function preCompute()
{
lpd = new Array(MAX + 1);
for(let i=0;i<lpd.length;i++)
{
lpd[i]=0;
}
lpd[0] = lpd[1] = 1;
for (let i = 2; i * i <= MAX; i++)
{
for (let j = i * 2; j <= MAX; j += i)
{
if (lpd[j] == 0)
{
lpd[j] = i;
}
}
}
for (let i = 2; i <= MAX; i++)
{
if (lpd[i] == 0)
{
lpd[i] = i;
}
}
}
// Function that returns the maximum
// length subsequence such that
// adjacent elements have a common factor.
function maxLengthSubsequence(arr,n)
{
let dp = new Array(N);
let pos
= new Map();
// Initialize dp array with 1.
for (let i = 0; i <= n; i++)
dp[i] = 1;
for (let i = 0; i <= n; i++)
{
while (arr[i] > 1) {
let p = lpd[arr[i]];
if (pos.has(p))
{
// p has appeared at least once.
dp[i] = Math.max(dp[i],
1 + dp[pos.get(p)]);
}
// Update latest occurrence of prime p.
pos.set(p, i);
while (arr[i] % p == 0)
arr[i] = Math.floor(arr[i]/p);
}
}
// Take maximum value as the answer.
let ans = Math.max(...dp);
return ans;
}
// Driver code
let arr=[13, 2, 8, 6, 3, 1, 9 ];
N = arr.length;
MAX = Math.max(...arr);
preCompute();
document.write(maxLengthSubsequence(arr, N - 1));
// This code is contributed by patel2127
</script>
Output
5
Time Complexity: O(N* log(N))Auxiliary Space: O(N) | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor | https://www.geeksforgeeks.org/maximum-length-subsequence-such-that-adjacent-elements-in-the-subsequence-have-a-common-factor/?ref=ml_lbp | NLP | Maximum length subsequence such that adjacent elements in the subsequence have a common factor | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [0.0193846598, 0.0214228015, -0.00545983901, 0.0230592638, 0.0299621671, 0.005259, 0.0121172713, 0.0162456241, -0.0242494196, 0.0165134091, -0.0167068094, 0.00617021276, 0.0576630384, -0.0210806318, 0.0118718017, -0.0143190594, 0.00338636455, -4.80595045e-05, 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29 Nov, 2024 | Longest subsequence such that difference between adjacents is one
29 Nov, 2024
Try it on GfG Practice
Given an array arr[] of size n, the task is to find the longest subsequence such that the absolute difference between adjacent elements is 1.
Examples:
Input: arr[] = [10, 9, 4, 5, 4, 8, 6]Output: 3Explanation: The three possible subsequences of length 3 are [10, 9, 8], [4, 5, 4], and [4, 5, 6], where adjacent elements have a absolute difference of 1. No valid subsequence of greater length could be formed.Input: arr[] = [1, 2, 3, 4, 5]Output: 5Explanation: All the elements can be included in the valid subsequence.
Using Recursion – O(2^n) Time and O(n) SpaceFor the recursive approach, we will consider two cases at each step:
If the element satisfies the condition (the absolute difference between adjacent elements is 1), we include it in the subsequence and move on to the next element.else, we skip the current element and move on to the next one.Mathematically, the recurrence relation will look like the following:
longestSubseq(arr, idx, prev) = max(longestSubseq(arr, idx + 1, prev), 1 + longestSubseq(arr, idx + 1, idx)) Base Case:
When idx == arr.size(), we have reached the end of the array, so return 0 (since no more elements can be included).
C++
// C++ program to find the longest subsequence such that
// the difference between adjacent elements is one using
// recursion.
#include <bits/stdc++.h>
using namespace std;
int subseqHelper(int idx, int prev, vector<int>& arr) {
// Base case: if index reaches the end of the array
if (idx == arr.size()) {
return 0;
}
// Skip the current element and move to the next index
int noTake = subseqHelper(idx + 1, prev, arr);
// Take the current element if the condition is met
int take = 0;
if (prev == -1 || abs(arr[idx] - arr[prev]) == 1) {
take = 1 + subseqHelper(idx + 1, idx, arr);
}
// Return the maximum of the two options
return max(take, noTake);
}
// Function to find the longest subsequence
int longestSubseq(vector<int>& arr) {
// Start recursion from index 0
// with no previous element
return subseqHelper(0, -1, arr);
}
int main() {
vector<int> arr = {10, 9, 4, 5, 4, 8, 6};
cout << longestSubseq(arr);
return 0;
}
Java
// Java program to find the longest subsequence such that
// the difference between adjacent elements is one using
// recursion.
import java.util.ArrayList;
class GfG {
// Helper function to recursively find the subsequence
static int subseqHelper(int idx, int prev,
ArrayList<Integer> arr) {
// Base case: if index reaches the end of the array
if (idx == arr.size()) {
return 0;
}
// Skip the current element and move to the next index
int noTake = subseqHelper(idx + 1, prev, arr);
// Take the current element if the condition is met
int take = 0;
if (prev == -1 || Math.abs(arr.get(idx)
- arr.get(prev)) == 1) {
take = 1 + subseqHelper(idx + 1, idx, arr);
}
// Return the maximum of the two options
return Math.max(take, noTake);
}
// Function to find the longest subsequence
static int longestSubseq(ArrayList<Integer> arr) {
// Start recursion from index 0
// with no previous element
return subseqHelper(0, -1, arr);
}
public static void main(String[] args) {
ArrayList<Integer> arr = new ArrayList<>();
arr.add(10);
arr.add(9);
arr.add(4);
arr.add(5);
arr.add(4);
arr.add(8);
arr.add(6);
System.out.println(longestSubseq(arr));
}
}
Python
# Python program to find the longest subsequence such that
# the difference between adjacent elements is one using
# recursion.
def subseq_helper(idx, prev, arr):
# Base case: if index reaches the end of the array
if idx == len(arr):
return 0
# Skip the current element and move to the next index
no_take = subseq_helper(idx + 1, prev, arr)
# Take the current element if the condition is met
take = 0
if prev == -1 or abs(arr[idx] - arr[prev]) == 1:
take = 1 + subseq_helper(idx + 1, idx, arr)
# Return the maximum of the two options
return max(take, no_take)
def longest_subseq(arr):
# Start recursion from index 0
# with no previous element
return subseq_helper(0, -1, arr)
if __name__ == "__main__":
arr = [10, 9, 4, 5, 4, 8, 6]
print(longest_subseq(arr))
C#
// C# program to find the longest subsequence such that
// the difference between adjacent elements is one using
// recursion.
using System;
using System.Collections.Generic;
class GfG {
// Helper function to recursively find the subsequence
static int SubseqHelper(int idx, int prev,
List<int> arr) {
// Base case: if index reaches the end of the array
if (idx == arr.Count) {
return 0;
}
// Skip the current element and move to the next index
int noTake = SubseqHelper(idx + 1, prev, arr);
// Take the current element if the condition is met
int take = 0;
if (prev == -1 || Math.Abs(arr[idx] - arr[prev]) == 1) {
take = 1 + SubseqHelper(idx + 1, idx, arr);
}
// Return the maximum of the two options
return Math.Max(take, noTake);
}
// Function to find the longest subsequence
static int LongestSubseq(List<int> arr) {
// Start recursion from index 0
// with no previous element
return SubseqHelper(0, -1, arr);
}
static void Main(string[] args) {
List<int> arr
= new List<int> { 10, 9, 4, 5, 4, 8, 6 };
Console.WriteLine(LongestSubseq(arr));
}
}
JavaScript
// JavaScript program to find the longest subsequence
// such that the difference between adjacent elements
// is one using recursion.
function subseqHelper(idx, prev, arr) {
// Base case: if index reaches the end of the array
if (idx === arr.length) {
return 0;
}
// Skip the current element and move to the next index
let noTake = subseqHelper(idx + 1, prev, arr);
// Take the current element if the condition is met
let take = 0;
if (prev === -1 || Math.abs(arr[idx] - arr[prev]) === 1) {
take = 1 + subseqHelper(idx + 1, idx, arr);
}
// Return the maximum of the two options
return Math.max(take, noTake);
}
function longestSubseq(arr) {
// Start recursion from index 0
// with no previous element
return subseqHelper(0, -1, arr);
}
const arr = [10, 9, 4, 5, 4, 8, 6];
console.log(longestSubseq(arr));
Output3Using Top-Down DP (Memoization) – O(n^2) Time and O(n^2) SpaceIf we notice carefully, we can observe that the above recursive solution holds the following two properties of Dynamic Programming:
1. Optimal Substructure: The solution to finding the longest subsequence such that the difference between adjacent elements is one can be derived from the optimal solutions of smaller subproblems. Specifically, for any given idx (current index) and prev (previous index in the subsequence), we can express the recursive relation as follows:
subseqHelper(idx, prev) = max(subseqHelper(idx + 1, prev), 1 + subseqHelper(idx + 1, idx))2. Overlapping Subproblems: When implementing a recursive approach to solve the problem, we observe that many subproblems are computed multiple times. For example, when computing subseqHelper(0, -1) for an array arr = [10, 9, 4, 5], the subproblem subseqHelper(2, -1) may be computed multiple times. To avoid this repetition, we use memoization to store the results of previously computed subproblems.
The recursive solution involves two parameters:
idx (the current index in the array).prev (the index of the last included element in the subsequence).We need to track both parameters, so we create a 2D array memo of size (n) x (n+1). We initialize the 2D array memo with -1 to indicate that no subproblems have been computed yet. Before computing a result, we check if the value at memo[idx][prev+1] is -1. If it is, we compute and store the result. Otherwise, we return the stored result.
C++
// C++ program to find the longest subsequence such that
// the difference between adjacent elements is one using
// recursion with memoization.
#include <bits/stdc++.h>
using namespace std;
// Helper function to recursively find the subsequence
int subseqHelper(int idx, int prev, vector<int>& arr,
vector<vector<int>>& memo) {
// Base case: if index reaches the end of the array
if (idx == arr.size()) {
return 0;
}
// Check if the result is already computed
if (memo[idx][prev + 1] != -1) {
return memo[idx][prev + 1];
}
// Skip the current element and move to the next index
int noTake = subseqHelper(idx + 1, prev, arr, memo);
// Take the current element if the condition is met
int take = 0;
if (prev == -1 || abs(arr[idx] - arr[prev]) == 1) {
take = 1 + subseqHelper(idx + 1, idx, arr, memo);
}
// Store the result in the memo table
return memo[idx][prev + 1] = max(take, noTake);
}
// Function to find the longest subsequence
int longestSubseq(vector<int>& arr) {
int n = arr.size();
// Create a memoization table initialized to -1
vector<vector<int>> memo(n, vector<int>(n + 1, -1));
// Start recursion from index 0 with no previous element
return subseqHelper(0, -1, arr, memo);
}
int main() {
// Input array of integers
vector<int> arr = {10, 9, 4, 5, 4, 8, 6};
cout << longestSubseq(arr);
return 0;
}
Java
// Java program to find the longest subsequence such that
// the difference between adjacent elements is one using
// recursion with memoization.
import java.util.ArrayList;
import java.util.Arrays;
class GfG {
// Helper function to recursively find the subsequence
static int subseqHelper(int idx, int prev,
ArrayList<Integer> arr,
int[][] memo) {
// Base case: if index reaches the end of the array
if (idx == arr.size()) {
return 0;
}
// Check if the result is already computed
if (memo[idx][prev + 1] != -1) {
return memo[idx][prev + 1];
}
// Skip the current element and move to the next index
int noTake = subseqHelper(idx + 1, prev, arr, memo);
// Take the current element if the condition is met
int take = 0;
if (prev == -1 || Math.abs(arr.get(idx)
- arr.get(prev)) == 1) {
take = 1 + subseqHelper(idx + 1, idx, arr, memo);
}
// Store the result in the memo table
memo[idx][prev + 1] = Math.max(take, noTake);
// Return the stored result
return memo[idx][prev + 1];
}
// Function to find the longest subsequence
static int longestSubseq(ArrayList<Integer> arr) {
int n = arr.size();
// Create a memoization table initialized to -1
int[][] memo = new int[n][n + 1];
for (int[] row : memo) {
Arrays.fill(row, -1);
}
// Start recursion from index 0
// with no previous element
return subseqHelper(0, -1, arr, memo);
}
public static void main(String[] args) {
ArrayList<Integer> arr = new ArrayList<>();
arr.add(10);
arr.add(9);
arr.add(4);
arr.add(5);
arr.add(4);
arr.add(8);
arr.add(6);
System.out.println(longestSubseq(arr));
}
}
Python
# Python program to find the longest subsequence such that
# the difference between adjacent elements is one using
# recursion with memoization.
def subseq_helper(idx, prev, arr, memo):
# Base case: if index reaches the end of the array
if idx == len(arr):
return 0
# Check if the result is already computed
if memo[idx][prev + 1] != -1:
return memo[idx][prev + 1]
# Skip the current element and move to the next index
no_take = subseq_helper(idx + 1, prev, arr, memo)
# Take the current element if the condition is met
take = 0
if prev == -1 or abs(arr[idx] - arr[prev]) == 1:
take = 1 + subseq_helper(idx + 1, idx, arr, memo)
# Store the result in the memo table
memo[idx][prev + 1] = max(take, no_take)
# Return the stored result
return memo[idx][prev + 1]
def longest_subseq(arr):
n = len(arr)
# Create a memoization table initialized to -1
memo = [[-1 for _ in range(n + 1)] for _ in range(n)]
# Start recursion from index 0 with
# no previous element
return subseq_helper(0, -1, arr, memo)
if __name__ == "__main__":
arr = [10, 9, 4, 5, 4, 8, 6]
print(longest_subseq(arr))
C#
// C# program to find the longest subsequence such that
// the difference between adjacent elements is one using
// recursion with memoization.
using System;
using System.Collections.Generic;
class GfG {
// Helper function to recursively find the subsequence
static int SubseqHelper(int idx, int prev,
List<int> arr, int[,] memo) {
// Base case: if index reaches the end of the array
if (idx == arr.Count) {
return 0;
}
// Check if the result is already computed
if (memo[idx, prev + 1] != -1) {
return memo[idx, prev + 1];
}
// Skip the current element and move to the next index
int noTake = SubseqHelper(idx + 1, prev, arr, memo);
// Take the current element if the condition is met
int take = 0;
if (prev == -1 || Math.Abs(arr[idx] - arr[prev]) == 1) {
take = 1 + SubseqHelper(idx + 1, idx, arr, memo);
}
// Store the result in the memoization table
memo[idx, prev + 1] = Math.Max(take, noTake);
// Return the stored result
return memo[idx, prev + 1];
}
// Function to find the longest subsequence
static int LongestSubseq(List<int> arr) {
int n = arr.Count;
// Create a memoization table initialized to -1
int[,] memo = new int[n, n + 1];
for (int i = 0; i < n; i++) {
for (int j = 0; j <= n; j++) {
memo[i, j] = -1;
}
}
// Start recursion from index 0 with no previous element
return SubseqHelper(0, -1, arr, memo);
}
static void Main(string[] args) {
List<int> arr
= new List<int> { 10, 9, 4, 5, 4, 8, 6 };
Console.WriteLine(LongestSubseq(arr));
}
}
JavaScript
// JavaScript program to find the longest subsequence
// such that the difference between adjacent elements
// is one using recursion with memoization.
function subseqHelper(idx, prev, arr, memo) {
// Base case: if index reaches the end of the array
if (idx === arr.length) {
return 0;
}
// Check if the result is already computed
if (memo[idx][prev + 1] !== -1) {
return memo[idx][prev + 1];
}
// Skip the current element and move to the next index
let noTake = subseqHelper(idx + 1, prev, arr, memo);
// Take the current element if the condition is met
let take = 0;
if (prev === -1 || Math.abs(arr[idx] - arr[prev]) === 1) {
take = 1 + subseqHelper(idx + 1, idx, arr, memo);
}
// Store the result in the memoization table
memo[idx][prev + 1] = Math.max(take, noTake);
// Return the stored result
return memo[idx][prev + 1];
}
function longestSubseq(arr) {
let n = arr.length;
// Create a memoization table initialized to -1
let memo =
Array.from({ length: n }, () => Array(n + 1).fill(-1));
// Start recursion from index 0 with no previous element
return subseqHelper(0, -1, arr, memo);
}
const arr = [10, 9, 4, 5, 4, 8, 6];
console.log(longestSubseq(arr));
Output3Using Bottom-Up DP (Tabulation) – O(n) Time and O(n) SpaceThe approach is similar to the recursive method, but instead of breaking down the problem recursively, we iteratively build the solution in a bottom-up manner.Instead of using recursion, we utilize a hashmap based dynamic programming table (dp) to store the lengths of the longest subsequences. This helps us efficiently calculate and update the subsequence lengths for all possible values of array elements.
Dynamic Programming Relation:
dp[x] represents the length of the longest subsequence ending with the element x.
For every element arr[i] in the array: If arr[i] + 1 or arr[i] – 1 exists in dp:
dp[arr[i]] = 1 + max(dp[arr[i] + 1], dp[arr[i] – 1]);This means we can extend the subsequences ending with arr[i] + 1 or arr[i] – 1 by including arr[i].
Otherwise, start a new subsequence:
dp[arr[i]] = 1;
C++
// C++ program to find the longest subsequence such that
// the difference between adjacent elements is one using
// Tabulation.
#include <bits/stdc++.h>
using namespace std;
int longestSubseq(vector<int>& arr) {
int n = arr.size();
// Base case: if the array has only
// one element
if (n == 1) {
return 1;
}
// Map to store the length of the longest subsequence
unordered_map<int, int> dp;
int ans = 1;
// Loop through the array to fill the map
// with subsequence lengths
for (int i = 0; i < n; ++i) {
// Check if the current element is adjacent
// to another subsequence
if (dp.count(arr[i] + 1) > 0
|| dp.count(arr[i] - 1) > 0) {
dp[arr[i]] = 1 +
max(dp[arr[i] + 1], dp[arr[i] - 1]);
}
else {
dp[arr[i]] = 1;
}
// Update the result with the maximum
// subsequence length
ans = max(ans, dp[arr[i]]);
}
return ans;
}
int main() {
vector<int> arr = {10, 9, 4, 5, 4, 8, 6};
cout << longestSubseq(arr);
return 0;
}
Java
// Java code to find the longest subsequence such that
// the difference between adjacent elements
// is one using Tabulation.
import java.util.HashMap;
import java.util.ArrayList;
class GfG {
static int longestSubseq(ArrayList<Integer> arr) {
int n = arr.size();
// Base case: if the array has only one element
if (n == 1) {
return 1;
}
// Map to store the length of the longest subsequence
HashMap<Integer, Integer> dp = new HashMap<>();
int ans = 1;
// Loop through the array to fill the map
// with subsequence lengths
for (int i = 0; i < n; ++i) {
// Check if the current element is adjacent
// to another subsequence
if (dp.containsKey(arr.get(i) + 1)
|| dp.containsKey(arr.get(i) - 1)) {
dp.put(arr.get(i), 1 +
Math.max(dp.getOrDefault(arr.get(i) + 1, 0),
dp.getOrDefault(arr.get(i) - 1, 0)));
}
else {
dp.put(arr.get(i), 1);
}
// Update the result with the maximum
// subsequence length
ans = Math.max(ans, dp.get(arr.get(i)));
}
return ans;
}
public static void main(String[] args) {
ArrayList<Integer> arr = new ArrayList<>();
arr.add(10);
arr.add(9);
arr.add(4);
arr.add(5);
arr.add(4);
arr.add(8);
arr.add(6);
System.out.println(longestSubseq(arr));
}
}
Python
# Python code to find the longest subsequence such that
# the difference between adjacent elements is
# one using Tabulation.
def longestSubseq(arr):
n = len(arr)
# Base case: if the array has only one element
if n == 1:
return 1
# Dictionary to store the length of the
# longest subsequence
dp = {}
ans = 1
for i in range(n):
# Check if the current element is adjacent to
# another subsequence
if arr[i] + 1 in dp or arr[i] - 1 in dp:
dp[arr[i]] = 1 + max(dp.get(arr[i] + 1, 0), \
dp.get(arr[i] - 1, 0))
else:
dp[arr[i]] = 1
# Update the result with the maximum
# subsequence length
ans = max(ans, dp[arr[i]])
return ans
if __name__ == "__main__":
arr = [10, 9, 4, 5, 4, 8, 6]
print(longestSubseq(arr))
C#
// C# code to find the longest subsequence such that
// the difference between adjacent elements
// is one using Tabulation.
using System;
using System.Collections.Generic;
class GfG {
static int longestSubseq(List<int> arr) {
int n = arr.Count;
// Base case: if the array has only one element
if (n == 1) {
return 1;
}
// Map to store the length of the longest subsequence
Dictionary<int, int> dp = new Dictionary<int, int>();
int ans = 1;
// Loop through the array to fill the map with
// subsequence lengths
for (int i = 0; i < n; ++i) {
// Check if the current element is adjacent to
// another subsequence
if (dp.ContainsKey(arr[i] + 1) || dp.ContainsKey(arr[i] - 1)) {
dp[arr[i]] = 1 + Math.Max(dp.GetValueOrDefault(arr[i] + 1, 0),
dp.GetValueOrDefault(arr[i] - 1, 0));
}
else {
dp[arr[i]] = 1;
}
// Update the result with the maximum
// subsequence length
ans = Math.Max(ans, dp[arr[i]]);
}
return ans;
}
static void Main(string[] args) {
List<int> arr
= new List<int> { 10, 9, 4, 5, 4, 8, 6 };
Console.WriteLine(longestSubseq(arr));
}
}
JavaScript
// Function to find the longest subsequence such that
// the difference between adjacent elements
// is one using Tabulation.
function longestSubseq(arr) {
const n = arr.length;
// Base case: if the array has only one element
if (n === 1) {
return 1;
}
// Object to store the length of the
// longest subsequence
let dp = {};
let ans = 1;
// Loop through the array to fill the object
// with subsequence lengths
for (let i = 0; i < n; i++) {
// Check if the current element is adjacent to
// another subsequence
if ((arr[i] + 1) in dp || (arr[i] - 1) in dp) {
dp[arr[i]] = 1 + Math.max(dp[arr[i] + 1]
|| 0, dp[arr[i] - 1] || 0);
} else {
dp[arr[i]] = 1;
}
// Update the result with the maximum
// subsequence length
ans = Math.max(ans, dp[arr[i]]);
}
return ans;
}
const arr = [10, 9, 4, 5, 4, 8, 6];
console.log(longestSubseq(arr));
Output3 | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one | https://www.geeksforgeeks.org/longest-subsequence-such-that-difference-between-adjacents-is-one/?ref=ml_lbp | NLP | Longest subsequence such that difference between adjacents is one | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [0.0365425162, -0.00474455673, -0.0164488442, 0.0393703952, 0.00664159423, 0.00385691621, 0.0202036425, 0.0272733476, -0.0405958109, 0.0174071826, 0.014634287, -0.0131810708, 0.0399045534, -0.0241155457, -0.0330233723, -0.00941056199, 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26 Apr, 2023 | Longest Increasing Subsequence using Longest Common Subsequence Algorithm
26 Apr, 2023
Given an array arr[] of N integers, the task is to find and print the Longest Increasing Subsequence.Examples:
Input: arr[] = {12, 34, 1, 5, 40, 80} Output: 4 {12, 34, 40, 80} and {1, 5, 40, 80} are the longest increasing subsequences.Input: arr[] = {10, 22, 9, 33, 21, 50, 41, 60, 80} Output: 6
Prerequisite: LCS, LISApproach: The longest increasing subsequence of any sequence is the subsequence of the sorted sequence of itself. It can be solved using a Dynamic Programming approach. The approach is the same as the classical LCS problem but instead of the second sequence, given sequence is taken again in its sorted form.Note: We should remove all duplicates otherwise it might give wrong result. For example in {1, 1, 1} we know the longest increasing subsequence(a1 < a2 < … ak) is of length 1, but if we try out this example in LIS using LCS method we would get 3 (because it finds the longest common subsequence). Below is the implementation of the above approach:
C++
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
//function to return size of array without duplicates
int removeDuplicates(vector<int> &arr)
{
int k = 0;
for (int i = 1; i < arr.size(); i++)
{
if (arr[i] != arr[k]) {
arr[++k] = arr[i];
}
}
return k + 1;
}
// Function to return the size of the
// longest increasing subsequence
int LISusingLCS(vector<int>& seq)
{
int n = seq.size();
// Create an 2D array of integer
// for tabulation
vector<vector<int> > L(n + 1, vector<int>(n + 1));
// Take the second sequence as the sorted
// sequence of the given sequence
vector<int> sortedseq(seq);
sort(sortedseq.begin(), sortedseq.end());
//remove duplicates
int m = removeDuplicates(sortedseq)
// Classical Dynamic Programming algorithm
// for Longest Common Subsequence
for (int i = 0; i <= n; i++) {
for (int j = 0; j <= m; j++) {
if (i == 0 || j == 0)
L[i][j] = 0;
else if (seq[i - 1] == sortedseq[j - 1])
L[i][j] = L[i - 1][j - 1] + 1;
else
L[i][j] = max(L[i - 1][j], L[i][j - 1]);
}
}
// Return the ans
return L[n][m];
}
// Driver code
int main()
{
vector<int> sequence{ 12, 34, 1, 5, 40, 80 };
cout << LISusingLCS(sequence) << endl;
return 0;
}
Java
//Java implementation of above approach
import java.util.*;
class GFG
{
// Function to return the size of the
// longest increasing subsequence
static int LISusingLCS(Vector<Integer> seq)
{
int n = seq.size();
// Create an 2D array of integer
// for tabulation
int L[][] = new int [n + 1][n + 1];
// Take the second sequence as the sorted
// sequence of the given sequence
Vector<Integer> sortedseq = new Vector<Integer>(seq);
Collections.sort(sortedseq);
// Classical Dynamic Programming algorithm
// for Longest Common Subsequence
for (int i = 0; i <= n; i++)
{
for (int j = 0; j <= n; j++)
{
if (i == 0 || j == 0)
L[i][j] = 0;
else if (seq.get(i - 1) == sortedseq.get(j - 1))
L[i][j] = L[i - 1][j - 1] + 1;
else
L[i][j] = Math.max(L[i - 1][j],
L[i][j - 1]);
}
}
// Return the ans
return L[n][n];
}
// Driver code
public static void main(String args[])
{
Vector<Integer> sequence = new Vector<Integer>();
sequence.add(12);
sequence.add(34);
sequence.add(1);
sequence.add(5);
sequence.add(40);
sequence.add(80);
System.out.println(LISusingLCS(sequence));
}
}
// This code is contributed by Arnab Kundu
Python3
# Python3 implementation of the approach
# Function to return the size of the
# longest increasing subsequence
def LISusingLCS(seq):
n = len(seq)
# Create an 2D array of integer
# for tabulation
L = [[0 for i in range(n + 1)]
for i in range(n + 1)]
# Take the second sequence as the sorted
# sequence of the given sequence
sortedseq = sorted(seq)
# Classical Dynamic Programming algorithm
# for Longest Common Subsequence
for i in range(n + 1):
for j in range(n + 1):
if (i == 0 or j == 0):
L[i][j] = 0
elif (seq[i - 1] == sortedseq[j - 1]):
L[i][j] = L[i - 1][j - 1] + 1
else:
L[i][j] = max(L[i - 1][j],
L[i][j - 1])
# Return the ans
return L[n][n]
# Driver code
sequence = [12, 34, 1, 5, 40, 80]
print(LISusingLCS(sequence))
# This code is contributed by mohit kumar
C#
// C# implementation of above approach
using System;
using System.Collections.Generic;
class GFG
{
// Function to return the size of the
// longest increasing subsequence
static int LISusingLCS(List<int> seq)
{
int n = seq.Count;
// Create an 2D array of integer
// for tabulation
int [,]L = new int [n + 1, n + 1];
// Take the second sequence as the sorted
// sequence of the given sequence
List<int> sortedseq = new List<int>(seq);
sortedseq.Sort();
// Classical Dynamic Programming algorithm
// for longest Common Subsequence
for (int i = 0; i <= n; i++)
{
for (int j = 0; j <= n; j++)
{
if (i == 0 || j == 0)
L[i, j] = 0;
else if (seq[i - 1] == sortedseq[j - 1])
L[i, j] = L[i - 1, j - 1] + 1;
else
L[i,j] = Math.Max(L[i - 1, j],
L[i, j - 1]);
}
}
// Return the ans
return L[n, n];
}
// Driver code
public static void Main(String []args)
{
List<int> sequence = new List<int>();
sequence.Add(12);
sequence.Add(34);
sequence.Add(1);
sequence.Add(5);
sequence.Add(40);
sequence.Add(80);
Console.WriteLine(LISusingLCS(sequence));
}
}
// This code is contributed by 29AjayKumar
Javascript
<script>
//Javascript implementation of above approach
// Function to return the size of the
// longest increasing subsequence
function LISusingLCS(seq)
{
let n = seq.length;
// Create an 2D array of integer
// for tabulation
let L = new Array(n + 1);
for(let i = 0; i < (n + 1); i++)
{
L[i] = new Array(n + 1);
for(let j = 0; j < (n + 1); j++)
{
L[i][j] = 0;
}
}
// Take the second sequence as the sorted
// sequence of the given sequence
let sortedseq =[...seq];
sortedseq.sort(function(a,b){return a-b;});
// Classical Dynamic Programming algorithm
// for Longest Common Subsequence
for (let i = 0; i <= n; i++)
{
for (let j = 0; j <= n; j++)
{
if (i == 0 || j == 0)
L[i][j] = 0;
else if (seq[i - 1] == sortedseq[j - 1])
L[i][j] = L[i - 1][j - 1] + 1;
else
L[i][j] = Math.max(L[i - 1][j],
L[i][j - 1]);
}
}
// Return the ans
return L[n][n];
}
// Driver code
let sequence = [12, 34, 1, 5, 40, 80];
document.write(LISusingLCS(sequence));
// This code is contributed by patel2127
</script>
Output:
4
Time Complexity: O(n2) where n is the length of the sequenceAuxiliary Space: O(n2)
Efficient approach: Space Optimization
In previous approach the current value i.e. L[i][j] is depend no the current and previous row values. So to optimize the space complexity we can only keep track of the current and previous values of L[j] instead of the entire 2D array. This reduces the space complexity to O(n) instead of O(n^2).
Implementation Steps:
Create a vector L of size n+1 to store the values of the Longest Increasing Subsequence.
Create a copy of the original sequence called sortedseq and sort it in descending order and remove duplicates.
Use a nested for-loop, where the outer loop iterates through i from 1 to n and the inner loop iterates through j from 1 to m.
Use two variables prev and curr to store the left and top values of the current cell L[i][j].
If seq[i-1] and sortedseq[j-1] are equal, update L[j] with prev+1. else update L[j] with max(L[j], L[j-1]).
Update prev to curr at the end of each inner loop iteration.
Return the value at L[m] as the Longest Increasing Subsequence.
Implementation:
C++
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
//function to return size of array without duplicates
int removeDuplicates(vector<int> &arr)
{
int k = 0;
for (int i = 1; i < arr.size(); i++)
{
if (arr[i] != arr[k]) {
arr[++k] = arr[i];
}
}
return k + 1;
}
// Function to return the size of the
// longest increasing subsequence
int LISusingLCS(vector<int>& seq)
{
int n = seq.size();
// Create an veector of integer
// to store values
vector<int> L(n + 1);
// Take the second sequence as the sorted
// sequence of the given sequence
vector<int> sortedseq(seq);
sort(sortedseq.begin(), sortedseq.end());
//remove duplicates
int m = removeDuplicates(sortedseq);
// Classical Dynamic Programming algorithm
// for Longest Common Subsequence
for (int i = 1; i <= n; i++) {
int prev = 0;
for (int j = 1; j <= m; j++) {
int curr = L[j];
if (seq[i - 1] == sortedseq[j - 1])
L[j] = prev + 1;
else
L[j] = max(L[j], L[j - 1]);
prev = curr;
}
}
// Return the answer
return L[m];
}
// Driver code
int main()
{
vector<int> sequence{ 12, 34, 1, 5, 40, 80 };
// function call
cout << LISusingLCS(sequence) << endl;
return 0;
}
Java
// Java code addition
import java.io.*;
import java.util.*;
// Function to return size of array without duplicates
class GFG{
public static int removeDuplicates(int[] arr) {
int k = 0;
for (int i = 1; i < arr.length; i++) {
if (arr[i] != arr[k]) {
arr[++k] = arr[i];
}
}
return k + 1;
}
// Function to return the size of the longest increasing subsequence
public static int LISusingLCS(int[] seq) {
int n = seq.length;
// Create an array of integer to store values
int[] L = new int[n + 1];
// Take the second sequence as the sorted sequence of the given sequence
int[] sortedseq = seq.clone();
Arrays.sort(sortedseq);
// Remove duplicates
int m = removeDuplicates(sortedseq);
// Classical Dynamic Programming algorithm for Longest Common Subsequence
for (int i = 1; i <= n; i++) {
int prev = 0;
for (int j = 1; j <= m; j++) {
int curr = L[j];
if (seq[i - 1] == sortedseq[j - 1])
L[j] = prev + 1;
else
L[j] = Math.max(L[j], L[j - 1]);
prev = curr;
}
}
// Return the answer
return L[m];
}
// Driver code
public static void main(String[] args) {
int[] sequence = {12, 34, 1, 5, 40, 80};
// Function call
System.out.println(LISusingLCS(sequence));
}
}
// The code is contributed by Nidhi goel.
Python3
# Python implementation of the approach
# function to return size of array without duplicates
def removeDuplicates(arr):
k = 0
for i in range(1, len(arr)):
if arr[i] != arr[k]:
k += 1
arr[k] = arr[i]
return k + 1
# Function to return the size of the
# longest increasing subsequence
def LISusingLCS(seq):
n = len(seq)
# Create a list of integer to store values
L = [0] * (n + 1)
# Take the second sequence as the sorted
# sequence of the given sequence
sortedseq = sorted(seq)
# remove duplicates
m = removeDuplicates(sortedseq)
# Classical Dynamic Programming algorithm
# for Longest Common Subsequence
for i in range(1, n + 1):
prev = 0
for j in range(1, m + 1):
curr = L[j]
if seq[i - 1] == sortedseq[j - 1]:
L[j] = prev + 1
else:
L[j] = max(L[j], L[j - 1])
prev = curr
# Return the answer
return L[m]
# Driver code
if __name__ == '__main__':
sequence = [12, 34, 1, 5, 40, 80]
# function call
print(LISusingLCS(sequence))
C#
using System;
using System.Linq;
// Function to return size of array without duplicates
class GFG {
public static int RemoveDuplicates(int[] arr)
{
int k = 0;
for (int i = 1; i < arr.Length; i++) {
if (arr[i] != arr[k]) {
arr[++k] = arr[i];
}
}
return k + 1;
}
// Function to return the size of the longest increasing
// subsequence
public static int LISusingLCS(int[] seq)
{
int n = seq.Length;
// Create an array of integer to store values
int[] L = new int[n + 1];
// Take the second sequence as the sorted sequence
// of the given sequence
int[] sortedseq = seq.Clone() as int[];
Array.Sort(sortedseq);
// Remove duplicates
int m = RemoveDuplicates(sortedseq);
// Classical Dynamic Programming algorithm for
// Longest Common Subsequence
for (int i = 1; i <= n; i++) {
int prev = 0;
for (int j = 1; j <= m; j++) {
int curr = L[j];
if (seq[i - 1] == sortedseq[j - 1])
L[j] = prev + 1;
else
L[j] = Math.Max(L[j], L[j - 1]);
prev = curr;
}
}
// Return the answer
return L[m];
}
// Driver code
public static void Main(string[] args)
{
int[] sequence = { 12, 34, 1, 5, 40, 80 };
// Function call
Console.WriteLine(LISusingLCS(sequence));
}
}
Javascript
// Function to return size of array without duplicates
function removeDuplicates(arr) {
let k = 0;
for (let i = 1; i < arr.length; i++) {
if (arr[i] != arr[k]) {
arr[++k] = arr[i];
}
}
return k + 1;
}
// Function to return the size of the longest increasing subsequence
function LISusingLCS(seq) {
let n = seq.length;
// Create an array of integer to store values
let L = new Array(n + 1).fill(0);
// Take the second sequence as the sorted sequence of the given sequence
let sortedseq = [...seq];
sortedseq.sort((a, b) => a - b);
// Remove duplicates
let m = removeDuplicates(sortedseq);
// Classical Dynamic Programming algorithm for Longest Common Subsequence
for (let i = 1; i <= n; i++) {
let prev = 0;
for (let j = 1; j <= m; j++) {
let curr = L[j];
if (seq[i - 1] == sortedseq[j - 1])
L[j] = prev + 1;
else
L[j] = Math.max(L[j], L[j - 1]);
prev = curr;
}
}
// Return the answer
return L[m];
}
// Driver code
let sequence = [12, 34, 1, 5, 40, 80];
// Function call
console.log(LISusingLCS(sequence));
Output
4
Time Complexity: O(n^2) where n is the length of the sequenceAuxiliary Space: O(n) | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm | https://www.geeksforgeeks.org/longest-increasing-subsequence-using-longest-common-subsequence-algorithm/?ref=lbp | NLP | Longest Increasing Subsequence using Longest Common Subsequence Algorithm | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | 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04 Mar, 2025 | Longest Common Subsequence (LCS)
04 Mar, 2025
Try it on GfG Practice
Given two strings, s1 and s2, the task is to find the length of the Longest Common Subsequence. If there is no common subsequence, return 0. A subsequence is a string generated from the original string by deleting 0 or more characters, without changing the relative order of the remaining characters.
For example, subsequences of “ABC” are “”, “A”, “B”, “C”, “AB”, “AC”, “BC” and “ABC”. In general, a string of length n has 2n subsequences.
Examples:
Input: s1 = “ABC”, s2 = “ACD”Output: 2Explanation: The longest subsequence which is present in both strings is “AC”.
Input: s1 = “AGGTAB”, s2 = “GXTXAYB”Output: 4Explanation: The longest common subsequence is “GTAB”.
Input: s1 = “ABC”, s2 = “CBA”Output: 1Explanation: There are three longest common subsequences of length 1, “A”, “B” and “C”.
Table of Content
[Naive Approach] Using Recursion – O(2 ^ min(m, n)) Time and O(min(m, n)) Space[Better Approach] Using Memoization – O(m * n) Time and O(m * n) Space[Expected Approach 1] Using Bottom-Up DP (Tabulation) – O(m * n) Time and O(m * n) Space[Expected Approach 2] Using Bottom-Up DP (Space-Optimization):Applications of LCSProblems based on LCS[Naive Approach] Using Recursion – O(2 ^ min(m, n)) Time and O(min(m, n)) SpaceThe idea is to compare the last characters of s1 and s2. While comparing the strings s1 and s2 two cases arise:
Match : Make the recursion call for the remaining strings (strings of lengths m-1 and n-1) and add 1 to result.Do not Match : Make two recursive calls. First for lengths m-1 and n, and second for m and n-1. Take the maximum of two results. Base case : If any of the strings become empty, we return 0.
For example, consider the input strings s1 = “ABX” and s2 = “ACX”.
LCS(“ABX”, “ACX”) = 1 + LCS(“AB”, “AC”) [Last Characters Match]
LCS(“AB”, “AC”) = max( LCS(“A”, “AC”) , LCS(“AB”, “A”) ) [Last Characters Do Not Match]
LCS(“A”, “AC”) = max( LCS(“”, “AC”) , LCS(“A”, “A”) ) = max(0, 1 + LCS(“”, “”)) = 1
LCS(“AB”, “A”) = max( LCS(“A”, “A”) , LCS(“AB”, “”) ) = max( 1 + LCS(“”, “”, 0)) = 1
So overall result is 1 + 1 = 2
C++
// A Naive recursive implementation of LCS problem
#include <bits/stdc++.h>
using namespace std;
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
int lcsRec(string &s1, string &s2,int m,int n) {
// Base case: If either string is empty, the length of LCS is 0
if (m == 0 || n == 0)
return 0;
// If the last characters of both substrings match
if (s1[m - 1] == s2[n - 1])
// Include this character in LCS and recur for remaining substrings
return 1 + lcsRec(s1, s2, m - 1, n - 1);
else
// If the last characters do not match
// Recur for two cases:
// 1. Exclude the last character of s1
// 2. Exclude the last character of s2
// Take the maximum of these two recursive calls
return max(lcsRec(s1, s2, m, n - 1), lcsRec(s1, s2, m - 1, n));
}
int lcs(string &s1,string &s2){
int m = s1.size(), n = s2.size();
return lcsRec(s1,s2,m,n);
}
int main() {
string s1 = "AGGTAB";
string s2 = "GXTXAYB";
int m = s1.size();
int n = s2.size();
cout << lcs(s1, s2) << endl;
return 0;
}
C
// A Naive recursive implementation of LCS problem
#include <stdio.h>
#include <string.h>
int max(int x, int y) {
return x > y ? x : y;
}
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
int lcsRec(char s1[], char s2[], int m, int n) {
// Base case: If either string is empty, the length of LCS is 0
if (m == 0 || n == 0)
return 0;
// If the last characters of both substrings match
if (s1[m - 1] == s2[n - 1])
// Include this character in LCS and recur for remaining substrings
return 1 + lcsRec(s1, s2, m - 1, n - 1);
else
// If the last characters do not match
// Recur for two cases:
// 1. Exclude the last character of S1
// 2. Exclude the last character of S2
// Take the maximum of these two recursive calls
return max(lcsRec(s1, s2, m, n - 1), lcsRec(s1, s2, m - 1, n));
}
int lcs(char s1[],char s2[]){
int m = strlen(s1);
int n = strlen(s2);
return lcsRec(s1,s2,m,n);
}
int main() {
char s1[] = "AGGTAB";
char s2[] = "GXTXAYB";
printf("%d\n", lcs(s1, s2));
return 0;
}
Java
// A Naive recursive implementation of LCS problem
class GfG {
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
static int lcsRec(String s1, String s2, int m, int n) {
// Base case: If either string is empty, the length of LCS is 0
if (m == 0 || n == 0)
return 0;
// If the last characters of both substrings match
if (s1.charAt(m - 1) == s2.charAt(n - 1))
// Include this character in LCS and recur for remaining substrings
return 1 + lcsRec(s1, s2, m - 1, n - 1);
else
// If the last characters do not match
// Recur for two cases:
// 1. Exclude the last character of S1
// 2. Exclude the last character of S2
// Take the maximum of these two recursive calls
return Math.max(lcsRec(s1, s2, m, n - 1), lcsRec(s1, s2, m - 1, n));
}
static int lcs(String s1,String s2){
int m = s1.length(), n = s2.length();
return lcsRec(s1,s2,m,n);
}
public static void main(String[] args) {
String s1 = "AGGTAB";
String s2 = "GXTXAYB";
System.out.println(lcs(s1, s2));
}
}
Python
# A Naive recursive implementation of LCS problem
# Returns length of LCS for s1[0..m-1], s2[0..n-1]
def lcsRec(s1, s2, m, n):
# Base case: If either string is empty, the length of LCS is 0
if m == 0 or n == 0:
return 0
# If the last characters of both substrings match
if s1[m - 1] == s2[n - 1]:
# Include this character in LCS and recur for remaining substrings
return 1 + lcsRec(s1, s2, m - 1, n - 1)
else:
# If the last characters do not match
# Recur for two cases:
# 1. Exclude the last character of S1
# 2. Exclude the last character of S2
# Take the maximum of these two recursive calls
return max(lcsRec(s1, s2, m, n - 1), lcsRec(s1, s2, m - 1, n))
def lcs(s1,s2):
m = len(s1)
n = len(s2)
return lcsRec(s1,s2,m,n)
if __name__ == "__main__":
s1 = "AGGTAB"
s2 = "GXTXAYB"
print(lcs(s1, s2))
C#
// A Naive recursive implementation of LCS problem
using System;
class GfG {
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
static int lcsRec(string s1, string s2, int m, int n) {
// Base case: If either string is empty, the length of LCS is 0
if (m == 0 || n == 0)
return 0;
// If the last characters of both substrings match
if (s1[m - 1] == s2[n - 1])
// Include this character in LCS and recur for remaining substrings
return 1 + lcsRec(s1, s2, m - 1, n - 1);
else
// If the last characters do not match
// Recur for two cases:
// 1. Exclude the last character of S1
// 2. Exclude the last character of S2
// Take the maximum of these two recursive calls
return Math.Max(lcsRec(s1, s2, m, n - 1), lcsRec(s1, s2, m - 1, n));
}
static int lcs(string s1,string s2){
int m = s1.Length , n = s2.Length;
return lcsRec(s1,s2,m,n);
}
static void Main() {
string s1 = "AGGTAB";
string s2 = "GXTXAYB";
Console.WriteLine(lcs(s1, s2));
}
}
JavaScript
// A Naive recursive implementation of LCS problem
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
function lcsRec(s1, s2, m, n) {
// Base case: If either string is empty, the length of LCS is 0
if (m === 0 || n === 0)
return 0;
// If the last characters of both substrings match
if (s1[m - 1] === s2[n - 1])
// Include this character in LCS and recur for remaining substrings
return 1 + lcsRec(s1, s2, m - 1, n - 1);
else
return Math.max(lcsRec(s1, s2, m, n - 1), lcsRec(s1, s2, m - 1, n));
}
function lcs(s1,s2){
let m = s1.length;
let n = s2.length;
return lcsRec(s1,s2,m,n);
}
// driver code
let s1 = "AGGTAB";
let s2 = "GXTXAYB";
let m = s1.length;
let n = s2.length;
console.log(lcs(s1, s2, m, n));
Output4
[Better Approach] Using Memoization (Top Down DP) – O(m * n) Time and O(m * n) SpaceTo optimize the recursive solution, we use a 2D memoization table of size (m+1)×(n+1)(m+1) \times (n+1)(m+1)×(n+1), initialized to −1-1−1 to track computed values. Before making recursive calls, we check this table to avoid redundant computations of overlapping subproblems. This prevents repeated calculations, improving efficiency through memoization or tabulation.
Overlapping Subproblems in Longest Common Subsequence
C++
// C++ implementation of Top-Down DP
// of LCS problem
#include <bits/stdc++.h>
using namespace std;
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
int lcsRec(string &s1, string &s2, int m, int n, vector<vector<int>> &memo) {
// Base Case
if (m == 0 || n == 0)
return 0;
// Already exists in the memo table
if (memo[m][n] != -1)
return memo[m][n];
// Match
if (s1[m - 1] == s2[n - 1])
return memo[m][n] = 1 + lcsRec(s1, s2, m - 1, n - 1, memo);
// Do not match
return memo[m][n] = max(lcsRec(s1, s2, m, n - 1, memo), lcsRec(s1, s2, m - 1, n, memo));
}
int lcs(string &s1,string &s2){
int m = s1.length();
int n = s2.length();
vector<vector<int>> memo(m + 1, vector<int>(n + 1, -1));
return lcsRec(s1, s2, m, n, memo);
}
int main() {
string s1 = "AGGTAB";
string s2 = "GXTXAYB";
cout << lcs(s1, s2) << endl;
return 0;
}
C
// C implementation of Top-Down DP
// of LCS problem
#include <stdio.h>
#include <string.h>
// Define a maximum size for the strings
#define MAX 1000
// Function to find the maximum of two integers
int max(int a, int b) {
return (a > b) ? a : b;
}
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
int lcsRec(const char *s1, const char *s2, int m, int n, int memo[MAX][MAX]) {
// Base Case
if (m == 0 || n == 0) {
return 0;
}
// Already exists in the memo table
if (memo[m][n] != -1) {
return memo[m][n];
}
// Match
if (s1[m - 1] == s2[n - 1]) {
return memo[m][n] = 1 + lcsRec(s1, s2, m - 1, n - 1, memo);
}
// Do not match
return memo[m][n] = max(lcsRec(s1, s2, m, n - 1, memo), lcsRec(s1, s2, m - 1, n, memo));
}
int lcs(char s1[],char s2[]){
int m = strlen(s1);
int n = strlen(s2);
// Create memo table with fixed size
int memo[MAX][MAX];
for (int i = 0; i <= m; i++) {
for (int j = 0; j <= n; j++) {
// Initialize memo table with -1
memo[i][j] = -1;
}
}
return lcsRec(s1, s2, m, n, memo);
}
int main() {
const char *s1 = "AGGTAB";
const char *s2 = "GXTXAYB";
printf("%d\n", lcs(s1, s2));
return 0;
}
Java
// Java implementation of Top-Down DP of LCS problem
import java.util.Arrays;
class GfG {
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
static int lcsRec(String s1, String s2, int m, int n,
int[][] memo) {
// Base Case
if (m == 0 || n == 0)
return 0;
// Already exists in the memo table
if (memo[m][n] != -1)
return memo[m][n];
// Match
if (s1.charAt(m - 1) == s2.charAt(n - 1)) {
return memo[m][n]
= 1 + lcsRec(s1, s2, m - 1, n - 1, memo);
}
// Do not match
return memo[m][n]
= Math.max(lcsRec(s1, s2, m, n - 1, memo),
lcsRec(s1, s2, m - 1, n, memo));
}
static int lcs(String s1, String s2){
int m = s1.length();
int n = s2.length();
int[][] memo = new int[m + 1][n + 1];
// Initialize the memo table with -1
for (int i = 0; i <= m; i++) {
Arrays.fill(memo[i], -1);
}
return lcsRec(s1, s2, m, n, memo);
}
public static void main(String[] args) {
String s1 = "AGGTAB";
String s2 = "GXTXAYB";
System.out.println(lcs(s1, s2));
}
}
Python
def lcsRec(s1, s2, m, n, memo):
# Base Case
if m == 0 or n == 0:
return 0
# Already exists in the memo table
if memo[m][n] != -1:
return memo[m][n]
# Match
if s1[m - 1] == s2[n - 1]:
memo[m][n] = 1 + lcsRec(s1, s2, m - 1, n - 1, memo)
return memo[m][n]
# Do not match
memo[m][n] = max(lcsRec(s1, s2, m, n - 1, memo),
lcsRec(s1, s2, m - 1, n, memo))
return memo[m][n]
def lcs(s1, s2):
m = len(s1)
n = len(s2)
memo = [[-1 for _ in range(n + 1)] for _ in range(m + 1)]
return lcsRec(s1,s2,m,n,memo)
if __name__ == "__main__":
s1 = "AGGTAB"
s2 = "GXTXAYB"
print(lcs(s1, s2))
C#
// C# implementation of Top-Down DP of LCS problem
using System;
class GfG {
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
static int lcsRec(string s1, string s2, int m,
int n, int[, ] memo) {
// Base Case
if (m == 0 || n == 0)
return 0;
// Already exists in the memo table
if (memo[m, n] != -1)
return memo[m, n];
// Match
if (s1[m - 1] == s2[n - 1]) {
return memo[m, n]
= 1 + lcsRec(s1, s2, m - 1, n - 1, memo);
}
// Do not match
return memo[m, n]
= Math.Max(lcsRec(s1, s2, m, n - 1, memo),
lcsRec(s1, s2, m - 1, n, memo));
}
static int lcs(string s1,string s2){
int m = s1.Length;
int n = s2.Length;
int[, ] memo = new int[m + 1, n + 1];
// Initialize memo array with -1
for (int i = 0; i <= m; i++) {
for (int j = 0; j <= n; j++) {
memo[i, j] = -1;
}
}
return lcsRec(s1,s2,m,n,memo);
}
public static void Main() {
string s1 = "AGGTAB";
string s2 = "GXTXAYB";
Console.WriteLine(lcs(s1, s2));
}
}
JavaScript
// A Top-Down DP implementation of LCS problem
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
function lcsRec(s1, s2, m, n, memo)
{
// Base Case
if (m === 0 || n === 0)
return 0;
// Already exists in the memo table
if (memo[m][n] !== -1)
return memo[m][n];
// Match
if (s1[m - 1] === s2[n - 1]) {
memo[m][n] = 1 + lcsRec(s1, s2, m - 1, n - 1, memo);
return memo[m][n];
}
// Do not match
memo[m][n] = Math.max(lcsRec(s1, s2, m, n - 1, memo),
lcsRec(s1, s2, m - 1, n, memo));
return memo[m][n];
}
function lcs(s1, s2)
{
const m = s1.length;
const n = s2.length;
const memo = Array.from({length : m + 1},
() => Array(n + 1).fill(-1));
return lcsRec(s1, s2, m, n, memo);
}
// driver code
const s1 = "AGGTAB";
const s2 = "GS1TS1AS2B";
console.log(lcs(s1, s2));
Output4
[Expected Approach 1] Using Bottom-Up DP (Tabulation) – O(m * n) Time and O(m * n) SpaceThere are two parameters that change in the recursive solution and these parameters go from 0 to m and 0 to n. So we create a 2D dp array of size (m+1) x (n+1).
We first fill the known entries when m is 0 or n is 0.Then we fill the remaining entries using the recursive formula.Say the strings are S1 = “AXTY” and S2 = “AYZX”, Follow below :
C++
#include <iostream>
#include <vector>
using namespace std;
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
int lcs(string &s1, string &s2) {
int m = s1.size();
int n = s2.size();
// Initializing a matrix of size (m+1)*(n+1)
vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
// Building dp[m+1][n+1] in bottom-up fashion
for (int i = 1; i <= m; ++i) {
for (int j = 1; j <= n; ++j) {
if (s1[i - 1] == s2[j - 1])
dp[i][j] = dp[i - 1][j - 1] + 1;
else
dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
}
}
// dp[m][n] contains length of LCS for s1[0..m-1]
// and s2[0..n-1]
return dp[m][n];
}
int main() {
string s1 = "AGGTAB";
string s2 = "GXTXAYB";
cout << lcs(s1, s2) << endl;
return 0;
}
C
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
int max(int x, int y);
// Function to find length of LCS for s1[0..m-1], s2[0..n-1]
int lcs(const char *S1, const char *S2) {
int m = strlen(S1);
int n = strlen(S2);
// Initializing a matrix of size (m+1)*(n+1)
int dp[m + 1][n + 1];
// Building dp[m+1][n+1] in bottom-up fashion
for (int i = 0; i <= m; i++) {
for (int j = 0; j <= n; j++) {
if (i == 0 || j == 0)
dp[i][j] = 0;
else if (S1[i - 1] == S2[j - 1])
dp[i][j] = dp[i - 1][j - 1] + 1;
else
dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
}
}
return dp[m][n];
}
int max(int x, int y) {
return (x > y) ? x : y;
}
int main() {
const char *S1 = "AGGTAB";
const char *S2 = "GXTXAYB";
printf("%d\n", lcs(S1, S2));
return 0;
}
Java
import java.util.Arrays;
class GfG {
// Returns length of LCS for s1[0..m-1], s2[0..n-1]
static int lcs(String S1, String S2) {
int m = S1.length();
int n = S2.length();
// Initializing a matrix of size (m+1)*(n+1)
int[][] dp = new int[m + 1][n + 1];
// Building dp[m+1][n+1] in bottom-up fashion
for (int i = 1; i <= m; i++) {
for (int j = 1; j <= n; j++) {
if (S1.charAt(i - 1) == S2.charAt(j - 1)) {
dp[i][j] = dp[i - 1][j - 1] + 1;
}
else {
dp[i][j] = Math.max(dp[i - 1][j],
dp[i][j - 1]);
}
}
}
// dp[m][n] contains length of LCS for S1[0..m-1]
// and S2[0..n-1]
return dp[m][n];
}
public static void main(String[] args)
{
String S1 = "AGGTAB";
String S2 = "GXTXAYB";
System.out.println( lcs(S1, S2));
}
}
Python
def lcs(S1, S2):
m = len(S1)
n = len(S2)
# Initializing a matrix of size (m+1)*(n+1)
dp = [[0] * (n + 1) for x in range(m + 1)]
# Building dp[m+1][n+1] in bottom-up fashion
for i in range(1, m + 1):
for j in range(1, n + 1):
if S1[i - 1] == S2[j - 1]:
dp[i][j] = dp[i - 1][j - 1] + 1
else:
dp[i][j] = max(dp[i - 1][j],
dp[i][j - 1])
# dp[m][n] contains length of LCS for S1[0..m-1]
# and S2[0..n-1]
return dp[m][n]
if __name__ == "__main__":
S1 = "AGGTAB"
S2 = "GXTXAYB"
print(lcs(S1, S2))
C#
using System;
class GfG {
// Returns length of LCS for S1[0..m-1], S2[0..n-1]
static int lcs(string S1, string S2) {
int m = S1.Length;
int n = S2.Length;
// Initializing a matrix of size (m+1)*(n+1)
int[, ] dp = new int[m + 1, n + 1];
// Building dp[m+1][n+1] in bottom-up fashion
for (int i = 1; i <= m; i++) {
for (int j = 1; j <= n; j++) {
if (S1[i - 1] == S2[j - 1]) {
dp[i, j] = dp[i - 1, j - 1] + 1;
}
else {
dp[i, j] = Math.Max(dp[i - 1, j],
dp[i, j - 1]);
}
}
}
// dp[m, n] contains length of LCS for S1[0..m-1]
// and S2[0..n-1]
return dp[m, n];
}
static void Main() {
string S1 = "AGGTAB";
string S2 = "GXTXAYB";
Console.WriteLine(lcs(S1, S2));
}
}
JavaScript
function lcs(S1, S2) {
const m = S1.length;
const n = S2.length;
// Initializing a matrix of size (m+1)*(n+1)
const dp = Array.from({length : m + 1},
() => Array(n + 1).fill(0));
// Building dp[m+1][n+1] in bottom-up fashion
for (let i = 1; i <= m; i++) {
for (let j = 1; j <= n; j++) {
if (S1[i - 1] === S2[j - 1]) {
dp[i][j] = dp[i - 1][j - 1] + 1;
}
else {
dp[i][j]
= Math.max(dp[i - 1][j], dp[i][j - 1]);
}
}
}
// dp[m][n] contains length of LCS for
// S1[0..m-1] and S2[0..n-1]
return dp[m][n];
}
const S1 = "AGGTAB";
const S2 = "GXTXAYB";
console.log(lcs(S1, S2));
Output4
[Expected Approach 2] Using Bottom-Up DP (Space-Optimization):One important observation in the above simple implementation is, in each iteration of the outer loop we only need values from all columns of the previous row. So there is no need to store all rows in our DP matrix, we can just store two rows at a time and use them. We can further optimize to use only one array.
Please refer this post: A Space Optimized Solution of LCS
Applications of LCSLCS is used to implement diff utility (find the difference between two data sources). It is also widely used by revision control systems such as Git for multiple changes made to a revision-controlled collection of files.
Problems based on LCSLCS of 3 StringsPrinting LCSLongest Palindromic SubsequenceShortest Common SupersequenceMinimum Insertions and DeletionsEdit DistanceMinimum Insertions for PalindromeLongest Common SubstringLongest Palindromic SubstringLongest Repeated SubsequenceCount Distinct SubsequencesRegular Expression MatchingRelated Links: Print LCS of two Strings Dynamic Programming LCS and Edit Distance Dynamic Programming Practice Problems | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS) | https://www.geeksforgeeks.org/longest-common-subsequence/ | NLP | Longest Common Subsequence (LCS) | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [0.0231207293, 0.00362362666, -0.0168694, 0.0390095301, 0.0304292701, 0.00898628775, 0.0370789692, 0.0257407725, -0.0407255813, 0.00855727494, 0.0206692275, -0.0194741208, 0.0418287553, -0.0335242935, -0.012288155, 0.0138050215, 0.0227989703, 0.0226304289, -0.00321759656, -0.034045238, -0.00854195282, 0.0150077902, -0.021971589, 0.0188612454, 0.00858791824, 0.0286672544, 0.0198724903, 0.00649648067, -0.0121042924, 0.0126328971, 0.0471301302, 0.00186927046, 0.0180338621, -0.0157355797, 0.0080133481, -0.0356693566, -0.000409621105, 0.0426561385, -0.0298163947, 0.00938465726, -0.00177255098, 0.00773755368, -0.00408711378, -0.00844236091, 0.0131538417, 0.0123877469, 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-0.000282736728, 0.000547278731, 0.00140961376] |
06 Mar, 2025 | Minimum insertions to form a palindrome with permutations allowed
06 Mar, 2025
Given a string of lowercase letters. Find minimum characters to be inserted in the string so that it can become palindrome. We can change the positions of characters in the string.
Examples:
Input: geeksforgeeksOutput: 2Explanation: geeksforgeeks can be changed as: geeksroforskeeg or geeksorfroskeeg and many more using two insertion.Input: aabbcOutput: 0Explanation: aabbc can be changed as: abcba or bacab without any insertion
Table of Content
[Expected Approach] Character Frequency Counting – O(n) Time and O(1) Space[Alternate Approach] using Bit manipulation – O(n) Time and O(1) Space[Expected Approach] Character Frequency Counting – O(n) Time and O(1) SpaceTo make a string palindromic, count the occurrences of each character. A palindrome can have at most one character with an odd frequency; the rest must occur an even number of times. The minimum insertions required are one less than the count of characters with odd frequencies. If the string is already a palindrome, no insertions are needed (result = 0).
C++
#include <bits/stdc++.h>
using namespace std;
int minInsertion(string &str)
{
int n = str.length();
int res = 0;
vector<int> count(26,0);
for (int i = 0; i < n; i++)
count[str[i] - 'a']++;
for (int i = 0; i < 26; i++)
if (count[i] % 2 == 1)
res++;
return (res == 0) ? 0 : res - 1;
}
// Driver program
int main()
{
string str = "geeksforgeeks";
cout << minInsertion(str);
return 0;
}
Java
public class GfG {
static int minInsertion(String str)
{
int n = str.length();
int res = 0;
int[] count = new int[26];
for (int i = 0; i < n; i++)
count[str.charAt(i) - 'a']++;
for (int i = 0; i < 26; i++) {
if (count[i] % 2 == 1)
res++;
}
return (res == 0) ? 0 : res - 1;
}
// Driver program
public static void main(String[] args)
{
String str = "geeksforgeeks";
System.out.println(minInsertion(str));
}
}
Python
import math as mt
def minInsertion(tr1):
n = len(str1)
res = 0
count = [0 for i in range(26)]
for i in range(n):
count[ord(str1[i]) - ord('a')] += 1
for i in range(26):
if (count[i] % 2 == 1):
res += 1
if (res == 0):
return 0
else:
return res - 1
# Driver Code
str1 = "geeksforgeeks"
print(minInsertion(str1))
C#
using System;
public class GfG {
static int minInsertion(String str)
{
int n = str.Length;
int res = 0;
int[] count = new int[26];
for (int i = 0; i < n; i++)
count[str[i] - 'a']++;
for (int i = 0; i < 26; i++) {
if (count[i] % 2 == 1)
res++;
}
return (res == 0) ? 0 : res - 1;
}
// Driver program
public static void Main()
{
string str = "geeksforgeeks";
Console.WriteLine(minInsertion(str));
}
}
JavaScript
function minInsertion(str)
{
let n = str.length;
let res = 0;
let count = new Array(26);
for (let i = 0; i < count.length; i++) {
count[i] = 0;
}
for (let i = 0; i < n; i++)
count[str[i].charCodeAt(0) - "a".charCodeAt(0)]++;
for (let i = 0; i < 26; i++) {
if (count[i] % 2 == 1)
res++;
}
return (res == 0) ? 0 : res - 1;
}
let str = "geeksforgeeks";
console.log(minInsertion(str));
Output2[Alternate Approach] using Bit manipulation – O(n) Time and O(1) SpaceInitialize a mask to 0 and toggle bits for each character based on its position in the alphabet. If the mask becomes 0, the string is already a palindrome (return 0). Otherwise, the minimum insertions required are the number of set bits in the mask minus one.
C++
#include <bits/stdc++.h>
using namespace std;
int minInsertion(string &str)
{
long long mask = 0;
for (auto c : str)
mask ^= (1 << (c - 'a'));
if (mask == 0)
return 0;
int count = 0;
while (mask) {
count += mask & 1;
mask = mask >> 1;
}
return count - 1;
}
// Driver program
int main()
{
string str = "geeksforgeeks";
cout << minInsertion(str);
return 0;
}
// This code is contributed by hkdass001
Java
import java.util.*;
public class GfG {
static int minInsertion(String str)
{
long mask = 0;
for (char c : str.toCharArray())
mask ^= (1 << (c - 'a'));
if (mask == 0)
return 0;
int count = 0;
while (mask != 0) {
count += mask & 1;
mask = mask >> 1;
}
return count - 1;
}
// Driver program
public static void main(String[] args)
{
String str = "geeksforgeeks";
System.out.println(minInsertion(str));
}
}
// This code is contributed by Karandeep1234
Python
def minInsertion(str):
mask = 0
for c in str:
mask ^= (1 << (ord(c) - ord('a')))
if mask == 0:
return 0
count = 0
while mask:
count += mask & 1
mask = mask >> 1
return count - 1
str = "geeksforgeeks"
print(minInsertion(str))
C#
using System;
using System.Collections.Generic;
class GfG
{
static int minInsertion(string str)
{
int mask = 0;
foreach(char c in str)
mask ^= (1 << (c - 'a'));
if (mask == 0)
return 0;
int count = 0;
while (mask>0) {
count += mask & 1;
mask = mask >> 1;
}
return count - 1;
}
// Driver program
static void Main(string[] args)
{
string str = "geeksforgeeks";
Console.Write(minInsertion(str));
}
}
JavaScript
function minInsertion(str) {
let mask = 0;
for (let c of str) {
mask ^= (1 << (c.charCodeAt(0) - 'a'.charCodeAt(0)));
}
if (mask === 0) {
return 0;
}
let count = 0;
while (mask) {
count += mask & 1;
mask = mask >> 1;
}
// return the count minus 1
return count - 1;
}
// Driver program
let str = "geeksforgeeks";
console.log(minInsertion(str));
Output2 | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed | https://www.geeksforgeeks.org/minimum-insertions-to-form-a-palindrome-with-permutations-allowed/?ref=lbp | NLP | Minimum insertions to form a palindrome with permutations allowed | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion 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13 Mar, 2023 | Lexicographically first palindromic string
13 Mar, 2023
Rearrange the characters of the given string to form a lexicographically first palindromic string. If no such string exists display message “no palindromic string”. Examples:
Input : malayalam
Output : aalmymlaa
Input : apple
Output : no palindromic string
Simple Approach: 1. Sort the string characters in alphabetical(ascending) order. 2. One be one find lexicographically next permutation of the given string. 3. The first permutation which is palindrome is the answer.
Efficient Approach: Properties for palindromic string: 1. If length of string is even, then the frequency of each character in the string must be even. 2. If the length is odd then there should be one character whose frequency is odd and all other chars must have even frequency and at-least one occurrence of the odd character must be present in the middle of the string.
Algorithm 1. Store frequency of each character in the given string 2. Check whether a palindromic string can be formed or not using the properties of palindromic string mentioned above. 3. If palindromic string cannot be formed, return “No Palindromic String”. 4. Else we create three strings and then return front_str + odd_str + rear_str.
odd_str : It is empty if there is no character with odd frequency. Else it contains all occurrences of odd character.
front_str : Contains half occurrences of all even occurring characters of string in increasing order.
rear_str Contains half occurrences of all even occurring characters of string in reverse order of front_str.
Below is implementation of above steps.
C++
// C++ program to find first palindromic permutation
// of given string
#include <bits/stdc++.h>
using namespace std;
const char MAX_CHAR = 26;
// Function to count frequency of each char in the
// string. freq[0] for 'a',...., freq[25] for 'z'
void countFreq(string str, int freq[], int len)
{
for (int i=0; i<len; i++)
freq[str.at(i) - 'a']++;
}
// Cases to check whether a palindr0mic
// string can be formed or not
bool canMakePalindrome(int freq[], int len)
{
// count_odd to count no of
// chars with odd frequency
int count_odd = 0;
for (int i=0; i<MAX_CHAR; i++)
if (freq[i]%2 != 0)
count_odd++;
// For even length string
// no odd freq character
if (len%2 == 0)
{
if (count_odd > 0)
return false;
else
return true;
}
// For odd length string
// one odd freq character
if (count_odd != 1)
return false;
return true;
}
// Function to find odd freq char and
// reducing its freq by 1returns "" if odd freq
// char is not present
string findOddAndRemoveItsFreq(int freq[])
{
string odd_str = "";
for (int i=0; i<MAX_CHAR; i++)
{
if (freq[i]%2 != 0)
{
freq[i]--;
odd_str = odd_str + (char)(i+'a');
return odd_str;
}
}
return odd_str;
}
// To find lexicographically first palindromic
// string.
string findPalindromicString(string str)
{
int len = str.length();
int freq[MAX_CHAR] = {0};
countFreq(str, freq, len);
if (!canMakePalindrome(freq, len))
return "No Palindromic String";
// Assigning odd freq character if present
// else empty string.
string odd_str = findOddAndRemoveItsFreq(freq);
string front_str = "", rear_str = " ";
// Traverse characters in increasing order
for (int i=0; i<MAX_CHAR; i++)
{
string temp = "";
if (freq[i] != 0)
{
char ch = (char)(i + 'a');
// Divide all occurrences into two
// halves. Note that odd character
// is removed by findOddAndRemoveItsFreq()
for (int j=1; j<=freq[i]/2; j++)
temp = temp + ch;
// creating front string
front_str = front_str + temp;
// creating rear string
rear_str = temp + rear_str;
}
}
// Final palindromic string which is
// lexicographically first
return (front_str + odd_str + rear_str);
}
// Driver program
int main()
{
string str = "malayalam";
cout << findPalindromicString(str);
return 0;
}
Java
// Java program to find first palindromic permutation
// of given string
class GFG {
static char MAX_CHAR = 26;
// Function to count frequency of each char in the
// string. freq[0] for 'a',...., freq[25] for 'z'
static void countFreq(String str, int freq[], int len)
{
for (int i = 0; i < len; i++)
{
freq[str.charAt(i) - 'a']++;
}
}
// Cases to check whether a palindr0mic
// string can be formed or not
static boolean canMakePalindrome(int freq[], int len)
{
// count_odd to count no of
// chars with odd frequency
int count_odd = 0;
for (int i = 0; i < MAX_CHAR; i++)
{
if (freq[i] % 2 != 0)
{
count_odd++;
}
}
// For even length string
// no odd freq character
if (len % 2 == 0)
{
if (count_odd > 0)
{
return false;
}
else
{
return true;
}
}
// For odd length string
// one odd freq character
if (count_odd != 1)
{
return false;
}
return true;
}
// Function to find odd freq char and
// reducing its freq by 1returns "" if odd freq
// char is not present
static String findOddAndRemoveItsFreq(int freq[])
{
String odd_str = "";
for (int i = 0; i < MAX_CHAR; i++)
{
if (freq[i] % 2 != 0)
{
freq[i]--;
odd_str = odd_str + (char) (i + 'a');
return odd_str;
}
}
return odd_str;
}
// To find lexicographically first palindromic
// string.
static String findPalindromicString(String str)
{
int len = str.length();
int freq[] = new int[MAX_CHAR];
countFreq(str, freq, len);
if (!canMakePalindrome(freq, len))
{
return "No Palindromic String";
}
// Assigning odd freq character if present
// else empty string.
String odd_str = findOddAndRemoveItsFreq(freq);
String front_str = "", rear_str = " ";
// Traverse characters in increasing order
for (int i = 0; i < MAX_CHAR; i++)
{
String temp = "";
if (freq[i] != 0)
{
char ch = (char) (i + 'a');
// Divide all occurrences into two
// halves. Note that odd character
// is removed by findOddAndRemoveItsFreq()
for (int j = 1; j <= freq[i] / 2; j++)
{
temp = temp + ch;
}
// creating front string
front_str = front_str + temp;
// creating rear string
rear_str = temp + rear_str;
}
}
// Final palindromic string which is
// lexicographically first
return (front_str + odd_str + rear_str);
}
// Driver program
public static void main(String[] args)
{
String str = "malayalam";
System.out.println(findPalindromicString(str));
}
}
// This code is contributed by Rajput-Ji
Python3
# Python3 program to find first palindromic permutation
# of given string
MAX_CHAR = 26;
# Function to count frequency of each char in the
# string. freq[0] for 'a',...., freq[25] for 'z'
def countFreq(str1, freq, len1):
for i in range(len1):
freq[ord(str1[i]) - ord('a')] += 1;
# Cases to check whether a palindr0mic
# string can be formed or not
def canMakePalindrome(freq, len1):
# count_odd to count no of
# chars with odd frequency
count_odd = 0;
for i in range(MAX_CHAR):
if (freq[i] % 2 != 0):
count_odd += 1;
# For even length string
# no odd freq character
if (len1 % 2 == 0):
if (count_odd > 0):
return False;
else:
return True;
# For odd length string
# one odd freq character
if (count_odd != 1):
return False;
return True;
# Function to find odd freq char and
# reducing its freq by 1returns "" if odd freq
# char is not present
def findOddAndRemoveItsFreq(freq):
odd_str = "";
for i in range(MAX_CHAR):
if (freq[i]%2 != 0):
freq[i]-=1;
odd_str += chr(i+ord('a'));
return odd_str;
return odd_str;
# To find lexicographically first palindromic
# string.
def findPalindromicString(str1):
len1 = len(str1);
freq=[0]*MAX_CHAR;
countFreq(str1, freq, len1);
if (canMakePalindrome(freq, len1) == False):
return "No Palindromic String";
# Assigning odd freq character if present
# else empty string.
odd_str = findOddAndRemoveItsFreq(freq);
front_str = "";
rear_str = " ";
# Traverse characters in increasing order
for i in range(MAX_CHAR):
temp = "";
if (freq[i] != 0):
ch = chr(i + ord('a'));
# Divide all occurrences into two
# halves. Note that odd character
# is removed by findOddAndRemoveItsFreq()
for j in range(1,int(freq[i]/2)+1):
temp += ch;
# creating front string
front_str += temp;
# creating rear string
rear_str = temp+rear_str;
# Final palindromic string which is
# lexicographically first
return (front_str + odd_str+rear_str);
# Driver code
str1 = "malayalam";
print(findPalindromicString(str1));
# This code is contributed by mits
C#
// C# program to find first palindromic permutation
// of given string
using System;
class GFG
{
static int MAX_CHAR = 26;
// Function to count frequency of each char in the
// string. freq[0] for 'a',...., freq[25] for 'z'
static void countFreq(string str, int[] freq, int len)
{
for (int i = 0; i < len; i++)
{
freq[str[i] - 'a']++;
}
}
// Cases to check whether a palindr0mic
// string can be formed or not
static bool canMakePalindrome(int[] freq, int len)
{
// count_odd to count no of
// chars with odd frequency
int count_odd = 0;
for (int i = 0; i < MAX_CHAR; i++)
{
if (freq[i] % 2 != 0)
{
count_odd++;
}
}
// For even length string
// no odd freq character
if (len % 2 == 0)
{
if (count_odd > 0)
{
return false;
}
else
{
return true;
}
}
// For odd length string
// one odd freq character
if (count_odd != 1)
{
return false;
}
return true;
}
// Function to find odd freq char and
// reducing its freq by 1returns "" if odd freq
// char is not present
static string findOddAndRemoveItsFreq(int[] freq)
{
string odd_str = "";
for (int i = 0; i < MAX_CHAR; i++)
{
if (freq[i] % 2 != 0)
{
freq[i]--;
odd_str = odd_str + (char) (i + 'a');
return odd_str;
}
}
return odd_str;
}
// To find lexicographically first
// palindromic string.
static string findPalindromicString(string str)
{
int len = str.Length;
int[] freq = new int[MAX_CHAR];
countFreq(str, freq, len);
if (!canMakePalindrome(freq, len))
{
return "No Palindromic String";
}
// Assigning odd freq character if present
// else empty string.
string odd_str = findOddAndRemoveItsFreq(freq);
string front_str = "", rear_str = " ";
// Traverse characters in increasing order
for (int i = 0; i < MAX_CHAR; i++)
{
String temp = "";
if (freq[i] != 0)
{
char ch = (char) (i + 'a');
// Divide all occurrences into two
// halves. Note that odd character
// is removed by findOddAndRemoveItsFreq()
for (int j = 1; j <= freq[i] / 2; j++)
{
temp = temp + ch;
}
// creating front string
front_str = front_str + temp;
// creating rear string
rear_str = temp + rear_str;
}
}
// Final palindromic string which is
// lexicographically first
return (front_str + odd_str + rear_str);
}
// Driver code
public static void Main()
{
string str = "malayalam";
Console.Write(findPalindromicString(str));
}
}
// This code is contributed by Ita_c.
PHP
<?php
// PHP program to find first palindromic permutation
// of given string
$MAX_CHAR = 26;
// Function to count frequency of each char in the
// string. freq[0] for 'a',...., freq[25] for 'z'
function countFreq($str, &$freq, $len)
{
for ($i = 0; $i < $len; $i++)
$freq[ord($str[$i]) - ord('a')]++;
}
// Cases to check whether a palindr0mic
// string can be formed or not
function canMakePalindrome($freq, $len)
{
global $MAX_CHAR;
// count_odd to count no of
// chars with odd frequency
$count_odd = 0;
for ($i = 0; $i < $MAX_CHAR; $i++)
if ($freq[$i] % 2 != 0)
$count_odd++;
// For even length string
// no odd freq character
if ($len % 2 == 0)
{
if ($count_odd > 0)
return false;
else
return true;
}
// For odd length string
// one odd freq character
if ($count_odd != 1)
return false;
return true;
}
// Function to find odd freq char and
// reducing its freq by 1returns "" if odd freq
// char is not present
function findOddAndRemoveItsFreq($freq)
{
global $MAX_CHAR;
$odd_str = "";
for ($i = 0; $i < $MAX_CHAR; $i++)
{
if ($freq[$i] % 2 != 0)
{
$freq[$i]--;
$odd_str .= chr($i+ord('a'));
return $odd_str;
}
}
return $odd_str;
}
// To find lexicographically first palindromic
// string.
function findPalindromicString($str)
{
global $MAX_CHAR;
$len = strlen($str);
$freq=array_fill(0, $MAX_CHAR, 0);
countFreq($str, $freq, $len);
if (!canMakePalindrome($freq, $len))
return "No Palindromic String";
// Assigning odd freq character if present
// else empty string.
$odd_str = findOddAndRemoveItsFreq($freq);
$front_str = "";
$rear_str = " ";
// Traverse characters in increasing order
for ($i = 0; $i < $MAX_CHAR; $i++)
{
$temp = "";
if ($freq[$i] != 0)
{
$ch = chr($i + ord('a'));
// Divide all occurrences into two
// halves. Note that odd character
// is removed by findOddAndRemoveItsFreq()
for ($j = 1; $j <= (int)($freq[$i]/2); $j++)
$temp .= $ch;
// creating front string
$front_str .= $temp;
// creating rear string
$rear_str = $temp.$rear_str;
}
}
// Final palindromic string which is
// lexicographically first
return ($front_str.$odd_str.$rear_str);
}
// Driver code
$str = "malayalam";
echo findPalindromicString($str);
// This code is contributed by mits
?>
Javascript
// JavaScript program to find first palindromic permutation
// of given string
const MAX_CHAR = 26;
// Function to count frequency of each char in the
// string. freq[0] for 'a',...., freq[25] for 'z'
function countFreq(str, freq, len) {
for (let i = 0; i < len; i++) {
freq[str.charCodeAt(i) - 'a'.charCodeAt()]++;
}
}
// Cases to check whether a palindr0mic
// string can be formed or not
function canMakePalindrome(freq, len) {
// count_odd to count no of
// chars with odd frequency
let count_odd = 0;
for (let i = 0; i < MAX_CHAR; i++) {
if (freq[i] % 2 !== 0) {
count_odd++;
}
}
// For even length string
// no odd freq character
if (len % 2 === 0) {
if (count_odd > 0) {
return false;
} else {
return true;
}
}
// For odd length string
// one odd freq character
if (count_odd !== 1) {
return false;
}
return true;
}
// Function to find odd freq char and
// reducing its freq by 1returns "" if odd freq
// char is not present
function findOddAndRemoveItsFreq(freq) {
let odd_str = "";
for (let i = 0; i < MAX_CHAR; i++) {
if (freq[i] % 2 !== 0) {
freq[i]--;
odd_str = odd_str + String.fromCharCode(i + 'a'.charCodeAt());
return odd_str;
}
}
return odd_str;
}
// To find lexicographically first
// palindromic string.
function findPalindromicString(str) {
const len = str.length;
const freq = new Array(MAX_CHAR).fill(0);
countFreq(str, freq, len);
if (!canMakePalindrome(freq, len)) {
return "No Palindromic String";
}
// Assigning odd freq character if present
// else empty string.
let odd_str = findOddAndRemoveItsFreq(freq);
let front_str = "",
rear_str = " ";
// Traverse characters in increasing order
for (let i = 0; i < MAX_CHAR; i++) {
let temp = "";
if (freq[i] !== 0) {
const ch = String.fromCharCode(i + 'a'.charCodeAt());
// Divide all occurrences into two
// halves. Note that odd character
// is removed by findOddAndRemoveItsFreq()
for (let j = 1; j <= freq[i] / 2; j++) {
temp = temp + ch;
}
// creating front string
front_str = front_str + temp;
// creating rear string
rear_str = temp + rear_str;
}
}
// Final palindromic string which is
// lexicographically first
return (front_str + odd_str + rear_str);
}
// Driver code
const str = "malayalam";
console.log(findPalindromicString(str));
// This code is contributed by phasing17.
Output
aalmymlaa
Time Complexity : O(n) where n is length of input string. Assuming that size of string alphabet is constant. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Lexicographically first palindromic string | https://www.geeksforgeeks.org/lexicographically-first-palindromic-string/?ref=lbp | NLP | Lexicographically first palindromic string | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, Longest subsequence such that difference between adjacents is one, Lexicographically first palindromic string, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of 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22 Nov, 2022 | Count palindrome words in a sentence
22 Nov, 2022
Given a string str and the task is to count palindrome words present in the string str.
Examples:
Input : Madam Arora teaches malayalam
Output : 3
The string contains three palindrome words (i.e.,
Madam, Arora, malayalam) so the count is three.
Input : Nitin speaks malayalam
Output : 2
The string contains two palindrome words (i.e.,
Nitin, malayalam) so the count is two.
Method 1:countPalin() function counts the number of palindrome words by extracting every word of the string and passing it to checkPalin() function. An extra space is added in the original string to extract last word. checkPalin() function check the word palindrome. It returns 1 if word is palindrome else returns 0. It makes sure that empty strings are not counted as palindrome as the user may enter more than one spaces in between or at the beginning of the string.
C++
/*C++ program to count number of palindrome
words in a sentence*/
#include <bits/stdc++.h>
using namespace std;
// Function to check if a word is
// palindrome
bool checkPalin(string word)
{
int n = word.length();
transform(word.begin(), word.end(), word.begin(), ::tolower);
for (int i = 0; i < n; i++,n--)
if (word.at(i) != word.at(n - 1))
return false;
return true;
}
// Function to count palindrome words
int countPalin(string str)
{
// to check last word for palindrome
str = str + " ";
// to store each word
string word = "";
int count = 0;
for (int i = 0; i < str.length(); i++)
{
char ch = str.at(i);
// extracting each word
if (ch != ' ')
word = word + ch;
else {
if (checkPalin(word))
count++;
word = "";
}
}
return count;
}
// Driver code
int main()
{
cout<<countPalin("Madam Arora teaches malayalam")<<endl;
cout<<countPalin("Nitin speaks malayalam")<<endl;
}
// This code is contributed by nidhi16bcs2007
Java
/*Java program to count number of palindrome
words in a sentence*/
class GFG {
// Function to check if a word is
// palindrome
static boolean checkPalin(String word)
{
int n = word.length();
word = word.toLowerCase();
for (int i=0; i<n; i++,n--)
if (word.charAt(i) != word.charAt(n - 1))
return false;
return true;
}
// Function to count palindrome words
static int countPalin(String str)
{
// to check last word for palindrome
str = str + " ";
// to store each word
String word = "";
int count = 0;
for (int i = 0; i < str.length(); i++)
{
char ch = str.charAt(i);
// extracting each word
if (ch != ' ')
word = word + ch;
else {
if (checkPalin(word))
count++;
word = "";
}
}
return count;
}
// Driver code
public static void main(String args[])
{
System.out.println(countPalin("Madam "
+ "Arora teaches malayalam"));
System.out.println(countPalin("Nitin "
+ "speaks malayalam"));
}
}
Python3
# Python3 program to count number of
# palindrome words in a sentence
# Function to check if a word is palindrome
def checkPalin(word):
if word.lower() == word.lower()[::-1]:
return True
# Function to count palindrome words
def countPalin(str):
count = 0
# splitting each word as spaces as
# delimiter and storing it into a list
listOfWords = str.split(" ")
# Iterating every element from list
# and checking if it is a palindrome.
for elements in listOfWords:
if (checkPalin(elements)):
# if the word is a palindrome
# increment the count.
count += 1
print (count)
# Driver code
countPalin("Madam Arora teaches malayalam")
countPalin("Nitin speaks malayalam")
# This code is contributed
# by Ronit Shrivastava.
C#
// C# program to count number of
// palindrome words in a sentence
using System;
class GFG
{
// Function to check if a word is
// palindrome
public static bool checkPalin(string word)
{
int n = word.Length;
word = word.ToLower();
for (int i = 0; i < n; i++,n--)
{
if (word[i] != word[n - 1])
{
return false;
}
}
return true;
}
// Function to count palindrome words
public static int countPalin(string str)
{
// to check last word for palindrome
str = str + " ";
// to store each word
string word = "";
int count = 0;
for (int i = 0; i < str.Length; i++)
{
char ch = str[i];
// extracting each word
if (ch != ' ')
{
word = word + ch;
}
else
{
if (checkPalin(word))
{
count++;
}
word = "";
}
}
return count;
}
// Driver code
public static void Main(string[] args)
{
Console.WriteLine(countPalin("Madam " +
"Arora teaches malayalam"));
Console.WriteLine(countPalin("Nitin " +
"speaks malayalam"));
}
}
// This code is contributed by Shrikant13
Javascript
<script>
/*Javascript program to count number of palindrome
words in a sentence*/
// Function to check if a word is
// palindrome
function checkPalin(word)
{
var n = word.length
word = word.toLowerCase();
for (var i = 0; i < n; i++,n--)
if (word[i] != word[n - 1])
return false;
return true;
}
// Function to count palindrome words
function countPalin( str)
{
// to check last word for palindrome
str = str + " ";
// to store each word
var word = "";
var count = 0;
for (var i = 0; i < str.length; i++)
{
var ch = str[i];
// extracting each word
if (ch != ' ')
word = word + ch;
else {
if (checkPalin(word))
count++;
word = "";
}
}
return count;
}
// Driver code
document.write( countPalin("Madam Arora teaches malayalam") + "<br>");
document.write( countPalin("Nitin speaks malayalam"));
// This code is contributed by itsok.
</script>
Output:
3
2
Time Complexity: O(n2), where n is the size of the given string.Auxiliary Space: O(n), where n is the size of the given string.
https://youtu.be/z
-5HChTA0ME | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Count palindrome words in a sentence | https://www.geeksforgeeks.org/java-program-count-number-palindrome-words-sentence/?ref=lbp | NLP | Count palindrome words in a sentence | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Count palindrome words in a sentence, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0116362898, 0.0195772257, -0.012628057, 0.022783488, 0.0087696733, 0.0270358622, -0.0088376021, 0.0166290924, -0.0151210632, -0.0122952042, 0.0060049505, 0.0268049035, 0.0206912663, -0.0259489939, -0.0275385398, -0.0170774274, -0.00381423044, 0.0108958604, -0.00507092243, 0.000541736197, -0.0042116167, 0.00424558157, -0.0362199023, 0.0168057103, -0.00414708396, 0.0344265699, 0.0339646526, 0.0123291686, 0.0309757628, -0.0131714921, 0.00765563222, -0.0192647502, -0.00760808168, -0.00573662948, -0.00847757701, -0.0108415168, 0.0351058617, 0.0130628049, 0.0108143445, -0.0288020242, 0.00961878896, 0.0199440438, -0.0137556838, -0.0293726306, -0.0104271481, -0.00308399042, -0.0159498, -0.0332853571, -0.0148629313, -0.027552126, 0.0152025782, -0.00898025371, 0.0111539913, 0.0333940461, 0.0335027315, -0.0110249259, 0.00266622519, -0.0321713164, 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11 Apr, 2023 | Print longest palindrome word in a sentence
11 Apr, 2023
Given a string str, the task is to print longest palindrome word present in the string str.Examples:
Input : Madam Arora teaches Malayalam Output: Malayalam Explanation: The string contains three palindrome words (i.e., Madam, Arora, Malayalam) but the length of Malayalam is greater than the other two.Input : Welcome to GeeksforGeeks Output : No Palindrome Word Explanation:The string does not contain any palindrome word so the output is No Palindrome Word.
Approach:
longestPalin() function finds the longest palindrome word by extracting every word of the string and passing it to checkPalin() function. An extra space is added in the original string to extract last word.
checkPalin() function checks if the word is palindrome. It returns true if word is palindrome else returns false. It makes sure that empty strings are not counted as palindrome as the user may enter more than one spaces in between or at the beginning of the string.
C++
/* C++ program to print longest palindrome
word in a sentence and its length*/
#include <iostream>
#include <algorithm>
#include <string>
using namespace std;
// Function to check if a
// word is palindrome
bool checkPalin(string word)
{
int n = word.length();
// making the check case
// case insensitive
// word = word.toLowerCase();
transform(word.begin(), word.end(),
word.begin(), ::tolower);
// loop to check palindrome
for (int i = 0; i < n; i++, n--)
if (word[i] != word[n - 1])
return false;
return true;
}
// Function to find longest
// palindrome word
string longestPalin(string str)
{
// to check last word for palindrome
str = str + " ";
// to store each word
string longestword = "", word = "";
int length, length1 = 0;
for (int i = 0; i < str.length(); i++)
{
char ch = str[i];
// extracting each word
if (ch != ' ')
word = word + ch;
else {
length = word.length();
if (checkPalin(word) &&
length > length1)
{
length1 = length;
longestword = word;
}
word = "";
}
}
return longestword;
}
// Driver code
int main()
{
string s = "My name is ava and i love"
" Geeksforgeeks";
if (longestPalin(s) == "")
cout<<"No Palindrome"<<" Word";
else
cout<<longestPalin(s);
return 0;
}
// This code is contributed by Manish
// Shaw (manishshaw1)
Java
/*Java program to print longest palindrome
word in a sentence and its length*/
public class GFG {
// Function to check if a
// word is palindrome
static boolean checkPalin(String word)
{
int n = word.length();
// making the check case
// case insensitive
word = word.toLowerCase();
// loop to check palindrome
for (int i = 0; i < n; i++, n--)
if (word.charAt(i) !=
word.charAt(n - 1))
return false;
return true;
}
// Function to find longest
// palindrome word
static String longestPalin(String str)
{
// to check last word for palindrome
str = str + " ";
// to store each word
String longestword = "", word = "";
int length, length1 = 0;
for (int i = 0; i < str.length(); i++)
{
char ch = str.charAt(i);
// extracting each word
if (ch != ' ')
word = word + ch;
else {
length = word.length();
if (checkPalin(word) &&
length > length1)
{
length1 = length;
longestword = word;
}
word = "";
}
}
return longestword;
}
// Driver code
public static void main(String args[])
{
String s = new String("My name is ava "
+ "and i love Geeksforgeeks");
if (longestPalin(s) == "")
System.out.println("No Palindrome"
+ " Word");
else
System.out.println(longestPalin(s));
}
}
Python3
# Python 3 program to print longest palindrome
# word in a sentence and its length
# Function to check if a word is palindrome
def checkPalin(word):
n = len(word)
# making the check case
# case insensitive
word = word.lower()
# loop to check palindrome
for i in range( n):
if (word[i] != word[n - 1]):
return False
n -= 1
return True
# Function to find longest
# palindrome word
def longestPalin(str):
# to check last word for palindrome
str = str + " "
# to store each word
longestword = ""
word = ""
length1 = 0
for i in range(len(str)):
ch = str[i]
# extracting each word
if (ch != ' '):
word = word + ch
else :
length = len(word)
if (checkPalin(word) and
length > length1):
length1 = length
longestword = word
word = ""
return longestword
# Driver code
if __name__ == "__main__":
s = "My name is ava and i love Geeksforgeeks"
if (longestPalin(s) == ""):
print("No Palindrome Word")
else:
print(longestPalin(s))
# This code is contributed by ita_c
Javascript
<script>
/*Javascript program to print longest palindrome
word in a sentence and its length*/
// Function to check if a
// word is palindrome
function checkPalin(word)
{
let n = word.length;
// making the check case
// case insensitive
word = word.toLowerCase();
// loop to check palindrome
for (let i = 0; i < n; i++, n--)
if (word[i] !=
word[n-1])
return false;
return true;
}
// Function to find longest
// palindrome word
function longestPalin(str)
{
// to check last word for palindrome
str = str + " ";
// to store each word
let longestword = "", word = "";
let length, length1 = 0;
for (let i = 0; i < str.length; i++)
{
let ch = str[i];
// extracting each word
if (ch != ' ')
word = word + ch;
else {
length = word.length;
if (checkPalin(word) &&
length > length1)
{
length1 = length;
longestword = word;
}
word = "";
}
}
return longestword;
}
// Driver code
let s="My name is ava "
+ "and i love Geeksforgeeks";
if (longestPalin(s) == "")
document.write("No Palindrome"
+ " Word");
else
document.write(longestPalin(s));
// This code is contributed by rag2127
</script>
C#
/* C# program to print longest palindrome
word in a sentence and its length*/
using System;
class GFG
{
// Function to check if a
// word is palindrome
static bool checkPalin(string word)
{
int n = word.Length;
// making the check case
// case insensitive
word = word.ToLower();
// loop to check palindrome
for (int i = 0; i < n; i++, n--)
if (word[i] != word[n - 1])
return false;
return true;
}
// Function to find longest
// palindrome word
static string longestPalin(string str)
{
// to check last word for palindrome
str = str + " ";
// to store each word
string longestword = "", word = "";
int length, length1 = 0;
for (int i = 0; i < str.Length; i++)
{
char ch = str[i];
// extracting each word
if (ch != ' ')
word = word + ch;
else {
length = word.Length;
if (checkPalin(word) &&
length > length1)
{
length1 = length;
longestword = word;
}
word = "";
}
}
return longestword;
}
// Driver code
public static void Main()
{
string s = "My name is ava and i"
+ " love Geeksforgeeks";
if (longestPalin(s) == "")
Console.Write("No Palindrome Word");
else
Console.Write(longestPalin(s));
}
}
// This code is contributed by Manish
// Shaw (manishshaw1)
Output:
ava
Time complexity : O(n^2)
Space complexity : O(n)
Method #2:Using sorted() method in Python:
The idea is to split the words of the string into a list .
Traverse the list and append all palindromic words to new list
Sort the newlist in increasing order of length of words using the sorted() method.
Finally, print the last string present in the list.
Below is the implementation of the above approach.:
C++
// C++ program for the above approach
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
bool isPalindrome(string s) {
return s == string(s.rbegin(), s.rend());
}
void largestPalin(vector<string> s) {
// Taking new list
vector<string> newlist;
// Traverse the list
for (string word : s) {
if (isPalindrome(word)) {
newlist.push_back(word);
}
}
// Using sorted() method
sort(newlist.begin(), newlist.end(), [](string a, string b) { return a.size() < b.size(); });
// Print last word
cout << newlist.back() << endl;
}
// Driver Code
int main() {
// Given string
string str = "My name is ava and i love Geeksforgeeks";
vector<string> words;
string word;
for (char c : str) {
if (c == ' ') {
words.push_back(word);
word.clear();
} else {
word += c;
}
}
if (!word.empty()) {
words.push_back(word);
}
largestPalin(words);
return 0;
}
// This code is contributed by Prajwal Kandekar
Java
import java.util.ArrayList;
import java.util.Collections;
public class Main {
// Function to check if a string is a palindrome
public static boolean isPalindrome(String s)
{
return s.equals(
new StringBuilder(s).reverse().toString());
}
// Function to find the largest palindrome in a list of
// words
public static void largestPalin(ArrayList<String> s)
{
// Create a new list to store all the palindromes
// found
ArrayList<String> newlist = new ArrayList<>();
// Iterate over each word in the input list
for (String word : s) {
// Check if the current word is a palindrome
if (isPalindrome(word)) {
// If it is, add it to the new list
newlist.add(word);
}
}
// Sort the new list in ascending order of length
Collections.sort(newlist,
(a, b) -> a.length() - b.length());
// Print the largest palindrome (last element in the
// sorted list)
System.out.println(newlist.get(newlist.size() - 1));
}
public static void main(String[] args)
{
// Input string to be processed
String str
= "My name is ava and i love Geeksforgeeks";
// Create a list to store all the words in the input
// string
ArrayList<String> words = new ArrayList<>();
// Create a string builder to build each word from
// the input string
StringBuilder word = new StringBuilder();
// Iterate over each character in the input string
for (char c : str.toCharArray()) {
// If the current character is a space, the
// current word is complete
if (c == ' ') {
// Add the current word to the list of words
words.add(word.toString());
// Reset the string builder to build the
// next word
word.setLength(0);
}
else {
// Otherwise, append the current character
// to the current word
word.append(c);
}
}
// If there is a word left in the string builder,
// add it to the list of words
if (word.length() > 0) {
words.add(word.toString());
}
// Find the largest palindrome in the list of words
largestPalin(words);
}
}
Python3
# Python3 program for the above approach
def ispalindrome(string):
if(string == string[::-1]):
return True
else:
return False
def largestPalin(s):
# Taking new list
newlist = []
# Traverse the list
for i in s:
if(ispalindrome(i)):
newlist.append(i)
# Using sorted() method
s = sorted(newlist, key=len)
# Print last word
print(s[len(s)-1])
# Driver Code
if __name__ == "__main__":
# Given string
s = "My name is ava and i love Geeksforgeeks"
# Convert string to list
l = list(s.split(" "))
largestPalin(l)
# This code is contributed by vikkycirus
Javascript
<script>
// JavaScript program for the above approach
function ispalindrome(string){
let temp = string
temp = temp.split('').reverse().join('')
if(string == temp)
return true
else
return false
}
function largestPalin(s){
// Taking new list
let newlist = []
// Traverse the list
for(let i of s){
if(ispalindrome(i))
newlist.push(i)
}
// Using sorted() method
newlist.sort((a,b)=>a.length - b.length)
s = newlist
// Print last word
document.write(s[s.length-1],"</br>")
}
// Driver Code
// Given string
let s = "My name is ava and i love Geeksforgeeks"
// Convert string to list
let l = s.split(" ")
largestPalin(l)
// This code is contributed by shinjanpatra
</script>
C#
// C# program for the above approach
using System;
using System.Collections.Generic;
using System.Linq;
public class Program {
// Function to check if a string is a palindrome
public static bool IsPalindrome(string s) {
return s.Equals(new string(s.Reverse().ToArray()));
}
// Function to find the largest palindrome in a list of
// words
public static void LargestPalin(List < string > s) {
// Create a new list to store all the palindromes
// found
List < string > newList = new List < string > ();
// Iterate over each word in the input list
foreach(string word in s) {
// Check if the current word is a palindrome
if (IsPalindrome(word)) {
// If it is, add it to the new list
newList.Add(word);
}
}
// Sort the new list in ascending order of length
newList.Sort((a, b) => a.Length - b.Length);
// Print the largest palindrome (last element in the
// sorted list)
Console.WriteLine(newList[newList.Count - 1]);
}
public static void Main(string[] args) {
// Input string to be processed
string str = "My name is ava and i love Geeksforgeeks";
// Create a list to store all the words in the input
// string
List < string > words = new List < string > ();
// Create a string builder to build each word from
// the input string
System.Text.StringBuilder word = new System.Text.StringBuilder();
// Iterate over each character in the input string
foreach(char c in str) {
// If the current character is a space, the
// current word is complete
if (c == ' ') {
// Add the current word to the list of words
words.Add(word.ToString());
// Reset the string builder to build the
// next word
word.Clear();
} else {
// Otherwise, append the current character
// to the current word
word.Append(c);
}
}
// If there is a word left in the string builder,
// add it to the list of words
if (word.Length > 0) {
words.Add(word.ToString());
}
// Find the largest palindrome in the list of words
LargestPalin(words);
}
}
// Contributed by adityasharmadev01
Output:
ava
Method #3:Using filter() method in Python:
First, the string is converted into a list of words using the re module.
Then the filter function is applied to the list of word to, using ispalindrome function to filter out only the palindrome words.
After max, the function is applied using the len as key to get a word with max length
C++
#include <algorithm>
#include <iostream>
#include <regex>
#include <string>
using namespace std;
bool ispalindrome(string word)
{
return word == string(word.rbegin(), word.rend());
}
void largestPalin(string s)
{
// Convert string to vector of words
regex pattern(R "(\b\w+\b)");
vector<string> words(
sregex_token_iterator(s.begin(), s.end(), pattern),
sregex_token_iterator());
// Using remove_if() and erase() functions to remove
// non-palindrome words
words.erase(remove_if(words.begin(), words.end(),
[](string word) {
return !ispalindrome(word);
}),
words.end());
// Using max_element() function to find the word with
// the maximum length
auto it = max_element(
words.begin(), words.end(), [](string a, string b) {
return a.length() < b.length();
});
// Printing the largest palindrome
cout << *it << endl;
}
int main()
{
string s = "My name is ava and i love Geeksforgeeks";
largestPalin(s);
return 0;
}
Java
// Java program for the above approach
import java.util.ArrayList;
import java.util.List;
public class Main {
public static boolean isPalindrome(String word)
{
return word.equals(
new StringBuilder(word).reverse().toString());
}
public static void largestPalin(String s)
{
// Convert string to list of words
String[] words = s.split("\\W+");
List<String> palindromeWords = new ArrayList<>();
// Using filter() function to filter palindrome
// words
for (String word : words) {
if (isPalindrome(word)) {
palindromeWords.add(word);
}
}
// Using max() function to find the word with the
// maximum length
String largestPalindrome
= palindromeWords.stream()
.max((a, b)
-> Integer.compare(a.length(),
b.length()))
.orElse(null);
System.out.println(largestPalindrome);
}
public static void main(String[] args)
{
String s
= "My name is ava and i love Geeksforgeeks";
largestPalin(s);
}
}
// Contributed by adityasha4x71
Python3
import re
def ispalindrome(word):
return word == word[::-1]
def largestPalin(s):
# Convert string to list of words
words = re.findall(r'\b\w+\b', s)
# Using filter() function to filter palindrome words
palindrome_words = filter(ispalindrome, words)
# Using max() function to find the word with the maximum length
largest_palindrome = max(palindrome_words, key=len)
print(largest_palindrome)
# Driver Code
if __name__ == "__main__":
s = "My name is ava and i love Geeksforgeeks"
largestPalin(s)
Javascript
// JavaScript program for above approach
function isPalindrome(word) {
return word === word.split('').reverse().join('');
}
function largestPalin(s) {
// Convert string to array of words
const words = s.match(/\b\w+\b/g);
// Using filter() method to filter palindrome words
const palindromeWords = words.filter(isPalindrome);
// Using reduce() method to find the word with the maximum length
const largestPalindrome = palindromeWords.reduce((a, b) => a.length >= b.length ? a : b, "");
console.log(largestPalindrome);
}
// Driver Code
const s = "My name is ava and i love Geeksforgeeks";
largestPalin(s);
// Contributed by adityasha4x71
C#
using System;
using System.Linq;
class Program {
static bool IsPalindrome(string word)
{
return word.SequenceEqual(word.Reverse());
}
static string LargestPalin(string s)
{
// Convert string to array of words
var words = s.Split(
new char[] { ' ' },
StringSplitOptions.RemoveEmptyEntries);
// Using LINQ to filter palindrome words
var palindromeWords = words.Where(IsPalindrome);
// Using LINQ to find the word with the maximum
// length
var largestPalindrome
= palindromeWords
.OrderByDescending(word = > word.Length)
.FirstOrDefault();
return largestPalindrome;
}
static void Main(string[] args)
{
string s
= "My name is ava and i love Geeksforgeeks";
string largestPalindrome = LargestPalin(s);
Console.WriteLine(largestPalindrome);
}
}
Output
ava
Time complexity:O(n)Auxiliary Space:O(n) | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence | https://www.geeksforgeeks.org/print-longest-palindrome-word-sentence/?ref=lbp | NLP | Print longest palindrome word in a sentence | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.00284268125, 0.013148359, -0.0124740843, 0.0430003442, -0.00546698971, 0.0289478432, -0.00709904078, 0.0170407631, -0.0253466032, -0.00225652196, 0.00207645982, 0.0380965248, 0.030817423, -0.0394450761, 0.0207952484, 0.00673125451, 0.00366445375, 0.0115546184, -0.0226495042, -0.0235689692, -0.0202129204, 0.0136387404, -0.051796563, -0.00929426495, 0.0144739216, 0.0446860306, 0.0154470224, 0.00533290068, 0.00647840183, 0.00158990931, 0.0317215659, -0.00395753328, -0.00585776241, 0.00832882617, -0.00185808679, -0.00860466622, 0.0201056488, 0.0117844846, -0.00294229016, 0.0052103051, 0.0178529583, 0.0169488173, -0.00712585868, -0.0338363349, 0.00162630482, 0.00861232821, -0.0253925771, 0.0179755539, 0.00786909368, -0.0283808392, 0.00699560111, -0.0166270044, -0.01377666, 0.0264346376, 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20 Jun, 2024 | Python String split()
20 Jun, 2024
Python String split() method splits a string into a list of strings after breaking the given string by the specified separator.
Example:
Python
string = "one,two,three"
words = string.split(',')
print(words)
Output:
['one', 'two', 'three']Python String split() Method SyntaxSyntax: str.split(separator, maxsplit)
Parametersseparator: This is a delimiter. The string splits at this specified separator. If is not provided then any white space is a separator.maxsplit: It is a number, that tells us to split the string into a maximum of the provided number of times. If it is not provided then the default is -1 which means there is no limit.ReturnsReturns a list of strings after breaking the given string by the specified separator.
What is the list split() Method?split() function operates on Python strings, by splitting a string into a list of strings. It is a built-in function in Python programming language.
It breaks the string by a given separator. Whitespace is the default separator if any separator is not given.
How to use list split() method in Python?Using the list split() method is very easy, just call the split() function with a string object and pass the separator as a parameter. Here we are using the Python String split() function to split different Strings into a list, separated by different characters in each case.
Example: In the above code, we have defined the variable ‘text’ with the string ‘geeks for geeks’ then we called the split() method for ‘text’ with no parameters which split the string with each occurrence of whitespace.
Python
text = 'geeks for geeks'
# Splits at space
print(text.split())
word = 'geeks, for, geeks'
# Splits at ','
print(word.split(','))
word = 'geeks:for:geeks'
# Splitting at ':'
print(word.split(':'))
word = 'CatBatSatFatOr'
# Splitting at t
print(word.split('t'))
Similarly, after that, we applied split() method on different strings with different delimiters as parameters based on which strings are split as seen in the output.
Output['geeks', 'for', 'geeks']
['geeks', ' for', ' geeks']
['geeks', 'for', 'geeks']
['Ca', 'Ba', 'Sa', 'Fa', 'Or']Time Complexity: O(n)Auxiliary Space: O(n)
How does split() work when maxsplit is specified?The maxsplit parameter is used to control how many splits to return after the string is parsed. Even if there are multiple splits possible, it’ll only do maximum that number of splits as defined by the maxsplit parameter.
Example: In the above code, we used the split() method with different values of maxsplit. We give maxsplit value as 0 which means no splitting will occur.
Python
word = 'geeks, for, geeks, pawan'
# maxsplit: 0
print(word.split(', ', 0))
# maxsplit: 4
print(word.split(', ', 4))
# maxsplit: 1
print(word.split(', ', 1))
The value of maxsplit 4 means the string is split at each occurrence of the delimiter, up to a maximum of 4 splits. And last maxsplit 1 means the string is split only at the first occurrence of the delimiter and the resulting lists have 1, 4, and 2 elements respectively.
Output['geeks, for, geeks, pawan']
['geeks', 'for', 'geeks', 'pawan']
['geeks', 'for, geeks, pawan']Time Complexity: O(n)Auxiliary Space: O(n)
How to Parse a String in Python using the split() Method?In Python, parsing strings is a common task when working with text data. String parsing involves splitting a string into smaller segments based on a specific delimiter or pattern. This can be easily done by using a split() method in Python.
Python
text = "Hello geek, Welcome to GeeksforGeeks."
result = text.split()
print(result)
Explanation: In the above code, we have defined a string ‘text’ that contains a sentence. By calling the split() method without providing a separator, the string is split into a list of substrings, with each word becoming an element of the list.
Output['Hello', 'geek,', 'Welcome', 'to', 'GeeksforGeeks.']Hope this tutorial on the string split() method helped you understand the concept of string splitting. split() method in Python has various applications like string parsing, string extraction, and many more. “How to split in Python?” is a very important question for Python job interviews and with this tutorial we have answered the question for you.
Check More: String Methods
For more informative content related to the Python string split() method you can check the following article:
Python program to split and join a stringSplit and Parse a string in PythonPython | Ways to split a string in different waysPython | Split string into list of charactersPython String split() – FAQsWhat does split('\t') do in Python?In Python, the split('\t') method splits a string into a list of substrings based on the tab (\t) delimiter. Here’s how it works:
text = "apple\tbanana\torange"result = text.split('\t')print(result) # Output: ['apple', 'banana', 'orange']In this example, the split('\t') method divides the string text wherever it encounters a tab character (\t) and returns a list containing the separated substrings.
What is input().split() in Python?input() is a built-in function in Python that reads a line from input, which is typically from the user via the console. split() is a method that splits a string into a list of substrings based on whitespace by default, or a specified delimiter. Together, input().split() allows you to read user input and split it into individual components based on whitespace.
Example:
# User input: "apple banana orange"words = input().split()print(words) # Output: ['apple', 'banana', 'orange']Here, input() reads the input from the user, and split() divides the input into a list of words based on whitespace.
How to split a number in Python?To split a number (typically an integer or float) into its individual digits, you can convert the number to a string and then split the string. Here’s an example:
number = 12345digits = list(str(number))print(digits) # Output: ['1', '2', '3', '4', '5']In this example, str(number) converts the integer 12345 into a string, and list() converts the string into a list of individual characters (‘1’, ‘2’, ‘3’, ‘4’, ‘5’).
How to split a string into lines using the split() method?To split a multi-line string into individual lines using the split() method, you can specify the newline character (\n) as the delimiter. Here’s an example:
multiline_text = "Line 1\nLine 2\nLine 3"lines = multiline_text.split('\n')print(lines) # Output: ['Line 1', 'Line 2', 'Line 3']In this example, split('\n') splits the multiline_text string wherever it encounters a newline character (\n) and returns a list of lines.
How to split a string number?If by “split a string number” you mean splitting a string representation of a number into its individual characters or parts, you can use the split() method with an empty string as the delimiter. Here’s an example:
number_str = "12345"digits = list(number_str)print(digits) # Output: ['1', '2', '3', '4', '5']In this example, list(number_str) converts the string "12345" into a list of individual characters (‘1’, ‘2’, ‘3’, ‘4’, ‘5’). | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split() | https://www.geeksforgeeks.org/python-string-split/ | NLP | Python String split() | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Artificial Intelligence Examples, Python String split(), Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [0.00975914951, 0.00105100602, -0.00745527958, 0.0422878526, 0.00598575501, 0.0153519548, -0.00336967874, -0.00408290932, 0.0121437619, 0.018570913, -0.018291004, -0.0196259562, -0.0122837164, -0.0125097977, -0.00156237895, 0.00669091148, -0.0160301961, 0.0102812881, -0.0118315555, -0.0107065346, 0.0207671244, 0.0148136672, -0.0858245343, -0.0157610532, -0.0109595302, 0.02394302, -0.000961515761, 0.00651865965, 0.00179249677, -0.00905399304, 0.0221343748, -0.0169560499, 0.00415288657, -0.021682214, -0.0143722715, -0.00622798456, -0.00424977858, 0.0235554539, -0.0177850127, -0.0147490725, 0.0274741855, -0.0095492173, 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24 Dec, 2024 | Python String strip() Method
24 Dec, 2024
strip() method removes all leading and trailing whitespace characters from a string in Python. We can also customize it to strip specific characters by passing a string of characters to remove. It doesn’t modify the original string but returns a new one.
Let’s take an example to remove whitespace from both ends of a string.
Python
s = " GeeksforGeeks "
res = s.strip()
print(res)
OutputGeeksforGeeks
Explanation:
The method removes spaces at the start and end of the string.Inner spaces are not affected. This is useful for cleaning up user inputs or formatted text.Table of Content
Syntax of strip() MethodExamples of strip() MethodFrequently Asked Questions (FAQs) on Python strip() MethodSyntax of strip() Methods.strip(chars)
Parameters:chars(optional)A string specifying the set of characters to remove from the beginning and end of the string.If omitted, strip() removes all leading and trailing whitespace by default.Return Type:String: A new string with the specified characters (or whitespace) removed from both ends is returned.Examples of strip() MethodRemoving Custom CharactersWe can also use custom characters from the beginning and end of a string. This is useful when we want to clean up specific unwanted characters such as symbols, punctuation, or any other characters that are not part of the core string content
Python
s = ' ##*#GeeksforGeeks#**## '
# removes all occurrences of '#', '*', and ' '
# from start and end of the string
res = s.strip('#* ')
print(res)
OutputGeeksforGeeks
Explanation:
strip(‘#* ‘) removes any #, *, and spaces from both beginning and end of the string.It stops stripping characters from both end once it encounters a character that are not in the specified set of characters.Removing Newline CharactersWe can also remove the leading and trailing newline characters (\n) from a string.
Python
s = '\nGeeks for Geeks\n'
# Removing newline characters from both ends
res = s.strip()
print(res)
OutputGeeks for Geeks
Frequently Asked Questions (FAQs) on Python strip() MethodWhat characters does strip() remove by default?By default, strip() removes whitespace characters, including spaces, tabs (\t), and newlines (\n).
Can strip() remove characters from the middle of a string?No, strip() only removes characters from the beginning and end of a string. Characters in the middle of the string remain unaffected.
How is strip() different from replace()?The strip() method is used for trimming characters from the ends of a string, while replace() can replace occurrences of a character or substring anywhere in the string. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split()/Python String strip() Method | https://www.geeksforgeeks.org/python-string-strip/?ref=ml_lbp | NLP | Python String strip() Method | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Artificial Intelligence Examples, Python String split(), Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.00154225237, 0.0186500642, -0.00354129751, 0.0352145694, -0.00547689945, -0.00583679648, 0.0216676649, -0.025543483, 0.00951420888, -0.0794358, -0.0610533543, 0.006538135, -0.0215569288, 0.0380199254, -0.0153002515, 0.00450563803, 0.00479401695, -0.011470574, 0.00261617685, -0.00722101703, 0.0369863734, 0.0118120154, -0.0632311925, -0.0417850055, 0.00861908, 0.0350853764, -0.0207633078, 0.00105143082, 0.00869751908, 0.0117566464, 0.0146542815, -0.01401754, -0.00200135214, -0.0193975437, -0.0501641519, -0.0280719921, 0.00581834046, -0.00851757079, 0.00309834699, 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07 Jan, 2025 | Python String rindex() Method
07 Jan, 2025
Python String rindex() method returns the highest index of the substring inside the string if the substring is found. Otherwise, it raises ValueError.
Let’s understand with the help of an example:
Python
s = 'geeks for geeks'
res= s.rindex('geeks')
print(res)
Output10
Note: If start and end indexes are not provided then by default Python String rindex() Method takes 0 and length-1 as starting and ending indexes where ending indexes is not included in our search.
Table of Content
Syntax of rindex() rindex() with start or end indexrindex() without start and end indexErrors and ExceptionsSyntax of rindex() string.rindex(value, start, end)Parameters:
value : Part that we are searching for.start (optional): Index where the search begins (default is 0).end (optional): Index where the search ends (default is the string’s length).Return:
It returns the highest index of the substring inside the string if substring is found. Otherwise it raises an exception.rindex() with start or end indexIf we provide the start and end value to check inside a string, Python String rindex() will search only inside that range.
Example:
Python
a= "ring ring"
# checks for the substring in the range 0-4 of the string
print(a.rindex("ring", 0, 4))
# same as using 0 & 4 as start, end value
print(a.rindex("ring", 0, -5))
b = "101001010"
# since there are no '101' substring after string[0:3]
# thus it will take the last occurrence of '101'
print(b.rindex('101', 2))
Output0
0
5
rindex() without start and end indexIf we don’t provide the start and end value to check inside a string, Python String rindex() will search the entire string .
Example:
Python
a = "ring ring"
# search for the substring,
# from right in the whole string
print(a.rindex("ring"))
b = "geeks"
# this will return the right-most 'e'
print(b.rindex('e'))
Output:
52Errors and ExceptionsValueError is raised when the substring is not found within the specified range or the entire string.
Example:
Python
s = 'geeks for geeks'
res = s.rindex('pawan')
print(res)
Exception:
Traceback (most recent call last): File "/home/dadc555d90806cae90a29998ea5d6266.py", line 6, in res= s.rindex('pawan')ValueError: substring not found | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split()/Python String strip() Method/Python String rindex() Method | https://www.geeksforgeeks.org/python-string-rindex-method/?ref=lbp | NLP | Python String rindex() Method | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Artificial Intelligence Examples, Python String split(), Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Python String rindex() Method, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0393413976, 0.0195203871, -0.00647840369, 0.0279979277, 0.00222836039, 0.000499470916, 0.0341506563, 0.00177993265, -0.00492769526, -0.00371518661, -0.0441313088, 0.0256731175, -0.00854267459, 0.00704457518, 0.0117944023, 0.00342709059, 0.0252522472, 0.0307636503, -0.0176966134, -0.039020732, -0.00152941432, -9.4414092e-05, -0.000753433851, -0.0145501038, -0.00993555691, 0.00170227198, -0.0298016593, 0.00168974604, -0.0190193504, -0.0191696621, 0.0308237746, -0.0361347608, 0.0328479633, 0.00835729111, -0.0170252249, 0.0141592957, 0.0123756053, 0.00837232266, 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05 Jan, 2025 | Python String istitle() Method
05 Jan, 2025
The istitle() method in Python is used to check whether a string follows the title case formatting. In a title-cased string, the first letter of each word is capitalized, and all other letters in the word are in lowercase. This method is especially useful when working with formatted text such as titles, headlines, or document headers.
Let’s understand with the help of an example:
Python
s = "Python is Fun"
# Checking if the string is in title case
res = s.istitle()
print(res)
OutputFalse
ExplanationThe string ‘s' is in title case because the first letter of each word is uppercase, and the rest of the letters are lowercase.The method returns True, confirming that the string adheres to the title case format.Syntax of istitle() Methodstring.istitle()
ParametersThe istitle() method does not take any parameters.Return TypeReturns True if the string is in title case.Returns False otherwise.Examples of istitle() method1. Checking a proper title-case stringHere, we test the istitle() method with a correctly formatted title-case string to verify its behavior.
Python
s = "Python Programming"
# Verifying if the string is in title case
result = s.istitle()
print(result)
OutputTrue
ExplanationThe method evaluates the string 's' and confirms it follows title case.Both words start with uppercase letters followed by lowercase letters resulting in True.2. String with improper casingIn this example, we analyze a string that does not conform to title case rules. This helps illustrate how istitle() handles such cases.
Python
s = "python Programming"
# Verifying if the string is in title case
res = s.istitle()
print(res)
OutputFalse
ExplanationThe string ‘s' does not adhere to title case because the first word, “python,” starts with a lowercase letter.As a result, the method returns False.3. Strings with special characters and numbersThis example demonstrates how istitle() behaves when the string contains special characters or numbers. These elements do not affect the title case evaluation.
Python
s = "Python 3.9 Is Awesome"
# Checking title case for a string with numbers and special characters
result = s.istitle()
print(result)
OutputTrue
ExplanationThe words “Python,” “Is,” and “Awesome” are in title case.Numbers and special characters do not affect the result, so the method returns True.4. Empty stringLet’s what happens if we pass an empty string to istitle().
Python
s = ""
# Checking an empty string
res = s.istitle()
print(res)
OutputFalse
Explanation
An empty string does not have any words to evaluate, so the method returns False.5. Mixed cases with acronymsHere, we examine a string containing an acronym to understand how istitle() processes such cases.
Python
s = "NASA Is Amazing"
# Verifying a string with an acronym
res = s.istitle()
print(res)
OutputFalse
ExplanationThe acronym “NASA” is all uppercase, but the other words adhere to title case.This is considered valid, so the method returns True.Frequently Asked Questions (FAQs) on istitle() Method1. Does the istitle() method consider single-word strings?Yes, it does. For example:
s = "Python"print(s.istitle()) # Output: True2. Does punctuation affect the result of the istitle() method?No, punctuation is ignored as long as the words are correctly title-cased:
s = "Hello, World!"print(s.istitle()) # Output: True
3. How does istitle() handle strings with digits?Digits do not affect the evaluation:
s = "Python 101"print(s.istitle()) # Output: True4. Is there any way to convert a string to title case?Yes, you can use the title() method to convert a string to title case:
s = "python programming"title_cased = s.title()print(title_cased) # Output: 'Python Programming' | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split()/Python String strip() Method/Python String rindex() Method/Python String istitle() Method | https://www.geeksforgeeks.org/python-string-istitle-method/?ref=lbp | NLP | Python String istitle() Method | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, Python String istitle() Method, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Artificial Intelligence Examples, Python String split(), Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Python String rindex() Method, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [0.0186049249, 0.0306866411, -0.00985946134, 0.073455, -0.00645430107, 0.0210970659, 0.0154237123, -0.0168592781, -0.00851003081, -0.00443876768, -0.00901535, 0.032248538, 0.0102269668, -0.00430956669, -0.0336496495, 0.00679883687, 0.0272412859, 0.00554415258, -0.0117256967, -0.04897, 0.0130579006, 0.0260239262, -0.059903264, -0.0147116724, 0.0120128095, 0.0193743873, -0.0093369158, 0.0275169145, 0.0275628511, 0.00163080206, -0.00150734349, -0.00558147766, 0.0191561822, -0.0110136559, -0.0191102438, -0.0267819036, -0.00371811376, 0.0584791824, 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10 Nov, 2024 | Python String isdigit() Method
10 Nov, 2024
The isdigit() method is a built-in Python function that checks if all characters in a string are digits. This method returns True if each character in the string is a numeric digit (0-9), and False otherwise.
Let’s start with a simple example of isdigit() method.
Python
s = "12345"
print(s.isdigit())
s2 = "1234a5"
print(s2.isdigit())
OutputTrue
False
Explanation: In this example, s.isdigit() returns True because “12345” consists entirely of numeric characters, while s2.isdigit() returns False due to the non-numeric character “a” in the string.
Table of Content
Syntax of isdigit()Example of isdigit()Checking Strings with Only Digits, Mixed Characters, and Empty StringsChecking Unicode Digits Using isdigit()Frequently Asked Questions on Python isdigit() MethodSyntax of isdigit()s.isdigit()
ParametersThe isdigit() method does not take any parametersReturn ValueReturns True if all characters in the string are numeric (0-9).Returns False if there are any non-numeric characters.Example of isdigit()Let’s explore some examples of isdigit() method for better understanding.
Checking Strings with Only Digits, Mixed Characters, and Empty StringsHere are example with a string containing only digits, a mixed-character string, and an empty string.
Python
# String containing only digits
s1 = "987654"
# Returns True
print(s1.isdigit())
# String with mixed characters (digit and alphabet)
s2 = "987b54"
# Returns False
print(s2.isdigit())
# Empty string
s3 = ""
# Returns False
print(s3.isdigit())
OutputTrue
False
False
Checking Unicode Digits Using isdigit()The isdigit() method can also be used to check numeric characters encoded in Unicode, such as the standard digit ‘1’ and other Unicode representations of numbers.
Python
# Unicode for '1'
s1 = "\u0031"
# Devanagari digit for '1'
s2 = "\u0967"
# Return True
print(s1.isdigit())
# Return False
print(s2.isdigit())
OutputTrue
True
Explanation:
The variable s1 holds \u0031, which represents the standard numeric digit ‘1’. Since this is a recognized numeric character, so s1.isdigit() returns True.The variable s2 contains \u0967, which represents the Devanagari digit ‘1’ used in Hindi and other Indian languages. Python recognizes this as numeric, so s2.isdigit() also returns True.Related Articles:
Python String isdecimal()Python String isnumeric() MethodPython String isalpha()Python String isalnum()Frequently Asked Questions on Python isdigit() MethodWhat does the isdigit() method do in Python?Thebmethod checks if all characters in a string are numeric digits (0-9). If all characters are digits, it returns True; otherwise, it returns False. This includes numeric characters from Unicode representations.
Can isdigit() detect negative numbers?No, isdigit() will return False if the string contains a negative sign (-). This method only returns True for strings that contain purely numeric characters without any additional symbols.
Does isdigit() work with decimal numbers?No, isdigit() does not consider decimal points (e.g., “12.34”) as numeric. If the string contains a decimal point or other symbols, isdigit() will return False.
Can isdigit() recognize numbers in non-Latin scripts?Yes, isdigit() can check digits from various Unicode scripts, such as Devanagari, Arabic, and others, as long as they are recognized numeric digits. For example, the Devanagari digit “१” (one) will return True when checked with isdigit().
How is isdigit() different from isnumeric()?While both isdigit() and isnumeric() check if a string contains only numbers, isnumeric() can identify additional numeric representations, such as fractions or Roman numerals, in Unicode. Therefore, isnumeric() may return True in cases where isdigit() returns False. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split()/Python String strip() Method/Python String rindex() Method/Python String istitle() Method/Python String isdigit() Method | https://www.geeksforgeeks.org/python-string-isdigit-method/?ref=lbp | NLP | Python String isdigit() Method | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, Python String istitle() Method, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Python String isdigit() Method, Artificial Intelligence Examples, Python String split(), Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Python String rindex() Method, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0163177773, 0.0163005199, -0.00272250618, 0.0515334606, -0.00184232974, -0.00320574013, 0.0456311, -0.0252662376, 0.00441166805, -0.0120118177, -0.00687745586, 0.00757641951, -0.0159639809, 0.0199679211, -0.0295290519, 0.0148421889, 0.0238165352, -0.00234497944, -0.00365014281, -0.00446128566, 0.00109968102, 0.0243515447, -0.0541222133, 0.0193638783, -0.00119514135, -0.00333086331, -0.0229881331, -0.00296196574, 0.0083918767, -0.00184772303, 0.0291666258, -0.0278204735, -0.00252403505, -0.0220734403, 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08 Mar, 2025 | expandtabs() method in Python
08 Mar, 2025
expandtabs() method in Python is used to replace all tab characters (\t) in a string with spaces. This method allows for customizable spacing, as we can specify the number of spaces for each tab. It is especially useful when formatting text for better readability or alignment. Let’s understand with the help of an example:
Python
s = "Name\tAge\tLocation"
# Expanding tabs with the default spacing
res = s.expandtabs()
print(res)
OutputName Age Location
Explanation:
string ‘s’ contains tab characters (\t).Using expandtabs(), each tab is replaced with 8 spaces (the default tab size).This improves readability by aligning the text.Table of Content
Syntax of expandtabs() methodExamples of expandtabs() methodFrequently Asked Questions (FAQs) on expandtabs() method in PythonSyntax of expandtabs() methodstring.expandtabs(tabsize)
Parameters: tabsize (optional) : Specifies the number of spaces per tab. The default value is 8.
Return Type: This method returns a new string with all the tab characters replaced with spaces.
Examples of expandtabs() method1. Using default tab sizeWhen we call the expandtabs() method without any arguments, it uses the default tab size of 8 spaces. This default behavior ensures that basic alignment is achieved without additional configuration.
Python
s = "A\tB\tC"
# Expanding tabs with default tab size
res = s.expandtabs()
print(res)
OutputA B C
Explanation:
tabs in the string ‘s’ are replaced by 8 spaces each.output shows the characters spaced apart for better alignment.2. Custom tab sizeWe can specify a custom tab size using the tabsize parameter. This allows us to format strings based on specific alignment requirements.
Python
s = "Python\tis\tfun"
# Expanding tabs with a custom size of 4 spaces
res = s.expandtabs(4)
print(res)
OutputPython is fun
Explanation:
tabsize=4 argument replaces each tab in s with 4 spaces.Customizing the tab size allows for more flexible formatting.3. Mixed spacing with tabs and textWhen working with text that contains both tabs (\t) and regular characters, Python’s expandtabs() method ensures proper alignment by replacing tabs with the appropriate number of spaces based on the specified tab size.
Python
s = "A\tBC\tDEFG"
# Expanding tabs with a size of 5 spaces
res = s.expandtabs(5)
print(res)
OutputA BC DEFG
Explanation:
“A\t” : “A” is at index 0, the next multiple of 5 is 5, so \t is replaced with 4 spaces.“BC\t” : “BC” starts at index 5, “C” is at 6, the next multiple of 5 is 10, so \t is replaced with 3 spaces.“DEFG” : Continues normally since there are no more tabs.4. No tabs in the stringIf the string does not contain any tabs, the method returns the original string unchanged. This ensures efficiency and avoids unnecessary processing.
Python
s = "Python is fun!"
# Expanding tabs in a string without tabs
result = s.expandtabs(4)
print(result)
Explanation: Since there are no tabs in the input string, the expandtabs() method has no effect.
Frequently Asked Questions (FAQs) on expandtabs() method in PythonQ1. What happens if the tabsize is set to 0?If tabsize=0, all tabs are effectively removed from the string.
s = "Hello\tWorld"result = s.expandtabs(0)print(result) # Output: 'HelloWorld'Q2. Can expandtabs() handle negative tabsize values?No, passing a negative value for tabsize raises a ValueError.
s = "Test\tString"# Raises ValueErrorresult = s.expandtabs(-4)Q3. Does expandtabs() modify the original string?No, expandtabs() returns a new string. The original string remains unchanged.
s = "Tab\tExample"result = s.expandtabs(4)print(s) # Output: 'Tab\tExample'print(result) # Output: 'Tab Example' | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to 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sum of MEX of all Subarrays starting from first index, Python String istitle() Method, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Python String isdigit() Method, Artificial Intelligence Examples, Python String split(), expandtabs() method in Python, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Python String rindex() Method, Loss Functions in Deep Learning, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.00343161053, -0.00330057624, -0.00844057463, 0.0429989696, 0.0517411716, 0.0390234441, 0.0171679426, -0.00154521363, -0.0103245, -0.0250398777, -0.0338611938, 0.0224884208, -0.017385507, 0.0280462466, -0.019323824, -0.00111811655, 0.00195067772, 0.00214104797, -0.0117485682, 0.000233790823, 0.0544310771, -0.00258359732, -0.0557760336, -0.047548078, -0.00617096527, 0.00669015711, -0.00267260149, 0.003955747, 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05 Nov, 2024 | String capitalize() Method in Python
05 Nov, 2024
The capitalize() method in Python is used to change the first letter of a string to uppercase and make all other letters lowercase. It is especially useful when we want to ensure that text follows title-like capitalization, where only the first letter is capitalized.
Let’s start with a simple example to understand the capitalize() functions:
Python
s = "hello WORLD"
res = s.capitalize()
print(res)
OutputHello world
Explanation: In this example, capitalize() method converts the first character “h” to uppercase and change the rest of characters to lowercase.
Table of Content
Syntax of capitalize() MethodExample of capitalize() MethodWhat happens if the first character is a number?Syntax of capitalize() Methods.capitalize()
ParametersThe capitalize() method does not accept any parameters.Return ValueThe method returns a new string with the first character capitalized and all other characters in lowercase. The original string remains unchanged.Example of capitalize() MethodThe capitalize() method only affects the first letter of the string and doesn’t capitalize each word in multi-word strings.
Python
s = "multiple WORDS IN a String"
res = s.capitalize()
print(res)
OutputMultiple words in a string
Explanation: Even though there are multiple words, only the first character of the entire string is affected, while the remaining words are converted to lowercase.
What happens if the first character is a number?When the first character of a string is a number, capitalize() method does not alter it because it only affects alphabetical characters. Instead, it will simply convert any following alphabetical characters to lowercase.
Python
s = "123hello WORLD"
res = s.capitalize()
print(res)
Output123hello world
Explanation: Since capitalize() only targets alphabetical characters for capitalization, the initial number remains unchanged. While rest of the characters follow the capitalization rule which results in “123hello world“
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07 Jan, 2025 | Python String upper() Method
07 Jan, 2025
upper() method in Python is a built-in string method that converts all lowercase letters in a string to uppercase. This method is simple to use and does not modify the original string; instead, it returns a new string with the modifications applied.
Example:
Python
s = "learn python with gfg!"
res = s.upper()
print(res)
OutputLEARN PYTHON WITH GFG!
Explanation:The upper() method converts all the lowercase letters to uppercase and returns a new string.The original string ‘s’ remains unchanged.Table of Content
Syntax of upper() methodExample of upper() method Frequently Asked Question on upper() Method Syntax of upper() method string.upper()
ParametersThe upper() method does not take any parameters. Return TypeThis method returns a new string in which all lowercase characters in the original string are converted to uppercase. If the original string has no lowercase letters then it returns the string unchanged.Example of upper() method1. Standardizing case for comparisonLet’s consider a scenario where we want to compare two strings without considering their case. The upper() method can help us standardize both strings to uppercase before comparison.
Python
s1 = "Python"
s2 = "PYTHON"
# Using upper() for comparison
res = s1.upper() == s2.upper()
print(res)
OutputTrue
ExplanationThe upper() method converts both s1 and s2 to uppercase.The comparison s1.upper() == s2.upper() evaluates to True as both strings become “PYTHON”.2. Handling mixed-case stringsupper() method is also very useful when we have a string with a mix of lowercase and uppercase letters, and we want to convert all characters to uppercase.
Python
# Converting mixed-case string to uppercase
s = "PyThoN is FuN"
res = s.upper()
print(res)
OutputPYTHON IS FUN
ExplanationThe upper() method processes the string ‘s’ and converts all lowercase letters to their uppercase equivalents.Non-alphabetic characters like spaces remain unchanged.Frequently Asked Question on upper() Method Q1. What does upper() method return? The upper() method returns a new string with all lowercase letters converted to uppercase and leaving other characters unchanged.
Q2. Does the upper() method modify the original string? No, upper() method does not modify the original string but it returns a new string instead.
Q3. Can the upper() method convert non-alphabetic characters?No, the upper() method only affects alphabetic characters. Non-alphabetic characters such as digits, spaces, and symbols remain unchanged.
Q4. Is the upper() method locale-sensitive?No, the upper() method is not locale-sensitive. For locale-specific behavior, consider using the locale module.
Q5. Can the upper() method handle empty strings? Yes, upper() method can handle empty strings and will return an empty string if called on one. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split()/Python String strip() Method/Python String rindex() Method/Python String istitle() Method/Python String isdigit() Method/expandtabs() method in Python/String capitalize() Method in Python/Python String upper() Method | https://www.geeksforgeeks.org/python-string-upper/ | NLP | Python String upper() Method | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, Python String istitle() Method, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Python String isdigit() Method, Artificial Intelligence Examples, Python String split(), expandtabs() method in Python, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Python String rindex() Method, Loss Functions in Deep Learning, Python String upper() Method, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, String capitalize() Method in Python, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.00702303136, 0.0298567973, -0.00430026976, 0.0521558151, 0.0399991944, 0.0248301607, 0.0306589194, 0.00218689884, 0.00983046181, -0.0676991716, -0.0342239104, 0.0435998365, 0.00395268342, 0.0123526929, -0.0268978551, 0.0368263535, -0.00938483793, 0.0247588605, 0.00203204458, -0.0149283987, 0.000684032566, 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27 Dec, 2024 | Python – String startswith()
27 Dec, 2024
startswith() method in Python is a built-in string method that checks whether a given string starts with a specific prefix. It helps in efficiently verifying whether a string begins with a certain substring, which can be useful in various scenarios like filtering or validating input. In this article, we will understand about startswith() method.
Let’s understand by taking a simple example:
Python
s = "GeeksforGeeks"
res = s.startswith("for")
print(res)
OutputFalse
Explanation:We create a string 's' with the value "GeeksforGeeks!".We then call the startswith() method on 's', passing "Geeks" as the prefix.The method checks if the string starts with "Geeks", and since it does, the result is True.Table of Content
Syntax of startswith() methodExamples of startswith() methodSyntax of startswith() methodstring.startswith(prefix[, start[, end]])
Parameters:prefix: The substring or a tuple of substrings to check for at the start of the string.start (optional): The index where the search for the prefix begins. By default, it starts from index 0.end (optional): The index where the search for the prefix ends. If not specified, the search goes till the end of the string.Return Type:The method returns a Boolean:True if the string starts with the specified prefix.False if it does not.Examples of startswith() methodBasic Prefix CheckHere’s a simple example where we check if the string starts with the word “Python”.
Python
s = "GeeksforGeeks"
res = s.startswith("for")
print(res)
OutputFalse
Explanation: The string starts with the word "Python", so the method returns True.Using start and end ParametersLet’s check the string using the start parameter to begin from a specific index.
Python
s = "GeeksforGeeks"
res = s.startswith("for", 9)
print(res)
OutputFalse
Explanation:
We start the check from index 9, where "Python" begins in the string.The method returns True because the substring at that position is "Python".3. Checking Multiple PrefixesWe can also check if the string starts with any one of several prefixes by passing a tuple of prefixes.
Python
s = "GeeksforGeeks"
res = s.startswith(("Geeks", "G"))
print(res)
OutputTrue
Explanation:
We pass a tuple with two prefixes: "Geeks" and "G".Since the string starts with "Geeks", the method returns True.FAQ’s on String startswith()Can startswith() check multiple prefixes?Yes, we can pass a tuple of prefixes, and it will return True if the string starts with any one of them.
What happens if we pass invalid start and end indices?If the start or end index is out of bounds, it will raise an IndexError.
Does the method modify the original string?No, the startswith() method only checks the prefix and returns a Boolean value. It doesn’t modify the string. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split()/Python String strip() Method/Python String rindex() Method/Python String istitle() Method/Python String isdigit() Method/expandtabs() method in Python/String capitalize() Method in Python/Python String upper() Method/Python – String startswith() | https://www.geeksforgeeks.org/python-string-startswith/?ref=lbp | NLP | Python – String startswith() | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, Python String istitle() Method, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Python String isdigit() Method, Artificial Intelligence Examples, Python String split(), expandtabs() method in Python, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Python String rindex() Method, Loss Functions in Deep Learning, Python String upper() Method, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Python – String startswith(), Best Programming Languages for Data Science in 2024, String capitalize() Method in Python, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [0.0275586452, 0.0329940878, -0.00124562217, 0.045352567, -0.0220850594, -0.00858704466, 0.0294658188, -0.0114907157, 0.0148187317, -0.0469927341, -0.0336997397, 0.0351491943, -0.00649392279, 0.0364651419, -0.022199491, 0.00654160231, 0.0266241301, 0.0320023559, 0.0179655664, -0.00617447169, 0.00699932361, 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12 Nov, 2024 | Python String rstrip() Method
12 Nov, 2024
The rstrip() method removes trailing whitespace characters from a string. We can also specify custom characters to remove from end of string.
Let’s take an example to remove whitespace from the ends of a string.
Python
s = "Hello Python! "
res = s.rstrip()
print(res)
OutputHello Python!
Syntax of rstrip() Methods.rstrip(chars)
s: The input stringchars (optional): A set of characters to remove as trailing charactersTable of Content
Syntax of rstrip() MethodExamples of rstrip() MethodRemove trailing whitespacesRemove Custom CharactersRemove Newline CharactersFrequently Asked Questions (FAQs) on Python rstrip() MethodExamples of rstrip() MethodRemove Trailing Whitespaces
Python
s = " Hello Python! "
res = s.rstrip()
print(res)
Output Hello Python!
Remove Custom CharactersIf we have a string with various characters that we want to remove from end of the string.
Python
s = ' ##*#Hello Python!#**## '
# removes all occurrences of '#', '*', and ' '
# from the end of string
res = s.rstrip('#* ')
print(res)
Output ##*#Hello Python!
Notes:
rstrip(‘#* ‘) removes any #, *, and spaces from the end of string.It stops stripping characters from the end of string once it encounters a character that are not in the specified set of characters.Remove Newline CharactersWe can also remove the trailing newline characters (\n) from a string.
Python
s = '\nHello Python!\n'
# Removing newline characters
# from the end of string
res = s.rstrip()
print(res)
OutputHello Python!
Frequently Asked Questions (FAQs) on Python rstrip() MethodWhat characters does rstrip() remove by default?By default, rstrip() removes whitespace characters including spaces, tabs (\t), and newlines (\n), from the right end of the string.
Can rstrip() remove characters from the middle of a string?No, rstrip() only removes characters from the end of a string. Characters in the middle of the string remain unaffected.
How is rstrip() different from strip() and lstrip()?The rstrip() method removes characters only from the end of a string, while lstrip() removes characters from left only and strip() removes characters from both end. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split()/Python String strip() Method/Python String rindex() Method/Python String istitle() Method/Python String isdigit() Method/expandtabs() method in Python/String capitalize() Method in Python/Python String upper() Method/Python String rstrip() Method | https://www.geeksforgeeks.org/python-string-rstrip/?ref=lbp | NLP | Python String rstrip() Method | Artificial Intelligence – Boon or Bane, AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, Python String istitle() Method, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Python String isdigit() Method, Artificial Intelligence Examples, Python String split(), expandtabs() method in Python, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Python String rindex() Method, Loss Functions in Deep Learning, Python String upper() Method, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, String capitalize() Method in Python, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Python String rstrip() Method, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [-0.0198686887, 0.00561662251, -0.00308600697, 0.0534609295, 0.0108301379, -0.0283787232, 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02 Jan, 2025 | Python String zfill()
02 Jan, 2025
zfill() method in Python is used to pad a string with zeros (0) on the left until it reaches a specified width. In this article, we’ll see how zfill() method works.
Python
s = "42"
padded_text = s.zfill(5)
print(padded_text)
Output00042
Explanation:The string "42" is padded with three zeros on the left to make its total length 5.The zfill() method ensures that the string is right-aligned and padded with zeros.Table of Content
Syntax of zfill() methodExamples of String zfill() methodFrequently Asked Questions (FAQs) on zfill()Syntax of zfill() methodstring.zfill(width)
Parameterswidth (required): The total length of the string after padding.If the specified width is less than or equal to the length of the original string, no padding is applied.Return TypeReturns a new string with zeros padded on the left to meet the specified width.Examples of String zfill() method1. Padding a shorter stringLet’s see how zfill() behaves with a string shorter than the specified width:
Python
s = "7"
padded_text = s.zfill(3)
print(padded_text)
Output007
Explanation:The original string "7" has a length of 1.The zfill(3) method pads the string with two zeros on the left to make its total length 3.2. String equal to the specified widthWhat happens when the string length matches the specified width?
Python
s = "12345"
padded_text = s.zfill(5)
print(padded_text)
Output12345
Explanation:The string "12345" already has a length of 5.No padding is added because the string length matches the specified width.3. String longer than the specified widthLet’s see how zfill() handles a string longer than the specified width:
Python
s = "Python"
padded_text = s.zfill(4)
print(padded_text)
OutputPython
Explanation:The string "Python" has a length of 6, which is greater than the specified width of 4.The method returns the original string without any changes.4. Using zfill() with negative and positive numbersWhen dealing with strings representing numbers, the zfill() method correctly handles the sign:
Python
#positive and negative numbers
s1 = "42"
s2 = "-42"
print(s1.zfill(5))
print(s2.zfill(5))
Output00042
-0042
Explanation:For "42", zeros are added to the left to make its total length 5.For "-42", the minus sign is preserved, and zeros are added after the sign to maintain the width.Frequently Asked Questions (FAQs) on zfill()1. Can zfill() be used with non-numerical strings?Yes, zfill()works with any string, not just numerical strings. For example:
s = "abc"
print(s.zfill(6)) # Output: 000abc2. What happens if the width is less than the string’s length?If the specified width is less than the string’s length, zfill() returns the original string without any changes.
3. Does zfill() modify the original string?No, the method returns a new string and does not alter the original string.
4. How does zfill() handle strings with a leading sign?If the string starts with a + or -, the zeros are added after the sign to maintain the correct numerical representation. | NLP/Natural Language Processing (NLP) Tutorial/AI ML DS - Projects/30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated]/Does Artificial Intelligence Require Coding?/Artificial Intelligence – Boon or Bane/Artificial Intelligence Examples/Agents in Artificial Intelligence/What are Diffusion Models?/ML | Common Loss Functions/Loss Functions in Deep Learning/Kaiming Initialization in Deep Learning/Swift - Initialization/Swift – If Statement/6 Best iOS Project Ideas For Beginners/Swift Programming Language/Introduction to Visual Programming Language/What is D Programming Language: Usage and Applications/Best Programming Languages for Data Science in 2024/5 Best Languages for Competitive Programming/MEX (Minimum Excluded) in Competitive Programming/Rearrange Array to maximize sum of MEX of all Subarrays starting from first index/Minimize moves to segregate even and odd by swapping adjacent elements/Minimum elements to be removed such that sum of adjacent elements is always even/Maximum sum such that exactly half of the elements are selected and no two adjacent/Maximum length subsequence such that adjacent elements in the subsequence have a common factor/Longest subsequence such that difference between adjacents is one/Longest Increasing Subsequence using Longest Common Subsequence Algorithm/Longest Common Subsequence (LCS)/Minimum insertions to form a palindrome with permutations allowed/Print longest palindrome word in a sentence/Python String split()/Python String strip() Method/Python String rindex() Method/Python String istitle() Method/Python String isdigit() Method/expandtabs() method in Python/String capitalize() Method in Python/Python String upper() Method/Python String zfill() | https://www.geeksforgeeks.org/python-string-zfill/?ref=next_article | NLP | Python String zfill() | Artificial Intelligence – Boon or Bane, Python String zfill(), AI ML DS - Projects, Longest Common Subsequence (LCS), Rearrange Array to maximize sum of MEX of all Subarrays starting from first index, Python String istitle() Method, MEX (Minimum Excluded) in Competitive Programming, Swift - Initialization, Minimum insertions to form a palindrome with permutations allowed, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, 6 Best iOS Project Ideas For Beginners, ML | Common Loss Functions, Python String strip() Method, Python String isdigit() Method, Artificial Intelligence Examples, Python String split(), expandtabs() method in Python, Longest subsequence such that difference between adjacents is one, What is D Programming Language: Usage and Applications, 30+ Best Artificial Intelligence Project Ideas with Source Code [2025 Updated], Swift – If Statement, Natural Language Processing (NLP) Tutorial, Python String rindex() Method, Loss Functions in Deep Learning, Python String upper() Method, Minimize moves to segregate even and odd by swapping adjacent elements, Maximum length subsequence such that adjacent elements in the subsequence have a common factor, Does Artificial Intelligence Require Coding?, Print longest palindrome word in a sentence, Best Programming Languages for Data Science in 2024, String capitalize() Method in Python, NLP, 5 Best Languages for Competitive Programming, Maximum sum such that exactly half of the elements are selected and no two adjacent, Swift Programming Language, Minimum elements to be removed such that sum of adjacent elements is always even, Agents in Artificial Intelligence, What are Diffusion Models?, Kaiming Initialization in Deep Learning, Introduction to Visual Programming Language | GeeksforGeeks | [6.18575868e-05, 0.0191875901, 0.00636177976, 0.0269053057, 0.0443501882, 0.0223173555, 0.0405446775, 0.00423896359, -0.0123056648, -0.0432832204, -0.0346585847, 0.0177560784, -0.0167780276, 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26 Mar, 2025 | Git Tutorial
26 Mar, 2025
Git is a powerful version control system widely used for tracking changes in source code during software development. Created by Linus Torvalds in 2005, Git has become an essential tool for developers worldwide. Understanding Git can significantly enhance your coding efficiency and collaboration.
This Git Tutorial from beginner to advanced will walk you through the basics of Git, making it easy to learn and implement in your projects. you will learn GitHub fundamentals and advanced concepts like branches, pushing merge conflicts, and many useful Git Commands.
Table of Content
Prerequisites
What is Git?
Why Use Git?
Working with Git
What is Github?
Introduction to Git
Git Basics
Git Installation
Git Commands
Git and GitHub
Git and GitHub in VS Code
Git and GitHub in Android Studio
Git and GitHub in Pycharm
Git and GitHub Deployment
Git Collaborating
Git Advanced
Git Workflow
Internal Working of Git
Git vs GitHub: Difference between Git and GitHub
Best Practices for Git
Common Git Problems and Their Fixes
Prerequisites
A Command Line Interface (CLI) installed.
Text Editor (e.g., Visual Studio Code, Sublime Text).
Basic Understanding of Programming Concepts
What is Git?
Git is a distributed version control system (DVCS) that allows developers to track and manage changes to their codebase. Unlike traditional version control systems, Git enables multiple developers to work on a project simultaneously without interfering with each other’s work.
Git was developed by Linus Torvalds in 2005 for Linux kernel development.
Git is 2.45.1 is the Latest Versions of GIT, released on May 2024.
Why Use Git?
Git offers numerous benefits to developers and development teams:
Version Control: Git helps in tracking changes, allowing you to revert to previous states if something goes wrong.
Collaboration: It enables multiple developers to work on a project simultaneously without interfering with each other’s work.
Backup: Your entire project history is saved in a Git repository, providing a backup of all versions.
Branching and Merging: Git’s branching model allows you to experiment with new features or bug fixes independently from the main project.
Open Source Projects: Most open source projects use Git for version control. Learning Git allows you to contribute to these projects.
Industry Standard: Git is widely used in the software industry, making it an essential skill for developers.
Working with Git
Initializing a Repository: When you initialize a folder with Git, it becomes a repository. Git logs all changes made to a hidden folder within that repository.
Staging Changes: Git marks modified files as “staged.” Staging prepares changes for a snapshot you want to keep.
Committing Changes: Once staged changes are satisfactory, commit them. Git maintains a complete record of each commit.
What is Github?
GitHub, a hosting service for Git repositories, allows you to access and download projects from any computer. Here’s what you can do with GitHub:
Store Repositories: GitHub hosts your repositories.
Collaborate: Work with other developers from any location.
Version Control: Manage collaborative workflows using Git and GitHub.
Introduction to Git
Version Control System
Introduction and Installation of Git
History of Git
Git Features
Introduction to GitHub
Git Repository
Git Features
Bare Repositories in Git
Git Ignore
Readme.md File
GitHub Readme File
GitHub Labels
Difference between CVS and GitHub
Git Basics
Git – SubGit
Git Environment Setup
Using Git on CLI
How to Setup a Repository
Working with Git Repositories
Using GitHub with SSH
Working on Git with GUI
Difference Between Git and GitHub
Working on Git Bash
States of a File in Git Working Directory
Use of Submodules in GitHub
How to Write Good Commit Messages on GitHub?
Deleting a Local GitHub Repository
Git Workflow Etiquettes
Git Packfiles
Git Garbage Collection
Git Flow vs GitHub Flow
Git – Difference Between HEAD, Working Tree and Index
Git Ignore
Git Installation
How to Install Git on Ubuntu
How to Use Git in Ubuntu
How to Setup Git Server on Ubuntu?
How to Add GIT Credentials in MacOS?
How to add GIT credentials on Windows?
How to add GIT credentials on Linux?
How to Setup Git on Anypoint Studio?
How to Install Git With Spyder
How to Install Git on VMWare
How to Install GIT in Conda?
How to Install GIT on GoDaddy Server on Linux?
How to Install Git on Windows Using Chocolatey?
How to install GIT by NPM Packages?
How to Install Git on Cygwin?
How to Install Git Large File Storage on Linux?
How to Install Sourcetree for GIT on Windows?
How to Install Sourcetree for GIT in MacOs?
How to Install Git on Raspberry Pi?
How to Install Git on Termux?
How to Set Up Git Using Git Config?
Git Commands
Useful Git Commands and Basic Concepts
Basic Git Commands with Examples
Essential Git Commands
Top 12 Most Used Git Commands For Developers
Save a File in Git
Difference between “add -A”, “add -u”, “add .”, and “add *”
Difference between “git add -A” and “git add”
Debugging in a Git
How to Add Code on GitHub Repository?
Pushing Changes to Git Repository
Examining Git
Git Checkout and Merge
Overturning Changes in Git
Git Submodules
Git Head
Git Clean
Git Rename
Git Fork
Git Init
Git Add
Git Commit
Git Origin Master
How to Set Upstream Branch on Git?
Git Push
Git Pull
Git Pull and Fetch
Git Merge
Git Stash
Git Remote
Git Patch
Git Patch Operations
Git Rebase
Git Clone
Git Alias
Git Ref and Reflog
Git Undo Commit
Git Undo
Git Stage
Git Squash
Git Move Files
Git diff
Git Status
Git Blame
Git Index
Git Prune
Git Checkout and Merge
Git Merge and Merge Conflicts
Recovering Lost Commits in Git
Git Tags
Git Hooks
Git Subtree
Git – Filtering the Commit History
Git – Cherry Pick
Git – git-show Command Line Utility
Git – Working Tree
Git Logs
Git – Changing History
Shallow Clone on Git Linux
Sync your fork with a master in GitHub
Error Searching and Handling in Git
Delete a Git Branch Locally and Remotely
How to Push Git Branch to Remote?
How to Add an Empty Directory to a Git Repository?
Difference Between Git Push Origin and Git Push Origin Master
Difference Between Git remote prune, Git prune, on and Git fetch –prune
Git – Difference Between Merging and Rebasing
How to Use Git Log to Format the Commit History?
How to Remove Local Untracked Files From Current Git Working Tree?
Git and GitHub
Create a Repository on GitHub
Introduction to Git Branch
How to Add Code of Conduct to Your Project on GitHub?
Difference Between Fork and Clone in GitHub
How to Add Audio Files on README .md File in a GitHub Repository From the Local System?
How to Add Videos on README .md File in a GitHub Repository?
How to Upload a Project on GitHub
How to Export a Git Project?
How to Push a Project and Contribute on GitHub?
How to Push Anything to GitHub using Git Bash?
How to Push Folders From a Local PC to GitHub using Git Commands?
How to Add Images on README .md File in a GitHub Repository From the Local System?
How to Transfer Local Repository to GitHub Organization?
How to Generate Personal Access Token in GitHub?
How to Add GIFs on README .md File in a GitHub Repository?
How to Change the Visibility of the GitHub Repository?
Issues in GitHub
Git – How to Solve “remote: Invalid username or password. fatal: Authentication failed”
Git – A lock file already exists in the repository, which blocks this operation from completing
Common Git Problems and Their Fixes
How to add a README to your GitHub profile?
How to Upload a Project through GitHub Desktop on GitHub
How to configure an OAuth App from GitHub?
How to move the most recent commit(s) to a new branch with Git
How to Use GIT with R and RStudio?
How to Use Git with Eclipse?
Git–Pack Objects
Git and GitHub in VS Code
How to Add GIT Credentials in VSCode?
How to Clone a Project From GitHub using VSCode?
How to Open a GitHub Repository in VS Code Online?
How to Integrate Git Bash with VS Code
Creating a Pull Request on any Public Repository from GitHub using VS Code
How to Install GitHub Copilot on VSCode?
Git and GitHub in Android Studio
How to Upload Project on GitHub from Android Studio
How to Clone Android Project from GitHub in Android Studio?
How to use Git Commands in Android Studio Terminal
How to Create a New Branch on GitHub using Android Studio?
How to Create a Pull Request on GitHub using Android Studio?
Git and GitHub in Pycharm
How to Create a New Branch on Github using Pycharm?
Create a Pull Request on GitHub using Pycharm
How to Upload a Project on GitHub from Pycharm?
How to Push Code to GitHub using Pycharm?
Git and GitHub Deployment
How to deploy the Node.js app on Heroku from GitHub?
Deployment of React Application using GitHub Pages
How to Publish a Static Website on GitHub
Host a free Static Website using GitHub
Publish Websites on GitHub Pages with a Custom Domain
How to Deploy a Basic Static HTML Website to Heroku using Git?
How to Deploy Angular Application to Firebase using GitHub?
How to Add Custom Domain To GitHub Pages?
How to Deploy a Django Application to Heroku with Git CLI?
How to create a cv using HTML and host it in GitHub?
Deployment of Angular Application using Github Pages
How to Build Portfolio Website And Host It on GitHub Pages?
Git Collaborating
What is Git Collaboration
What are GitHub Collaborators
GitHub Discussion
Forking Workflow in Open Source Ecosystem
How to Clone Github Repository and Push Changes in Colaboratory?
How to make your first Open Source Pull Request
How to setup Gitlab Repository in Windows 10
Merge Strategies in Git
How to Handle Merge Conflicts
GitHub App to Add or Remove Labels to Issues
How to Create Pull Request on GitHub without Using any IDE?
How to Clone Web Project from GitHub in Pycharm using Git?
How to Clone a project from GitHub using Eclipse?
How to Export Eclipse Projects to GitHub?
Creating New Branch on Github without using any IDE
How to Upload Project on GitHub from Jupyter Notebook?
Git Advanced
How to Handle Big Repositories with Git?
How to Protect Your Private Email Addresses in Git & Github?
How to send an Email using Git send-email via Gmail?
Dynamic Quote Generator for GitHub Readme
Automating some git commands with Python
How to Install and Use Git in Google Colab?
Downloading gists from Github made simple
Introduction to Bitbucket
Difference between Bitbucket and GitHub
Using Bitbucket as an extension to GitHub Capabilities
Working on Bitbucket using Git
Introduction to Mercurial
Difference between MERCURIAL and GIT
How to Make a GitHub Bot
Jenkins and GIT Integration using SSH Key
GitHub App to Build Form using Typeform and Probot
How to Trigger WebHooks without Events – Probot Github App
Difference between Gitlab and GitHub
Difference between Git and SVN
Link your GitHub Account with R Studio
Continuous Integration and Continuous Development(CI/CD)
How to Add GIT Credentials in Jenkins?
Implementation of CI/CD in .NET application Using Shell Executor on GitLab
Implementation of CI/CD in Java application(Linux) Using Shell and Docker Executor on GitLab
Implementation of CI/CD in C/C++ Application(Linux) Using Shell and Docker Executor on GitLab
How to Publish Docker Image to Dockerhub Using Github Actions?
Installing Private Git Server on K8s Cluster with Gitea and AKS
Flutter – Building and Releasing APK using GitHub Actions
How to Upload Android APK to Testers Group in Firebase Using GitHub Actions?
Basic CI Workflow For Android using GitHub Actions
GitHub Actions For Android
Git Workflow
A Git workflow is a set of guidelines that help teams collaborate effectively. Some common workflows include:
Feature Branch Workflow: Each feature gets its own branch.
GitFlow Workflow: A more structured workflow involving feature, release, and hotfix branches.
Forking Workflow: Fork the project, make changes, and then create a pull request.
Internal Working of Git
Git uses a decentralized model where each developer has their own copy of the repository and works immediately on the project. Git manages the projects with repositories and can clone a project to operate locally on it.
With staging and committing it track changes and control. You can pull the latest code of the project to the local copy, and push local updates to the main projects.
Git vs GitHub: Difference between Git and GitHub
Aspect
Git
GitHub
Definition
Git is a distributed version control system that tracks changes in the source code.
GitHub is a cloud-based Git repository hosting service that enhances collaboration and code management.
Purpose
To manage versions of code and track changes locally.
To host Git repositories online and allow collaboration and version control via Git.
Installation
Git is a command-line tool installed locally on your machine.
GitHub is accessed via the web and requires no installation.
Maintenance
Maintained by the Linux community.
Maintained by Microsoft since 2018.
Focus
Git focuses on version control and managing code changes.
GitHub focuses on hosting, collaboration, and project management.
History
Git was released in 2005 by Linus Torvalds.
GitHub was launched in 2008 as a platform for Git repository hosting.
User Management
Git does not have built-in user management.
GitHub includes built-in user management, allowing for collaboration and permissions.
Licensing
Git is open-source and free to use.
GitHub offers free-tier and paid plans with additional features.
Tool Integration
Git has minimal external tool integration.
GitHub provides an active marketplace for integrations, including CI/CD, project management, and more.
Interface
Git provides the Git GUI for graphical management.
GitHub provides GitHub Desktop and web interfaces for managing repositories.
Competition
Git competes with CVS, Mercurial, and Subversion.
GitHub competes with GitLab, Bitbucket, and SourceForge.
Best Practices for Git
Commit Frequently: Commit your changes regularly to avoid large, hard-to-merge commits.
Write Meaningful Commit Messages: Write clear, concise commit messages that describe what changes were made.
Use Branches for Features: Always create a new branch for new features or bug fixes to keep the main branch stable.
Keep Your Repositories Organized: Maintain a clean and structured directory in your repository.
Common Git Problems and Their Fixes
Merge Conflicts: Always check for conflicting code before merging. Resolve conflicts manually and commit the resolved files.
Detached HEAD State: When in a detached HEAD state, use git checkout <branch_name> to switch back to your branch.
Commit Not Pushed: Ensure that you have pushed your commits to the remote repository using git push.
Git and GitHub – FAQs
What is GitHub?
Git and GitHub are not the same, GitHub makes tools that use Git. GitHub is the popular host of code and maintained by Microsoft since 2018.
Why Should I Use Git?
Git is a useful tool that helps to manage changes in code or any documents, It generally allows collaboration between developers and writers and enables them easy version control.
Can Git be used for non-code files?
Yes, Git can be used to manage changes happening in any text-based files, documents, configuration files, and even images. However, Git may not be the best tool for managing large binary files.
How do I resolve conflicts in Git?
When multiple developers make changes to the same file, a conflict can occur. To resolve this, you need to identify the conflicting lines of code, make the necessary modifications, and then commit the changes to the repository.
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