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taco | verifiable_code | https://www.hackerrank.com/challenges/sam-and-substrings/problem | Solve the following coding problem using the programming language python:
Samantha and Sam are playing a numbers game. Given a number as a string, no leading zeros, determine the sum of all integer values of substrings of the string.
Given an integer as a string, sum all of its substrings cast as integers. As the number may become large, return the value modulo $10^9+7$.
Example
$n=\text{'}42\text{'}$
Here $n$ is a string that has $3$ integer substrings: $\begin{array}{c}A\end{array}$, $2$, and $\textbf{42}$. Their sum is $48$, and $48\ \text{modulo}\ (10^9+7)=48$.
Function Description
Complete the substrings function in the editor below.
substrings has the following parameter(s):
string n: the string representation of an integer
Returns
int: the sum of the integer values of all substrings in $n$, modulo $10^9+7$
Input Format
A single line containing an integer as a string, without leading zeros.
Constraints
$1\leq ncastas an integer\leq2\times10^5$
Sample Input 0
16
Sample Output 0
23
Explanation 0
The substrings of 16 are 16, 1 and 6 which sum to 23.
Sample Input 1
123
Sample Output 1
164
Explanation 1
The substrings of 123 are 1, 2, 3, 12, 23, 123 which sum to 164.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import operator
MOD = 1000000007
s = input()
n = len(s)
a = []
p10 = 0
for i in range(n, 0, -1):
p10 = (p10 * 10 + 1) % MOD
a.append(p10 * i % MOD)
b = [ord(c) - ord('0') for c in s]
print(sum(map(operator.mul, reversed(a), b)) % MOD)
``` | vfc_137827 | {
"difficulty": "medium",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://www.hackerrank.com/challenges/sam-and-substrings/problem",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "16\n",
"output": "23\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "123\n",
"output": "164\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/XYPIZQ | Solve the following coding problem using the programming language python:
Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.
ChefX showed ChefY his new pizza slice design. The design is a planar figure that can be drawn in the following way:
Draw a point $\mathsf{A}_0$ and two rays from this point such that the angle between them is $\alpha < \pi/2$.
Mark $N$ points $\mathsf{A}_1, \mathsf{A}_2, \mathsf{A}_3, \ldots, \mathsf{A}_N$ on one ray in this order ($\mathsf{A}_1$ is closest to $\mathsf{A}_0$).
Mark $N$ points $\mathsf{B}_1, \mathsf{B}_2, \mathsf{B}_3, \ldots, \mathsf{B}_N$ on the other ray in this order ($\mathsf{B}_1$ is closest to $\mathsf{A}_0$).
For each valid $i$, draw a line segment between points $\mathsf{A}_i$ and $\mathsf{B}_{i+1}$.
For each valid $i$, draw a line segment between points $\mathsf{B}_i$ and $\mathsf{A}_{i+1}$.
Finally, draw a line segment between points $\mathsf{A}_N$ and $\mathsf{B}_N$.
All these $2N-1$ line segments must have equal lengths, which must also be equal to $|\mathsf{A}_0\mathsf{A}_1| = |\mathsf{A}_0\mathsf{B}_1|$.
The result should look roughly like this:
ChefY wants to show ChefX that he does not know his own design very well. He asks ChefX to compute the angle between three of the marked points in this figure. It is clear that there are only four types of angles:
1. $\angle \mathsf{A}_x\mathsf{A}_y\mathsf{B}_z$
2. $\angle \mathsf{A}_x\mathsf{B}_y\mathsf{A}_z$
3. $\angle \mathsf{A}_x\mathsf{B}_y\mathsf{B}_z$
4. $\angle \mathsf{B}_x\mathsf{A}_y\mathsf{B}_z$
Can you help ChefX find the angle ChefY asks for? It can be proved that under the given constraints, each angle can be written as $\pi \cdot m / n$, where $m$ and $n$ are coprime integers; you should find $m$ and $n$.
------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first and only line of each test case contains five space-separated integers $N$, $t$, $x$, $y$ and $z$. Here, $t$ denotes the type of the angle as listed above.
------ Output ------
For each query, print a single line containing two space-separated integers $m$ and $n$.
------ Constraints ------
$1 ≤ T ≤ 10^{5}$
$2 ≤ N ≤ 10^{9}$
$1 ≤ t ≤ 4$
each angle is between three of the points $A_{0}, A_{1}, \ldots, A_{N}, B_{1}, \ldots, B_{N}$
$|x-y| = 1$
$|y-z| = 1$
each angle is non-zero
------ Subtasks ------
Subtask #1 (10 points): $1 ≤ T ≤ 10$
Subtask #2 (90 points): original constraints
----- Sample Input 1 ------
1
175456798 1 151163203 151163204 151163205
----- Sample Output 1 ------
66583464 116971199
----- explanation 1 ------
Example case 1: The type is $1$, so the angle we want is $\mathsf{A}_{151163203}\mathsf{A}_{151163204}\mathsf{B}_{151163205}$. The angle is $(66583464/116971199) \pi \doteq \mathrm{1.7883}$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import math
t = int(input())
for i in range(t):
a = [int(x) for x in input().split()]
n = a[0]
op = a[1]
x = a[2]
y = a[3]
z = a[4]
n1 = n * 2 + 1
if op == 1:
if x < y and y < z:
m = n1 - z
elif x > y and y > z:
m = n1 - z
else:
m = x
elif op == 2:
m = n1 - (z + x)
elif op == 3:
if x > y and y > z:
m = n1 - x
elif x < y and y < z:
m = n1 - x
else:
m = x
elif op == 4:
m = n1 - (z + x)
gc = math.gcd(m, n1)
m2 = int(m / gc)
n2 = int(n1 / gc)
print(m2, end=' ')
print(n2)
``` | vfc_137831 | {
"difficulty": "hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/XYPIZQ",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "1\n175456798 1 151163203 151163204 151163205",
"output": "66583464 116971199",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/335/F | Solve the following coding problem using the programming language python:
A nearby pie shop is having a special sale. For each pie you pay full price for, you may select one pie of a strictly lesser value to get for free. Given the prices of all the pies you wish to acquire, determine the minimum total amount you must pay for all of the pies.
Input
Input will begin with an integer n (1 ≤ n ≤ 500000), the number of pies you wish to acquire. Following this is a line with n integers, each indicating the cost of a pie. All costs are positive integers not exceeding 109.
Output
Print the minimum cost to acquire all the pies.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
6
3 4 5 3 4 5
Output
14
Input
5
5 5 5 5 5
Output
25
Input
4
309999 6000 2080 2080
Output
314159
Note
In the first test case you can pay for a pie with cost 5 and get a pie with cost 4 for free, then pay for a pie with cost 5 and get a pie with cost 3 for free, then pay for a pie with cost 4 and get a pie with cost 3 for free.
In the second test case you have to pay full price for every pie.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
h = [i for i in range(500001)]
t = [i for i in range(500001)]
ans = 0
len = 0
nw = 0
tot = 0
cnt = 0
a = []
def work(x):
y = x >> 1
while y and h[y] > h[x]:
tmp = h[x]
h[x] = h[y]
h[y] = tmp
x = y
y = x >> 1
def pop():
global len
h[1] = h[len]
len -= 1
x = 1
y = 2
if y < len and h[y + 1] < h[y]:
y += 1
while y <= len and h[y] < h[x]:
tmp = h[x]
h[x] = h[y]
h[y] = tmp
x = y
y = x << 1
if y < len and h[y + 1] < h[y]:
y += 1
def solve():
global cnt, len, tot, nw, a
n = int(input())
a = list(map(int, input().split()))
ans = sum(a)
a.sort(reverse=True)
a.insert(0, -1)
for i in range(1, n + 1):
if not nw:
nw = a[i]
tot = 1
elif nw > a[i]:
tot -= 1
cnt += 1
t[cnt] = a[i]
if not tot:
nw = 0
else:
tot += 1
if tot >= 2 and len and (h[1] < a[i] * 2):
if h[1] < a[i]:
cnt += 1
t[cnt] = a[i]
cnt += 1
t[cnt] = a[i]
else:
cnt += 1
t[cnt] = h[1]
cnt += 1
t[cnt] = a[i] * 2 - h[1]
pop()
tot -= 2
if not tot:
nw = 0
if i == n or a[i + 1] != a[i]:
if nw == a[i] and len and (h[1] < a[i]):
pop()
cnt += 1
t[cnt] = a[i]
for j in range(1, cnt + 1):
len += 1
h[len] = t[j]
work(len)
cnt = 0
for i in range(1, len + 1):
ans -= h[i]
print(ans)
solve()
``` | vfc_137835 | {
"difficulty": "very_hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/335/F",
"time_limit": "5.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "30\n3 6 3 8 6 4 4 2 4 10 8 5 9 6 7 7 9 4 7 4 10 1 9 10 4 7 7 4 2 3\n",
"output": "96\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1\n1\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "50\n4 2 6 7 2 6 3 8 8 2 4 8 4 4 1 4 5 2 2 5 6 4 3 3 3 6 8 2 1 3 1 8 2 3 7 4 7 5 4 8 3 5 7 8 6 7 5 8 7 1\n",
"output": "130\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "40\n2 6 5 5 6 6 7 8 6 5 3 9 9 1 8 3 7 3 7 2 3 1 3 1 5 8 1 3 8 2 3 2 2 1 4 4 4 3 5 5\n",
"output": "100\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "10\n1 1 1 1 1 2 3 4 5 6\n",
"output": "16\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n505072434 3351179\n",
"output": "505072434\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1213/E | Solve the following coding problem using the programming language python:
You are given two strings $s$ and $t$ both of length $2$ and both consisting only of characters 'a', 'b' and 'c'.
Possible examples of strings $s$ and $t$: "ab", "ca", "bb".
You have to find a string $res$ consisting of $3n$ characters, $n$ characters should be 'a', $n$ characters should be 'b' and $n$ characters should be 'c' and $s$ and $t$ should not occur in $res$ as substrings.
A substring of a string is a contiguous subsequence of that string. So, the strings "ab", "ac" and "cc" are substrings of the string "abacc", but the strings "bc", "aa" and "cb" are not substrings of the string "abacc".
If there are multiple answers, you can print any of them.
-----Input-----
The first line of the input contains one integer $n$ ($1 \le n \le 10^5$) — the number of characters 'a', 'b' and 'c' in the resulting string.
The second line of the input contains one string $s$ of length $2$ consisting of characters 'a', 'b' and 'c'.
The third line of the input contains one string $t$ of length $2$ consisting of characters 'a', 'b' and 'c'.
-----Output-----
If it is impossible to find the suitable string, print "NO" on the first line.
Otherwise print "YES" on the first line and string $res$ on the second line. $res$ should consist of $3n$ characters, $n$ characters should be 'a', $n$ characters should be 'b' and $n$ characters should be 'c' and $s$ and $t$ should not occur in $res$ as substrings.
If there are multiple answers, you can print any of them.
-----Examples-----
Input
2
ab
bc
Output
YES
acbbac
Input
3
aa
bc
Output
YES
cacbacbab
Input
1
cb
ac
Output
YES
abc
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
n = int(input())
l = ['abc' * n, 'acb' * n, 'bca' * n, 'cab' * n, 'bca' * n, 'cba' * n, 'b' * n + 'c' * n + 'a' * n, 'a' * n + 'b' * n + 'c' * n, 'c' * n + 'a' * n + 'b' * n]
a = input()
b = input()
print('YES')
for i in l:
if a not in i and b not in i:
print(i)
break
``` | vfc_137839 | {
"difficulty": "hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1213/E",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\nab\nbc\n",
"output": "YES\nacbacb\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3\naa\nbc\n",
"output": "YES\nacbacbacb\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1\ncb\nac\n",
"output": "YES\nabc\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/384/A | Solve the following coding problem using the programming language python:
Iahub likes chess very much. He even invented a new chess piece named Coder. A Coder can move (and attack) one square horizontally or vertically. More precisely, if the Coder is located at position (x, y), he can move to (or attack) positions (x + 1, y), (x–1, y), (x, y + 1) and (x, y–1).
Iahub wants to know how many Coders can be placed on an n × n chessboard, so that no Coder attacks any other Coder.
-----Input-----
The first line contains an integer n (1 ≤ n ≤ 1000).
-----Output-----
On the first line print an integer, the maximum number of Coders that can be placed on the chessboard.
On each of the next n lines print n characters, describing the configuration of the Coders. For an empty cell print an '.', and for a Coder print a 'C'.
If there are multiple correct answers, you can print any.
-----Examples-----
Input
2
Output
2
C.
.C
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
n = int(input())
print(n % 2 + n * n // 2)
for i in range(n):
if i % 2:
print(''.join(('C' if j % 2 else '.' for j in range(n))))
else:
print(''.join(('.' if j % 2 else 'C' for j in range(n))))
``` | vfc_137844 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/384/A",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n",
"output": "2\nC.\n.C\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/TWOTRAINS | Solve the following coding problem using the programming language python:
There are 2 trains A and B and N stations in a line from 1 to N in order. There is also an array P of length N-1 such that P_{i} (1≤ i < N) denotes the amount of time any train takes to go from the i-th station to the (i+1)-th station.
Initially, both trains are at station 1. Train A departs from station 1 and stops directly at station N. For safety purposes, it is maintained that train B cannot depart from station i unless train A has already reached station (i+1) (1 ≤ i < N).
Find the minimum time after which train B reaches station N, once train A departs from station 1.
------ Input Format ------
- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of two lines of input.
- The first line of each test case contains an integer N, denoting number of stations.
- The next line contains N-1 space-separated integers, P_{1},P_{2},\ldots ,P_{N-1}.
------ Output Format ------
For each test case, output on a new line the minimum time after which train B reaches station N.
------ Constraints ------
$1 ≤ T ≤ 100$
$2 ≤ N ≤ 10^{5}$
$1 ≤ P_{i} ≤ 10^{3}$
- The sum of $N$ over all test cases won't exceed $10^{5}$.
----- Sample Input 1 ------
3
2
4
3
3 5
4
5 2 6
----- Sample Output 1 ------
8
13
19
----- explanation 1 ------
Test case $1$: $A$ reaches station $2$ at $t=4$ and at this time $B$ departs from station $1$ and reaches station $2$ at $t=4+4=8$.
Test case $2$: Following is the timeline of two trains-
- At $t=3$, $A$ reaches station $2$ and $B$ departs from station $1$.
- At $t=6$, $B$ reaches station $2$ but $A$ has not yet reached station $3$, so train $B$ will wait at station $2$.
- At $t=8$, $A$ reaches station $3$ and $B$ departs from station $2$.
- At $t=8+5=13$, train $B$ reaches station $3$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for _ in range(int(input())):
n = int(input())
p = list(map(int, input().split()))
x = p[0]
y = 2 * x
for i in range(1, n - 1):
x += p[i]
if y < x:
y += x - y + p[i]
else:
y += p[i]
print(y)
``` | vfc_137848 | {
"difficulty": "easy",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/TWOTRAINS",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n2\n4\n3\n3 5\n4\n5 2 6\n",
"output": "8\n13\n19\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1728/A | Solve the following coding problem using the programming language python:
The title is a reference to the very first Educational Round from our writers team, Educational Round 18.
There is a bag, containing colored balls. There are $n$ different colors of balls, numbered from $1$ to $n$. There are $\mathit{cnt}_i$ balls of color $i$ in the bag. The total amount of balls in the bag is odd (e. g. $\mathit{cnt}_1 + \mathit{cnt}_2 + \dots + \mathit{cnt}_n$ is odd).
In one move, you can choose two balls with different colors and take them out of the bag.
At some point, all the remaining balls in the bag will have the same color. That's when you can't make moves anymore.
Find any possible color of the remaining balls.
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of testcases.
The first line of each testcase contains a single integer $n$ ($1 \le n \le 20$) — the number of colors.
The second line contains $n$ integers $\mathit{cnt}_1, \mathit{cnt}_2, \dots, \mathit{cnt}_n$ ($1 \le \mathit{cnt}_i \le 100$) — the amount of balls of each color in the bag.
The total amount of balls in the bag is odd (e. g. $\mathit{cnt}_1 + \mathit{cnt}_2 + \dots + \mathit{cnt}_n$ is odd).
-----Output-----
For each testcase, print a single integer — any possible color of the remaining balls, after you made some moves and can't make moves anymore.
-----Examples-----
Input
3
3
1 1 1
1
9
2
4 7
Output
3
1
2
-----Note-----
In the first testcase, your first and only move can be one of the following:
take balls with colors $1$ and $2$;
take balls with colors $1$ and $3$;
take balls with colors $2$ and $3$.
After the move, exactly one ball will remain. Its color can be $3, 2$ or $1$ depending on the move.
In the second testcase, you can't make moves at all — there is only color of balls already. This color is $1$.
In the third testcase, you can keep removing one ball of color $1$ and one ball of color $2$ until there are no more balls of color $1$. At the end, three balls of color $2$ remain.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for _ in range(int(input())):
x = int(input())
l = list(map(int, input().split()))
ma = max(l)
print(l.index(ma) + 1)
``` | vfc_137856 | {
"difficulty": "easy",
"memory_limit": "256 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1728/A",
"time_limit": "2 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n3\n1 1 1\n1\n9\n2\n4 7\n",
"output": "1\n1\n2\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/find-the-frequency/1 | Solve the following coding problem using the programming language python:
Given a vector of N positive integers and an integer X. The task is to find the frequency of X in vector.
Example 1:
Input:
N = 5
vector = {1, 1, 1, 1, 1}
X = 1
Output:
5
Explanation: Frequency of 1 is 5.
Your Task:
Your task is to complete the function findFrequency() which should count the frequency of X and return it.
Write your solution by modifying this code:
```python
#User function Template for python3
"""
You're given an array (arr) of length n
Return the frequency of element x in the given array
"""
def findFrequency (arr, n, x):
# Your Code Here
```
Your solution should implemented in the function "findFrequency". The inputs will be passed to it and it should return the correct solution.
Now solve the problem and return the code. | ```python
def findFrequency(arr, n, x):
c = 0
for i in arr:
if i == x:
c += 1
return c
``` | vfc_137861 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/find-the-frequency/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": "findFrequency",
"input": "N = 5\nvector = {1, 1, 1, 1, 1}\nX = 1",
"output": "5",
"type": "function_call"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/COST_MANIA | Solve the following coding problem using the programming language python:
Kiteretsu goes to his Chemistry Lab to perform the perfect reaction.
In his lab, he found N reagents numbered 1 to N. The i^{th} reagent has two properties - A_{i} and B_{i}.
A reaction can be performed between the reagents i and j only if A_{i} ≤ j.
If a reaction is performed between reagents i and j, i \cdot j amount of heat is produced. Out of this, D \cdot (B_{i} \oplus B_{j}) is absorbed and the rest heat is released. Here, \oplus denotes the [bitwise XOR] operation.
More formally, in a reaction between reagents i and j, the heat released is given by:
H(i,j)= i \cdot j - D \cdot (B_{i} \oplus B_{j})
Find the maximum possible heat which can be released in a reaction.
Note: The input of this problem is large, so use fast input/output methods.
------ Input Format ------
- The first line will contain T - the number of test cases. Then the test cases follow.
- First line of each test case contains two integers N, D.
- Second line of each test case contains N integers A_{1}, A_{2}, \ldots, A_{N}.
- Third line of each test case contains N integers B_{1}, B_{2}, \ldots, B_{N}
------ Output Format ------
For each test case, print a single line, a single integer denoting the maximum possible heat that can be released in a reaction.
------ Constraints ------
$1 ≤ T ≤ 10$
$2 ≤ N ≤ 10^{6}$
$1 ≤ D ≤ 2000$
$(i+1) ≤ A_{i} ≤ N$ $\forall$ $(1 ≤ i < N)$
$A_{N}=N+1$
$1 ≤ B_{i} ≤ N$
- Sum of $N$ over all test cases does not exceed $10^{6}$.
----- Sample Input 1 ------
2
5 2
2 4 5 5 6
1 3 2 2 5
2 3
2 3
1 2
----- Sample Output 1 ------
6
-7
----- explanation 1 ------
Test Case $1$: Let us choose $i = 2$ and $j = 4$. Since $A_{2} ≤ 4$, a reaction can take place.
The heat released in this reaction is $2\cdot 4 - 2\cdot (3 \oplus 2) = 8-2 \cdot 1 = 6$. It can be proven that for no other reaction, the heat released is greater than $6$.
Some other reactions can take place between $(2, 5)$, $(3,5)$. Note that no reaction is possible between $(3,4)$ as $A_{3} \nleq 4$.
Test Case $2$: The only possible reaction is between reagents $1$ and $2$. The heat released in this reaction is $1 \cdot 2 - 3\cdot (1 \oplus 2) = 2 - 3\cdot 3 = -7$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
t = int(input())
for _ in range(t):
(n, d) = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
mx_heat = None
for i in range(n - 1, 0, -1):
if mx_heat is not None and i * (i + 1) <= mx_heat:
break
for j in range(i - 1, -1, -1):
if mx_heat is not None and (i + 1) * (j + 1) <= mx_heat:
break
if a[i] <= j + 1:
heat = (i + 1) * (j + 1) - d * (b[i] ^ b[j])
if mx_heat is None:
mx_heat = heat
else:
mx_heat = max(mx_heat, heat)
elif a[j] <= i + 1:
heat = (i + 1) * (j + 1) - d * (b[i] ^ b[j])
if mx_heat is None:
mx_heat = heat
else:
mx_heat = max(mx_heat, heat)
print(mx_heat)
``` | vfc_137866 | {
"difficulty": "very_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/COST_MANIA",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n5 2\n2 4 5 5 6\n1 3 2 2 5\n2 3\n2 3\n1 2\n",
"output": "6\n-7\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1371/C | Solve the following coding problem using the programming language python:
Anna is a girl so brave that she is loved by everyone in the city and citizens love her cookies. She is planning to hold a party with cookies. Now she has $a$ vanilla cookies and $b$ chocolate cookies for the party.
She invited $n$ guests of the first type and $m$ guests of the second type to the party. They will come to the party in some order. After coming to the party, each guest will choose the type of cookie (vanilla or chocolate) to eat. There is a difference in the way how they choose that type:
If there are $v$ vanilla cookies and $c$ chocolate cookies at the moment, when the guest comes, then if the guest of the first type: if $v>c$ the guest selects a vanilla cookie. Otherwise, the guest selects a chocolate cookie. if the guest of the second type: if $v>c$ the guest selects a chocolate cookie. Otherwise, the guest selects a vanilla cookie.
After that: If there is at least one cookie of the selected type, the guest eats one. Otherwise (there are no cookies of the selected type), the guest gets angry and returns to home.
Anna wants to know if there exists some order of guests, such that no one guest gets angry. Your task is to answer her question.
-----Input-----
The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases. Next $t$ lines contain descriptions of test cases.
For each test case, the only line contains four integers $a$, $b$, $n$, $m$ ($0 \le a,b,n,m \le 10^{18}, n+m \neq 0$).
-----Output-----
For each test case, print the answer in one line. If there exists at least one valid order, print "Yes". Otherwise, print "No".
You can print each letter in any case (upper or lower).
-----Example-----
Input
6
2 2 1 2
0 100 0 1
12 13 25 1
27 83 14 25
0 0 1 0
1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000
Output
Yes
No
No
Yes
No
Yes
-----Note-----
In the first test case, let's consider the order $\{1, 2, 2\}$ of types of guests. Then: The first guest eats a chocolate cookie. After that, there are $2$ vanilla cookies and $1$ chocolate cookie. The second guest eats a chocolate cookie. After that, there are $2$ vanilla cookies and $0$ chocolate cookies. The last guest selects a chocolate cookie, but there are no chocolate cookies. So, the guest gets angry.
So, this order can't be chosen by Anna.
Let's consider the order $\{2, 2, 1\}$ of types of guests. Then: The first guest eats a vanilla cookie. After that, there is $1$ vanilla cookie and $2$ chocolate cookies. The second guest eats a vanilla cookie. After that, there are $0$ vanilla cookies and $2$ chocolate cookies. The last guest eats a chocolate cookie. After that, there are $0$ vanilla cookies and $1$ chocolate cookie.
So, the answer to this test case is "Yes".
In the fifth test case, it is illustrated, that the number of cookies ($a + b$) can be equal to zero, but the number of guests ($n + m$) can't be equal to zero.
In the sixth test case, be careful about the overflow of $32$-bit integer type.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for _ in range(int(input())):
(a, b, n, m) = list(map(int, input().split()))
r = min(a, b)
s = a + b
if n + m > s:
print('No')
elif r < m:
print('No')
else:
print('Yes')
``` | vfc_137870 | {
"difficulty": "easy",
"memory_limit": "256 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1371/C",
"time_limit": "1 second"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "6\n2 2 1 2\n0 100 0 1\n12 13 25 1\n27 83 14 25\n0 0 1 0\n1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000\n",
"output": "Yes\nNo\nNo\nYes\nNo\nYes\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/DEC15/problems/CHCINEMA | Solve the following coding problem using the programming language python:
Probably everyone has experienced an awkward situation due to shared armrests between seats in cinemas. A highly accomplished cinema manager named "Chef" decided to solve this problem.
When a customer wants to buy a ticket, the clerk at the ticket window asks the visitor if they need the armrests, and if so, which of them: left, right, or both. We know that out of the audience expected to show up, L of them only need the left armrest, R of them need just the right one, Z need none and B need both. Your task is to calculate the maximum number of people that can attend the show. In the cinema hall there are N rows with M seats each. There is only one armrest between two adjacent seats. Seats at the beginning and at the end of the row have two armrests
-----Input-----
Input begins with an integer T: the number of test cases.
Each test case consists of a single line with 6 space-separated integers: N, M, Z, L, R, B.
-----Output-----
For each test case, output a line containing the answer for the task.
-----Constraints and Subtasks-----
- 1 ≤ T ≤ 105
Subtask 1 : 10 points
- 1 ≤ N, M ≤ 3
- 0 ≤ Z, L, R, B ≤ 3
Subtask 2 : 20 points
- 1 ≤ N, M ≤ 30
- 0 ≤ Z, L, R ≤ 30
- 0 ≤ B ≤ 109
Subtask 3 : 30 points
- 1 ≤ N, M ≤ 106
- 0 ≤ Z, L, R ≤ 106
- 0 ≤ B ≤ 1016
Subtask 4 : 40 points
- 1 ≤ N, M ≤ 108
- 0 ≤ Z, L, R, B ≤ 1016
-----Example-----
Input:2
2 2 3 2 1 1
3 3 1 2 0 9
Output:4
8
-----Explanation-----
'L' - needs left
'R - needs right
'Z' - doesn't need any
'B' - needs both
'-' - empty place
Example case 1.
ZZ
ZB
Example case 2.
LLB
BZB
B-B
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for i in range(eval(input())):
(n, m, z, l, r, b) = list(map(int, input().split()))
rows = n
columns = m
hand_rest = n * (m + 1)
if m % 2 == 0:
hand_rest -= max(0, n - l - r)
if l + r + 2 * b <= hand_rest:
print(min(n * m, l + r + z + b))
else:
temp = l + r + (hand_rest - l - r) / 2
print(min(n * m, temp + z))
``` | vfc_137874 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/DEC15/problems/CHCINEMA",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n2 2 3 2 1 1\n3 3 1 2 0 9\n",
"output": "4\n8\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/667/C | Solve the following coding problem using the programming language python:
First-rate specialists graduate from Berland State Institute of Peace and Friendship. You are one of the most talented students in this university. The education is not easy because you need to have fundamental knowledge in different areas, which sometimes are not related to each other.
For example, you should know linguistics very well. You learn a structure of Reberland language as foreign language. In this language words are constructed according to the following rules. First you need to choose the "root" of the word — some string which has more than 4 letters. Then several strings with the length 2 or 3 symbols are appended to this word. The only restriction — it is not allowed to append the same string twice in a row. All these strings are considered to be suffixes of the word (this time we use word "suffix" to describe a morpheme but not the few last characters of the string as you may used to).
Here is one exercise that you have found in your task list. You are given the word s. Find all distinct strings with the length 2 or 3, which can be suffixes of this word according to the word constructing rules in Reberland language.
Two strings are considered distinct if they have different length or there is a position in which corresponding characters do not match.
Let's look at the example: the word abacabaca is given. This word can be obtained in the following ways: <image>, where the root of the word is overlined, and suffixes are marked by "corners". Thus, the set of possible suffixes for this word is {aca, ba, ca}.
Input
The only line contains a string s (5 ≤ |s| ≤ 104) consisting of lowercase English letters.
Output
On the first line print integer k — a number of distinct possible suffixes. On the next k lines print suffixes.
Print suffixes in lexicographical (alphabetical) order.
Examples
Input
abacabaca
Output
3
aca
ba
ca
Input
abaca
Output
0
Note
The first test was analysed in the problem statement.
In the second example the length of the string equals 5. The length of the root equals 5, so no string can be used as a suffix.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
s = input()[5:][::-1]
n = len(s)
mu = set()
can2 = [0] * (n + 1)
can3 = [0] * (n + 1)
if n >= 2:
mu.add(s[0:2][::-1])
can2[2] = 1
if n >= 3:
mu.add(s[0:3][::-1])
can3[3] = 1
if n >= 4 and s[0:2] != s[2:4]:
mu.add(s[2:4][::-1])
can2[4] = 1
if n >= 5:
mu.add(s[2:5][::-1])
mu.add(s[3:5][::-1])
can2[5] = 1
can3[5] = 1
for i in range(6, n + 1):
if can2[i - 3]:
mu.add(s[i - 3:i][::-1])
can3[i] = 1
if can2[i - 2]:
if s[i - 2:i] != s[i - 4:i - 2]:
mu.add(s[i - 2:i][::-1])
can2[i] = 1
if can3[i - 2]:
mu.add(s[i - 2:i][::-1])
can2[i] = 1
if can3[i - 3]:
if s[i - 3:i] != s[i - 6:i - 3]:
mu.add(s[i - 3:i][::-1])
can3[i] = 1
print(len(mu))
print('\n'.join(sorted(list(mu))))
``` | vfc_137879 | {
"difficulty": "medium_hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/667/C",
"time_limit": "1.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "aaaaaxyxxxx\n",
"output": "5\nxx\nxxx\nxyx\nyx\nyxx\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "aaaaaxxxxxx\n",
"output": "2\nxx\nxxx\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "gzqgchv\n",
"output": "1\nhv\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "aaaaaxyxy\n",
"output": "2\nxy\nyxy\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "glaoyryxrgsysy\n",
"output": "10\ngs\ngsy\nrgs\nry\nryx\nsy\nxr\nysy\nyx\nyxr\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "xxxxxababc\n",
"output": "5\nab\naba\nabc\nba\nbc\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1425/D | Solve the following coding problem using the programming language python:
Mr. Chanek The Ninja is one day tasked with a mission to handle mad snakes that are attacking a site. Now, Mr. Chanek already arrived at the hills where the destination is right below these hills. The mission area can be divided into a grid of size 1000 × 1000 squares. There are N mad snakes on the site, the i'th mad snake is located on square (X_i, Y_i) and has a danger level B_i.
Mr. Chanek is going to use the Shadow Clone Jutsu and Rasengan that he learned from Lord Seventh to complete this mission. His attack strategy is as follows:
1. Mr. Chanek is going to make M clones.
2. Each clone will choose a mad snake as the attack target. Each clone must pick a different mad snake to attack.
3. All clones jump off the hills and attack their respective chosen target at once with Rasengan of radius R. If the mad snake at square (X, Y) is attacked with a direct Rasengan, it and all mad snakes at squares (X', Y') where max(|X' - X|, |Y' - Y|) ≤ R will die.
4. The real Mr. Chanek will calculate the score of this attack. The score is defined as the square of the sum of the danger levels of all the killed snakes.
Now Mr. Chanek is curious, what is the sum of scores for every possible attack strategy? Because this number can be huge, Mr. Chanek only needs the output modulo 10^9 + 7.
Input
The first line contains three integers N M R (1 ≤ M ≤ N ≤ 2 ⋅ 10^3, 0 ≤ R < 10^3), the number of mad snakes, the number of clones, and the radius of the Rasengan.
The next N lines each contains three integers, X_i, Y_i, dan B_i (1 ≤ X_i, Y_i ≤ 10^3, 1 ≤ B_i ≤ 10^6). It is guaranteed that no two mad snakes occupy the same square.
Output
A line with an integer that denotes the sum of scores for every possible attack strategy.
Example
Input
4 2 1
1 1 10
2 2 20
2 3 30
5 2 40
Output
33800
Note
Here is the illustration of all six possible attack strategies. The circles denote the chosen mad snakes, and the blue squares denote the region of the Rasengan:
<image>
So, the total score of all attacks is: 3.600 + 3.600 + 4.900 + 3.600 + 10.000 + 8.100 = 33.800.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 4)
from sys import stdin, stdout
from collections import defaultdict, Counter
from functools import lru_cache
M = 10 ** 9 + 7
fact = [1] * 2001
def fac(n):
if n == 0 or n == 1:
return 1
elif fact[n] != 1:
return fact[n]
fact[n] = fac(n - 1) * (n % M) % M
return fact[n]
ncr = [[0 for i in range(2001)] for j in range(2001)]
def choose(n, k):
if n < k:
return 0
if k == 0 or k == n:
return 1
elif k == 1 or k == n - 1:
return n % M
elif ncr[n][k] != 0:
return ncr[n][k]
else:
ncr[n][k] = fac(n) * (pow(fac(k), M - 2, M) * pow(fac(n - k), M - 2, M)) % M % M
return ncr[n][k]
def find_inter(x1, y1, x2, y2, x3, y3, x4, y4):
x5 = max(x1, x3)
y5 = max(y1, y3)
x6 = min(x2, x4)
y6 = min(y2, y4)
if x5 > x6 or y5 > y6:
return [0]
return [1, x5, y5, x6, y6]
def main():
(n, m, r) = [int(s) for s in input().split()]
snakes = [[int(s) for s in input().split()] for i in range(n)]
X = max([i[0] for i in snakes])
Y = max([i[1] for i in snakes])
num = [1] * n
for i in range(n - 1):
for j in range(i + 1, n):
if max(abs(snakes[i][0] - snakes[j][0]), abs(snakes[i][1] - snakes[j][1])) <= r:
num[i] += 1
num[j] += 1
ans = 0
ncm = choose(n, m)
for i in range(n):
v = (ncm - choose(n - num[i], m)) % M * (snakes[i][2] ** 2 % M) % M
ans = (ans + v) % M
pre = [[0 for i in range(Y + r + 1)] for j in range(X + r + 1)]
for i in range(n):
pre[snakes[i][0]][snakes[i][1]] = 1
for i in range(1, X + r + 1):
pre[i][0] += pre[i - 1][0]
for i in range(1, Y + r + 1):
pre[0][i] += pre[0][i - 1]
for i in range(1, X + r + 1):
for j in range(1, Y + r + 1):
pre[i][j] += pre[i][j - 1] + pre[i - 1][j] - pre[i - 1][j - 1]
num1 = [[0 for i in range(n)] for j in range(n)]
for i in range(n - 1):
for j in range(i + 1, n):
(x1, y1, x2, y2) = (snakes[i][0], snakes[i][1], snakes[j][0], snakes[j][1])
inter = find_inter(max(x1 - r, 0), max(y1 - r, 0), x1 + r, y1 + r, max(x2 - r, 0), max(y2 - r, 0), x2 + r, y2 + r)
if inter[0] == 1:
(blx, bly, trx, ty) = inter[1:]
num1[i][j] = pre[trx][ty]
if blx - 1 >= 0 and bly - 1 >= 0:
num1[i][j] += pre[blx - 1][bly - 1]
if blx - 1 >= 0:
num1[i][j] -= pre[blx - 1][ty]
if bly - 1 >= 0:
num1[i][j] -= pre[trx][bly - 1]
ans1 = 0
for i in range(n - 1):
for j in range(i + 1, n):
x = num[i]
y = num[j]
z = num1[i][j]
v = (ncm + (choose(n - x - y + z, m) - (choose(n - x, m) + choose(n - y, m)) % M) % M) % M * (snakes[i][2] * snakes[j][2] % M) % M
ans1 = (ans1 + v) % M
print((ans + 2 * ans1 % M) % M)
main()
``` | vfc_137883 | {
"difficulty": "hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1425/D",
"time_limit": "2.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "4 1 0\n1 1 10\n1 999 30\n1 1000 40\n1 2 20\n",
"output": "3000\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1 1 0\n1 1 10\n",
"output": "100\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "20 17 0\n1 964 972064\n1 529 914335\n1 926 994468\n1 603 980092\n1 545 946148\n1 88 952185\n1 979 918633\n1 438 967889\n1 871 926455\n1 424 952048\n1 892 911827\n1 779 947360\n1 800 977424\n1 792 958202\n1 833 941466\n1 21 910590\n1 384 963993\n1 72 975862\n1 569 953738\n1 646 978054\n",
"output": "351865268\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/JUNE09/problems/D7 | Solve the following coding problem using the programming language python:
The Chef has been kidnapped by aliens ( they want to utilize his excellent cooking skills :P ) and has been transported to the alien planet "ZX532". Interestingly, "ZX532" uses a different time scale which has Y AlienHours on the face of a clock (instead of the 12 hours that we have). They also have 'X*Y' AlienMinutes (instead of the 60 that we have). X is defined as the number of minute divisions between each hour (the earth clock has X=5).
The Chef has been forced to cook a lot of dishes by the aliens. He is short of ingredients and hence needs to go out to the market to get them. However when he returns, he makes an interesting observation. The hands of AlienClock have exactly swapped position from the time he left (the big hand and the little hand have switched)!
Given the times between which The Chef might have left and the times between which The Chef may have returned, you are supposed to find out the actual time when he left. If there is more than one possibility, print the one that maximizes the amount of time that The Chef is out.Details of the Clock
The AlienClock is circular and has exactly 2 hands : the hour hand and the minute hand. The whole circumference of the AlienClock is divided into Y divisions , each of which is further divided into X subdivisions [ X and Y are both positive integers ]. The clock is not discrete but continuous (the hands move continuously instead of moving at certain intervals such as every second, etc.... ).
-----Input-----
First line of input contains t (1≤ t ≤ 100) - the number of test cases. Each test case contains 2 lines each. The first line contains 2 space separated integers , X and Y (same as those specified in the problem statement; X ≤ 109 and Y ≤ 109 ).
The next line contains 8 space separated integers (a,b,c,d,e,f,g,h; 0 ≤ a ≤ c < Y; 0 ≤ e ≤ g < Y; a ≤ e; 0 ≤ b,d,f,h < X*Y ): specifying the times between which The Chef might have left (a:b => a hours and b minutes TO c:d => c hours and d minutes) and the times between which The Chef may have returned (The Chef returns sometime between e:f and g:h).
The interval at which The Chef re-enters the kitchen will never start prior to the interval at which he first leaves the kitchen to purchase the ingredients.
-----Output-----
The output should contain one line for each test case specifying the time when The Chef left the kitchen. This should be in the form (h:m => h hours and m minutes). h will be an integer, and m should be rounded to 2 decimal places. In case, there is no solution possible, output -1 for that test case.
-----Example-----
Input:
3
5 12
1 0 2 0 4 0 5 0
5 12
3 30 4 0 5 0 6 0
5 12
3 0 4 0 5 0 6 0
Output:
1:20.56
-1
3:26.43
Note: Be careful with precision.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import decimal
from decimal import *
def solve(a, b, min1, min2, min3, min4, x, y):
if a > b:
return []
solMin1 = (a / y + b) / (y - 1 / y)
solMin2 = (b / y + a) / (y - 1 / y)
solMin1 *= x * y
solMin2 *= x * y
if solMin1 >= min1 and solMin1 <= min2 and (solMin2 >= min3) and (solMin2 <= min4):
return [a, solMin1, b, solMin2]
return []
def integerPart(x):
return Decimal(str(x).split('.')[0])
def fractionalPart(x):
t = str(x).split('.')
if len(t) > 0:
return '.' + t[1]
return 0
getcontext().prec = 30
for i in range(eval(input())):
(x, y) = input().split()
(a, b, c, d, e, f, g, h) = input().split()
x = Decimal(x)
y = Decimal(y)
a = Decimal(a)
b = Decimal(b)
c = Decimal(c)
d = Decimal(d)
e = Decimal(e)
f = Decimal(f)
g = Decimal(g)
h = Decimal(h)
if a > g or (a == g and b > h):
print('-1')
continue
solutionh = Decimal('-1')
solutionm = Decimal('-1')
diff = Decimal('-10000000000000000')
solution1 = []
solution2 = []
solution3 = []
solution4 = []
solution5 = []
solution6 = []
solution7 = []
solution8 = []
solution9 = []
solution10 = []
solution11 = []
solution12 = []
solution13 = []
solution14 = []
l1 = 0
if g == e:
l1 = f
solution1 = solve(a + 0, g + 0, b, x * y, l1, h, x, y)
if a < y - 1 and len(solution1) == 0:
solution2 = solve(a + 1, g + 0, 0, x * y, l1, h, x, y)
if g >= 1 and len(solution1) == 0 and (len(solution2) == 0):
solution4 = solve(a + 0, g - 1, b, x * y, 0, x * y, x, y)
if g - e >= 2 and c - a >= 2:
solution5 = solve(a + 1, g - 1, 0, x * y, 0, x * y, x, y)
if len(solution1) == 0 and len(solution2) == 0 and (len(solution4) == 0):
solution10 = solve(a, e, 0, x * y, 0, x * y, x, y)
solution11 = solve(c, e, 0, x * y, 0, x * y, x, y)
solution12 = solve(c, g, 0, x * y, 0, x * y, x, y)
if a < y - 1 and len(solution1) == 0 and (len(solution2) == 0) and (len(solution4) == 0) and (c - a >= 2):
solution13 = solve(a + 1, e, 0, x * y, 0, x * y, x, y)
if g >= 1 and len(solution1) == 0 and (len(solution2) == 0) and (len(solution4) == 0) and (g - e >= 2):
solution14 = solve(c, g - 1, 0, x * y, 0, x * y, x, y)
if len(solution1) > 0:
if solution1[0] < c or (solution1[0] == c and solution1[1] <= d):
if solution1[2] > e or (solution1[2] == e and solution1[3] >= f):
t = (solution1[2] - solution1[0]) * x * y + (solution1[3] - solution1[1])
if t > diff:
diff = t
solutionh = solution1[0]
solutionm = solution1[1]
if len(solution2) > 0:
if solution2[0] < c or (solution2[0] == c and solution2[1] <= d):
if solution2[2] > e or (solution2[2] == e and solution2[3] >= f):
t = (solution2[2] - solution2[0]) * x * y + (solution2[3] - solution2[1])
if t > diff:
diff = t
solutionh = solution2[0]
solutionm = solution2[1]
if len(solution4) > 0:
if solution4[0] < c or (solution4[0] == c and solution4[1] <= d):
if solution4[2] > e or (solution4[2] == e and solution4[3] >= f):
t = (solution4[2] - solution4[0]) * x * y + (solution4[3] - solution4[1])
if t > diff:
diff = t
solutionh = solution4[0]
solutionm = solution4[1]
if len(solution5) > 0:
if solution5[0] < c or (solution5[0] == c and solution5[1] <= d):
if solution5[2] > e or (solution5[2] == e and solution5[3] >= f):
t = (solution5[2] - solution5[0]) * x * y + (solution5[3] - solution5[1])
if t > diff:
diff = t
solutionh = solution5[0]
solutionm = solution5[1]
if len(solution10) > 0:
if solution10[0] > a or (solution10[0] == a and solution10[1] >= b):
if solution10[0] < c or (solution10[0] == c and solution10[1] <= d):
if solution10[2] > e or (solution10[2] == e and solution10[3] >= f):
if solution10[2] < g or (solution10[2] == g and solution10[3] <= h):
t = (solution10[2] - solution10[0]) * x * y + (solution10[3] - solution10[1])
if t > diff:
diff = t
solutionh = solution10[0]
solutionm = solution10[1]
if len(solution11) > 0:
if solution11[0] > a or (solution11[0] == a and solution11[1] >= b):
if solution11[0] < c or (solution11[0] == c and solution11[1] <= d):
if solution11[2] > e or (solution11[2] == e and solution11[3] >= f):
if solution11[2] < g or (solution11[2] == g and solution11[3] <= h):
t = (solution11[2] - solution11[0]) * x * y + (solution11[3] - solution11[1])
if t > diff:
diff = t
solutionh = solution11[0]
solutionm = solution11[1]
if len(solution12) > 0:
if solution12[0] > a or (solution12[0] == a and solution12[1] >= b):
if solution12[0] < c or (solution12[0] == c and solution12[1] <= d):
if solution12[2] > e or (solution12[2] == e and solution12[3] >= f):
if solution12[2] < g or (solution12[2] == g and solution12[3] <= h):
t = (solution12[2] - solution12[0]) * x * y + (solution12[3] - solution12[1])
if t > diff:
diff = t
solutionh = solution12[0]
solutionm = solution12[1]
if len(solution13) > 0:
if solution13[0] > a or (solution13[0] == a and solution13[1] >= b):
if solution13[0] < c or (solution13[0] == c and solution13[1] <= d):
if solution13[2] > e or (solution13[2] == e and solution13[3] >= f):
if solution13[2] < g or (solution13[2] == g and solution13[3] <= h):
t = (solution13[2] - solution13[0]) * x * y + (solution13[3] - solution13[1])
if t > diff:
diff = t
solutionh = solution13[0]
solutionm = solution13[1]
if len(solution14) > 0:
if solution14[0] > a or (solution14[0] == a and solution14[1] >= b):
if solution14[0] < c or (solution14[0] == c and solution14[1] <= d):
if solution14[2] > e or (solution14[2] == e and solution14[3] >= f):
if solution14[2] < g or (solution14[2] == g and solution14[3] <= h):
t = (solution14[2] - solution14[0]) * x * y + (solution14[3] - solution14[1])
if t > diff:
diff = t
solutionh = solution14[0]
solutionm = solution14[1]
limit1 = (y - 1 / y) * (f / (x * y)) - e / y
if limit1 <= a + 1:
limit1 = a + 1
limit1 = Decimal(str(int(limit1)))
limit2 = (y - 1 / y) * (d / (x * y)) - c / y
if limit2 >= g - 1:
limit2 = g - 1
limit2 = Decimal(str(int(limit2)))
if limit1 >= a + 1 and limit1 <= c - 1:
solutionNew = solve(limit1, e, 0, x * y, 0, x * y, x, y)
if len(solutionNew) > 0:
if solutionNew[0] > a or (solutionNew[0] == a and solutionNew[1] >= b):
if solutionNew[0] < c or (solutionNew[0] == c and solutionNew[1] <= d):
if solutionNew[2] > e or (solutionNew[2] == e and solutionNew[3] >= f):
if solutionNew[2] < g or (solutionNew[2] == g and solutionNew[3] <= h):
t = (solutionNew[2] - solutionNew[0]) * x * y + (solutionNew[3] - solutionNew[1])
if t > diff:
diff = t
solutionh = solutionNew[0]
solutionm = solutionNew[1]
if limit1 + 1 >= a + 1 and limit1 + 1 <= c - 1:
solutionNew = solve(limit1 + 1, e, 0, x * y, 0, x * y, x, y)
if len(solutionNew) > 0:
if solutionNew[0] > a or (solutionNew[0] == a and solutionNew[1] >= b):
if solutionNew[0] < c or (solutionNew[0] == c and solutionNew[1] <= d):
if solutionNew[2] > e or (solutionNew[2] == e and solutionNew[3] >= f):
if solutionNew[2] < g or (solutionNew[2] == g and solutionNew[3] <= h):
t = (solutionNew[2] - solutionNew[0]) * x * y + (solutionNew[3] - solutionNew[1])
if t > diff:
diff = t
solutionh = solutionNew[0]
solutionm = solutionNew[1]
if limit2 >= e + 1 and limit2 <= g - 1:
solutionNew = solve(c, limit2, 0, x * y, 0, x * y, x, y)
if len(solutionNew) > 0:
if solutionNew[0] > a or (solutionNew[0] == a and solutionNew[1] >= b):
if solutionNew[0] < c or (solutionNew[0] == c and solutionNew[1] <= d):
if solutionNew[2] > e or (solutionNew[2] == e and solutionNew[3] >= f):
if solutionNew[2] < g or (solutionNew[2] == g and solutionNew[3] <= h):
t = (solutionNew[2] - solutionNew[0]) * x * y + (solutionNew[3] - solutionNew[1])
if t > diff:
diff = t
solutionh = solutionNew[0]
solutionm = solutionNew[1]
if limit1 - 1 >= e + 1 and limit2 - 1 <= g - 1:
solutionNew = solve(c, limit2 - 1, 0, x * y, 0, x * y, x, y)
if len(solutionNew) > 0:
if solutionNew[0] > a or (solutionNew[0] == a and solutionNew[1] >= b):
if solutionNew[0] < c or (solutionNew[0] == c and solutionNew[1] <= d):
if solutionNew[2] > e or (solutionNew[2] == e and solutionNew[3] >= f):
if solutionNew[2] < g or (solutionNew[2] == g and solutionNew[3] <= h):
t = (solutionNew[2] - solutionNew[0]) * x * y + (solutionNew[3] - solutionNew[1])
if t > diff:
diff = t
solutionh = solutionNew[0]
solutionm = solutionNew[1]
if solutionh == -1 or diff < 0:
print('-1')
else:
tz = solutionm
solutionm *= 100
try:
r1 = integerPart(solutionm)
r1 = str(r1)
r1 = Decimal(r1)
r2 = solutionm - r1
if r2 >= Decimal('.5'):
r1 += Decimal('1')
t1 = (r1 - r1 % 100) / 100
t2 = r1 % 100
t1 = int(t1)
if t2 == 0:
t2 = '00'
elif t2 < 10:
t2 = '0' + str(t2)
else:
t2 = str(t2)
except:
exit(0)
print(str(solutionh) + ':%d.%s' % (t1, t2))
``` | vfc_137887 | {
"difficulty": "hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/JUNE09/problems/D7",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n5 12\n1 0 2 0 4 0 5 0\n5 12\n3 30 4 0 5 0 6 0\n5 12\n3 0 4 0 5 0 6 0\n\n\n",
"output": "1:20.56\n-1\n3:26.43\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/991/D | Solve the following coding problem using the programming language python:
Bishwock is a chess figure that consists of three squares resembling an "L-bar". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states:
XX XX .X X.
X. .X XX XX
Bishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't occupy the same square.
Vasya has a board with $2\times n$ squares onto which he wants to put some bishwocks. To his dismay, several squares on this board are already occupied by pawns and Vasya can't put bishwocks there. However, pawns also don't attack bishwocks and they can occupy adjacent squares peacefully.
Knowing the positions of pawns on the board, help Vasya to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns.
-----Input-----
The input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols "0" (zero) that denote the empty squares and symbols "X" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed $100$.
-----Output-----
Output a single integer — the maximum amount of bishwocks that can be placed onto the given board.
-----Examples-----
Input
00
00
Output
1
Input
00X00X0XXX0
0XXX0X00X00
Output
4
Input
0X0X0
0X0X0
Output
0
Input
0XXX0
00000
Output
2
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
a = input()
b = input()
ct = 0
i = 0
while i < len(a):
if i + 2 < len(a) and a[i] == '0' and (a[i + 1] == '0') and (a[i + 2] == '0') and (b[i] == '0') and (b[i + 1] == '0') and (b[i + 2] == '0'):
ct += 2
i += 2
elif a[i:i + 2].count('0') + b[i:i + 2].count('0') >= 3:
ct += 1
i += 1
i += 1
print(ct)
``` | vfc_137895 | {
"difficulty": "medium",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/991/D",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "00\n00\n",
"output": "1",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "00X00X0XXX0\n0XXX0X00X00\n",
"output": "4",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "0X0X0\n0X0X0\n",
"output": "0",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "0XXX0\n00000\n",
"output": "2",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "0\n0\n",
"output": "0",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "0\nX\n",
"output": "0",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/GOODBINSTR | Solve the following coding problem using the programming language python:
You are given a binary string S. A binary string is a string consisting of only 0's and 1's.
A binary string is called *good* if it has an equal number of occurrences of \texttt{01} substrings and \texttt{10} substrings. Note that these substrings may overlap. For example, the string 1101001 is *good* since there are two occurrences of \texttt{01} (11\underline{01}001 and 11010\underline{01}) and two occurrences of \texttt{10} (1\underline{10}1001 and 110\underline{10}01).
Find the number of indices i (1 ≤ i ≤ |S|) such that after flipping S_{i}, the resultant binary string is *good*. (If S_{i} is 0, flipping it changes it to 1, and if S_{i} is 1, flipping it changes it to 0)
Note: A string A is a substring of a string B if A can be obtained from B by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.
------ Input Format ------
- The first line contains a single integer T — the number of test cases. Then the test cases follow.
- The second line of each test case contains a binary string S containing 0s and 1s only.
------ Output Format ------
For each test case, output on a single line the number indices i such that flipping S_{i} results in a *good* binary string.
------ Constraints ------
$1 ≤ T ≤ 10^{5}$
$2 ≤ |S| ≤ 2\cdot10^{5}$
- The sum of lengths of $S$ over all test cases does not exceed $2\cdot10^{5}$.
----- Sample Input 1 ------
2
10100
11111
----- Sample Output 1 ------
2
3
----- explanation 1 ------
Test case 1: When $i = 1$, flipping $S_{1}$ produces the string $00100$, which is *good* since there is one occurrence of $\texttt{01}$ ($0\underline{01}00$) and one occurrence of $\texttt{10}$ ($00\underline{10}0$).
When $i = 5$, flipping $S_{5}$ produces the string $10101$, which is *good* since there are two occurrences of $\texttt{01}$ ($1\underline{01}01$ and $101\underline{01}$) and are two occurrences of $\texttt{10}$ ($\underline{10}101$ and $10\underline{10}1$).
It can be shown that for $i = 2, 3, 4$ flipping $S_{i}$ does not result in a *good* binary string.
Thus the number of indices resulting in a good binary string is $2$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
tc = int(input())
for t in range(tc):
b = input()
if b[0] == b[-1]:
print(len(b) - 2)
else:
print(2)
``` | vfc_137899 | {
"difficulty": "medium",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/GOODBINSTR",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n10100\n11111",
"output": "2\n3",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/partition-a-number-into-two-divisible-parts3605/1 | Solve the following coding problem using the programming language python:
Given a number (as string) and two integers a and b, divide the string in two non-empty parts such that the first part is divisible by a and the second part is divisible by b. In case multiple answers exist, return the string such that the first non-empty part has minimum length.
Example 1:
Input:
1200 4 3
Output:
12 00
Explanation:
12 is divisible by 4, and
00 is divisible by 3.
Example 2:
Input:
125 12 5
Output:
12 5
Explanation:
12 is divisible by 12, and
5 is divisible by 5.
Your Task:
You don't need to read input or print anything. Your task is to complete the function stringPartition() which takes the string S and returns a string which will be in the form of first sub-string + " " (Single Space) + second sub-string. If not found return -1 as a string.
Expected Time Complexity: O(N)
Expected Auxiliary Space: O(N)
Constraints:
1<=N<=10^{6}
1<=a,b<=N
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def stringPartition(ob,S,a,b):
# Code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def stringPartition(ob, S, a, b):
for i in range(len(S)):
j = S[:i + 1]
k = S[i + 1:]
if len(j) >= 1 and len(k) >= 1:
if int(j) % a == 0 and int(k) % b == 0:
return j + ' ' + k
return -1
``` | vfc_137904 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/partition-a-number-into-two-divisible-parts3605/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "1200 4 3",
"output": "12 00",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "125 12 5",
"output": "12 5",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1254/B2 | Solve the following coding problem using the programming language python:
This is the harder version of the problem. In this version, $1 \le n \le 10^6$ and $0 \leq a_i \leq 10^6$. You can hack this problem if you locked it. But you can hack the previous problem only if you locked both problems
Christmas is coming, and our protagonist, Bob, is preparing a spectacular present for his long-time best friend Alice. This year, he decides to prepare $n$ boxes of chocolate, numbered from $1$ to $n$. Initially, the $i$-th box contains $a_i$ chocolate pieces.
Since Bob is a typical nice guy, he will not send Alice $n$ empty boxes. In other words, at least one of $a_1, a_2, \ldots, a_n$ is positive. Since Alice dislikes coprime sets, she will be happy only if there exists some integer $k > 1$ such that the number of pieces in each box is divisible by $k$. Note that Alice won't mind if there exists some empty boxes.
Charlie, Alice's boyfriend, also is Bob's second best friend, so he decides to help Bob by rearranging the chocolate pieces. In one second, Charlie can pick up a piece in box $i$ and put it into either box $i-1$ or box $i+1$ (if such boxes exist). Of course, he wants to help his friend as quickly as possible. Therefore, he asks you to calculate the minimum number of seconds he would need to make Alice happy.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 10^6$) — the number of chocolate boxes.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^6$) — the number of chocolate pieces in the $i$-th box.
It is guaranteed that at least one of $a_1, a_2, \ldots, a_n$ is positive.
-----Output-----
If there is no way for Charlie to make Alice happy, print $-1$.
Otherwise, print a single integer $x$ — the minimum number of seconds for Charlie to help Bob make Alice happy.
-----Examples-----
Input
3
4 8 5
Output
9
Input
5
3 10 2 1 5
Output
2
Input
4
0 5 15 10
Output
0
Input
1
1
Output
-1
-----Note-----
In the first example, Charlie can move all chocolate pieces to the second box. Each box will be divisible by $17$.
In the second example, Charlie can move a piece from box $2$ to box $3$ and a piece from box $4$ to box $5$. Each box will be divisible by $3$.
In the third example, each box is already divisible by $5$.
In the fourth example, since Charlie has no available move, he cannot help Bob make Alice happy.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def simple_div(x):
if not x & 1:
yield 2
while not x & 1:
x >>= 1
i = 3
while i * i <= x:
if x % i == 0:
yield i
while x % i == 0:
x //= i
i += 2
if x != 1:
yield x
def __main__():
n = int(input())
a = list(map(int, input().split()))
sa = sum(a)
a.pop()
if sa == 1:
print(-1)
return
res = 1 << 64
for d in simple_div(sa):
tmp = 0
m = 0
half = d >> 1
for x in a:
m = (x + m) % d
tmp += m if m <= half else d - m
if res <= tmp:
break
else:
res = tmp
print(res)
__main__()
``` | vfc_137905 | {
"difficulty": "hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1254/B2",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n4 8 5\n",
"output": "9\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
In this problem you will be given an integer array A of size N, your task is find whether given array is sorted or not (in ascending order) , if print "YES" else print "NO".
Array a[n] is sorted if a[0] ≤ a[1] ≤ ... a[n - 1].
Input
First line of input contains contains integer T denoting number of test cases.
For each test case T, first line of input contains number N denoting size of array A and second line contains N space seperated integers denoting elements of array A.
Output
Print "YES" or "NO" as explained above.
Constraints
1 ≤ T ≤ 10
1 ≤ N ≤ 100,000
1 ≤ A[i] ≤ 10,00,00,00,000
SAMPLE INPUT
3
4
1 2 3 4
3
7 66 10
2
1 0
SAMPLE OUTPUT
YES
NO
NO
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
noc = eval(input())
while noc:
noc -= 1
l = eval(input())
ins = list(map(int, input().split()))
if sorted(ins) == ins:
print("YES")
else:
print("NO")
``` | vfc_137909 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n4\n1 2 3 4\n3\n7 66 10 \n2 \n1 0",
"output": "YES\nYES\nNO\nNO\nYES",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://www.codechef.com/COOK72/problems/CHEFCBA | Solve the following coding problem using the programming language python:
Chef recently learned about ratios and proportions. He wrote some positive integers a, b, c, d on a paper. Chef wants to know whether he can shuffle these numbers so as to make some proportion? Formally, four numbers x, y, z, w are said to make a proportion if ratio of x : y is same as that of z : w.
-----Input-----
Only line of the input contains four space separated positive integers - a, b, c, d.
-----Output-----
Print "Possible" if it is possible to shuffle a, b, c, d to make proportion, otherwise "Impossible" (without quotes).
-----Constraints-----
- 1 ≤ a, b, c, d ≤ 1000
-----Example-----
Input:
1 2 4 2
Output:
Possible
-----Explanation-----
By swapping 4 and the second 2, we get 1 2 2 4. Note that 1 2 2 4 make proportion as 1 : 2 = 2 : 4. Hence answer is "Possible"
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def permutate(arr):
if len(arr) == 1:
yield arr
for x in range(len(arr)):
for perm in permutate(arr[:x] + arr[x + 1:]):
yield ([arr[x]] + perm)
vals = [int(x) for x in input().split()]
founded = False
for val in permutate(vals):
if val[0] / float(val[1]) == val[2] / float(val[3]):
print('Possible')
founded = True
break
if not founded:
print('Impossible')
``` | vfc_137914 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/COOK72/problems/CHEFCBA",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "1 2 4 2\n",
"output": "Possible\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/234/A | Solve the following coding problem using the programming language python:
One fine October day a mathematics teacher Vasily Petrov went to a class and saw there n pupils who sat at the $\frac{n}{2}$ desks, two people at each desk. Vasily quickly realized that number n is even. Like all true mathematicians, Vasily has all students numbered from 1 to n.
But Vasily Petrov did not like the way the children were seated at the desks. According to him, the students whose numbers differ by 1, can not sit together, as they talk to each other all the time, distract others and misbehave.
On the other hand, if a righthanded student sits at the left end of the desk and a lefthanded student sits at the right end of the desk, they hit elbows all the time and distract each other. In other cases, the students who sit at the same desk, do not interfere with each other.
Vasily knows very well which students are lefthanders and which ones are righthanders, and he asks you to come up with any order that meets these two uncomplicated conditions (students do not talk to each other and do not bump their elbows). It is guaranteed that the input is such that at least one way to seat the students always exists.
-----Input-----
The first input line contains a single even integer n (4 ≤ n ≤ 100) — the number of students in the class. The second line contains exactly n capital English letters "L" and "R". If the i-th letter at the second line equals "L", then the student number i is a lefthander, otherwise he is a righthander.
-----Output-----
Print $\frac{n}{2}$ integer pairs, one pair per line. In the i-th line print the numbers of students that will sit at the i-th desk. The first number in the pair stands for the student who is sitting to the left, and the second number stands for the student who is sitting to the right. Separate the numbers in the pairs by spaces. If there are multiple solutions, print any of them.
-----Examples-----
Input
6
LLRLLL
Output
1 4
2 5
6 3
Input
4
RRLL
Output
3 1
4 2
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def lefthanders_and_righthanders(n_int, student_list) -> list:
sitting_order = []
for i in range(n_int // 2):
if student_list[i] == 'R' and student_list[i + n_int // 2] == 'L':
sitting_order.append((i + n_int // 2 + 1, i + 1))
print(i + n_int // 2 + 1, i + 1)
else:
sitting_order.append((i + 1, i + n_int // 2 + 1))
print(i + 1, i + n_int // 2 + 1)
return sitting_order
def __starting_point():
with open('input.txt', 'r') as f_input:
n = int(f_input.readline())
students = f_input.readline()
sitting = lefthanders_and_righthanders(n, students)
with open('output.txt', 'w') as f_output:
for each in sitting:
f_output.write(str(each[0]) + ' ' + str(each[1]) + '\n')
__starting_point()
``` | vfc_137918 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/234/A",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "6\nLLRLLL\n",
"output": "1 4\n2 5\n6 3\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\nRRLL\n",
"output": "3 1\n4 2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\nLLRR\n",
"output": "1 3\n2 4\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "6\nRLLRRL\n",
"output": "1 4\n2 5\n3 6\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "8\nLRLRLLLR\n",
"output": "1 5\n6 2\n3 7\n4 8\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "10\nRLLRLRRRLL\n",
"output": "1 6\n2 7\n3 8\n9 4\n5 10\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/drive-the-car2541/1 | Solve the following coding problem using the programming language python:
Suppose you are a car driver and you have to drive a car on a track divided into "N" number of sub-tracks. You are also given the value of "K" i.e. the total kilometers the car can drive on each sub-track. If the car can't cover a sub-track, you can add any unit of Petrol to it. With each unit of petrol added, the total kilometers your car can travel will increase by one unit. You have to return the minimum unit of Petrol that if added to your car at each sub-tracks your car will be able to cover all the sub-tracks. If no extra unit of petrol is required, return -1.
Example 1:
Input:
N = 5, K = 7
arr[] = {2, 5, 4, 5, 2}
Output:
-1
Explanation:
No extra petrol required, as K is greater
than all the elemnts in the array hence -1.
Example 2:
Input:
N = 5, K = 4
arr[] = {1, 6, 3, 5, 2}
Output:
2
Explanation:
You are given 5 sub-tracks with different
kilometers. Your car can travel 4 km on
each sub-track. So, when you come on
sub-track 2nd you have to cover 6 km of
distance, so you need to have 2 unit of
petrol more to cover the distance, for
3rd sub-track, your car can travel 4km
and you need extra 1 unit of pertrol.So
if you add 2 units of petrol at each sub-track
you can cover all the subtracks.
Your Task:
You don't need to read input or print anything. Your task is to complete the function required() which takes the array arr[], its size n and an integer k as inputs and returns the minimum unit of Petrol your car requires to cover all the sub-tracks. If no extra unit of petrol is required, return -1.
Expected Time Complexity: O(N)
Expected Auxiliary Space: O(1)
Constraints:
1 ≤ N ≤ 10^{5}
1 ≤ K ≤ 10^{18}
1 ≤ A[] ≤ 10^{18}
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def required(self, a, n, k):
# Your code goes here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def required(self, a, n, k):
g = max(a)
if g > k:
return g - k
return -1
``` | vfc_137926 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/drive-the-car2541/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "N = 5, K = 7\narr[] = {2, 5, 4, 5, 2}",
"output": "-1",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "N = 5, K = 4\narr[] = {1, 6, 3, 5, 2}",
"output": "2",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1614/A | Solve the following coding problem using the programming language python:
Businessman Divan loves chocolate! Today he came to a store to buy some chocolate. Like all businessmen, Divan knows the value of money, so he will not buy too expensive chocolate. At the same time, too cheap chocolate tastes bad, so he will not buy it as well.
The store he came to has $n$ different chocolate bars, and the price of the $i$-th chocolate bar is $a_i$ dollars. Divan considers a chocolate bar too expensive if it costs strictly more than $r$ dollars. Similarly, he considers a bar of chocolate to be too cheap if it costs strictly less than $l$ dollars. Divan will not buy too cheap or too expensive bars.
Divan is not going to spend all his money on chocolate bars, so he will spend at most $k$ dollars on chocolates.
Please determine the maximum number of chocolate bars Divan can buy.
-----Input-----
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). Description of the test cases follows.
The description of each test case consists of two lines. The first line contains integers $n$, $l$, $r$, $k$ ($1 \le n \le 100$, $1 \le l \le r \le 10^9$, $1 \le k \le 10^9$) — the lowest acceptable price of a chocolate, the highest acceptable price of a chocolate and Divan's total budget, respectively.
The second line contains a sequence $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$) integers — the prices of chocolate bars in the store.
-----Output-----
For each test case print a single integer — the maximum number of chocolate bars Divan can buy.
-----Examples-----
Input
8
3 1 100 100
50 100 50
6 3 5 10
1 2 3 4 5 6
6 3 5 21
1 2 3 4 5 6
10 50 69 100
20 30 40 77 1 1 12 4 70 10000
3 50 80 30
20 60 70
10 2 7 100
2 2 2 2 2 7 7 7 7 7
4 1000000000 1000000000 1000000000
1000000000 1000000000 1000000000 1000000000
1 1 1 1
1
Output
2
2
3
0
0
10
1
1
-----Note-----
In the first example Divan can buy chocolate bars $1$ and $3$ and spend $100$ dollars on them.
In the second example Divan can buy chocolate bars $3$ and $4$ and spend $7$ dollars on them.
In the third example Divan can buy chocolate bars $3$, $4$, and $5$ for $12$ dollars.
In the fourth example Divan cannot buy any chocolate bar because each of them is either too cheap or too expensive.
In the fifth example Divan cannot buy any chocolate bar because he considers the first bar too cheap, and has no budget for the second or third.
In the sixth example Divan can buy all the chocolate bars in the shop.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for _ in range(int(input())):
(n, l, r, k) = [int(i) for i in input().split()]
a = sorted([int(i) for i in input().split()])
result = 0
c = 0
for i in range(n):
if a[i] >= l and r >= a[i] and (c + a[i] <= k):
c += a[i]
result += 1
print(result)
``` | vfc_137931 | {
"difficulty": "easy",
"memory_limit": "256 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1614/A",
"time_limit": "1 second"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "8\n3 1 100 100\n50 100 50\n6 3 5 10\n1 2 3 4 5 6\n6 3 5 21\n1 2 3 4 5 6\n10 50 69 100\n20 30 40 77 1 1 12 4 70 10000\n3 50 80 30\n20 60 70\n10 2 7 100\n2 2 2 2 2 7 7 7 7 7\n4 1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000 1000000000\n1 1 1 1\n1\n",
"output": "2\n2\n3\n0\n0\n10\n1\n1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/cutting-binary-string1342/1 | Solve the following coding problem using the programming language python:
Given a string s containing 0's and 1's. You have to return the smallest positive integer C, such that the binary string can be cut into C pieces and each piece should be of the power of 5 with no leading zeros.
Note: The string s is a binary string. And if no such cuts are possible, then return -1.
Example 1:
Input:
s = "101101101"
Output:
3
Explanation:
We can split the given string into
three 101s, where 101 is the binary
representation of 5.
Example 2:
Input:
s = "00000"
Output:
-1
Explanation:
0 is not a power of 5.
Your Task:
Your task is to complete the function cuts() which take a single argument(string s). You need not take any input or print anything. Return an int C if the cut is possible else return -1.
Expected Time Complexity: O(|s|*|s|*|s|).
Expected Auxiliary Space: O(|s|).
Constraints:
1<= |s| <=50
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def cuts(self, s):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def cuts(self, s):
c = list(s)
l = len(c)
dp = [0] * (l + 1)
dp[0] = 0
for i in range(1, l + 1):
index = i - 1
if c[index] == '0':
dp[i] = -1
else:
dp[i] = -1
t = 1000
count = 0
for j in range(i):
if c[index - j] == '1':
count += Solution.num(j)
if Solution.check(count) and dp[index - j] != -1:
w = 1 + dp[index - j]
t = min(w, t)
if t != 1000:
dp[i] = t
return dp[l]
def num(y):
if y == 0:
return 1
x = 2
for i in range(1, y):
x = x << 1
return x
@staticmethod
def check(n):
if n == 0:
return False
if n == 1:
return True
if n % 5 != 0:
return False
else:
return Solution.check(n // 5)
``` | vfc_137940 | {
"difficulty": "medium",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/cutting-binary-string1342/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "s = \"101101101\"",
"output": "3",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "s = \"00000\"",
"output": "-1",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
There are many caves deep in mountains found in the countryside. In legend, each cave has a treasure hidden within the farthest room from the cave's entrance. The Shogun has ordered his Samurais to explore these caves with Karakuri dolls (robots) and to find all treasures. These robots move in the caves and log relative distances and directions between rooms.
Each room in a cave is mapped to a point on an integer grid (x, y >= 0). For each cave, the robot always starts from its entrance, runs along the grid and returns to the entrance (which also serves as the exit). The treasure in each cave is hidden in the farthest room from the entrance, using Euclid distance for measurement, i.e. the distance of the room at point (x, y) from the entrance (0, 0) is defined as the square root of (x*x+y*y). If more than one room has the same farthest distance from the entrance, the treasure is hidden in the room having the greatest value of x. While the robot explores a cave, it records how it has moved. Each time it takes a new direction at a room, it notes the difference (dx, dy) from the last time it changed its direction. For example, suppose the robot is currently in the room at point (2, 4). If it moves to room (6, 4), the robot records (4, 0), i.e. dx=6-2 and dy=4-4. The first data is defined as the difference from the entrance. The following figure shows rooms in the first cave of the Sample Input. In the figure, the farthest room is the square root of 61 distant from the entrance.
<image>
Based on the records that the robots bring back, your job is to determine the rooms where treasures are hidden.
Input
In the first line of the input, an integer N showing the number of caves in the input is given. Integers dxi and dyi are i-th data showing the differences between rooms. Note that since the robot moves along the grid, either dxi or dyi is zero. An integer pair dxi = dyi = 0 signals the end of one cave's data which means the robot finished the exploration for the cave and returned back to the entrance. The coordinates are limited to (0,0)-(1000,1000).
Output
Print the position (x, y) of the treasure room on a line for each cave.
Example
Input
3
1 0
0 1
-1 0
1 0
0 5
-1 0
0 -1
5 0
0 1
0 -1
1 0
0 -4
-3 0
0 3
2 0
0 -2
-1 0
0 1
0 -1
1 0
0 2
-2 0
0 -3
3 0
0 4
-4 0
0 -5
-2 0
0 0
1 0
-1 0
0 0
2 0
0 1
-1 0
0 1
-1 0
0 -2
0 0
Output
6 5
1 0
2 1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for _ in range(int(input())):
m = dx = dy = 0
while 1:
(x, y) = map(int, input().split())
if x == y == 0:
break
dx += x
dy += y
l = dx * dx + dy * dy
if m == l and mx < dx or m < l:
(m, mx, my) = (l, dx, dy)
print(mx, my)
``` | vfc_137942 | {
"difficulty": "unknown_difficulty",
"memory_limit": "134.217728 megabytes",
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "1.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n1 0\n0 1\n-1 0\n1 0\n0 5\n-1 0\n0 -1\n5 0\n0 1\n0 -1\n1 0\n0 -4\n-3 0\n0 3\n0 0\n0 -2\n-1 0\n0 1\n0 -1\n1 0\n0 2\n-2 0\n0 -3\n3 0\n0 4\n-4 0\n0 -5\n-2 0\n0 0\n1 0\n-1 0\n0 0\n2 0\n0 1\n-1 0\n0 1\n-1 0\n0 -2\n0 0",
"output": "6 5\n-5 -4\n1 0\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/message-spreading4258/1 | Solve the following coding problem using the programming language python:
There are N students in a class, each in possession of a different funny story.
They want to share funny stories with each other by sending electronic messages. Assume that a sender includes all the funny stories he or she knows at the time the message is sent and that a message may only have one addressee. What is the minimum number of messages they need to send to guarantee that every one of them gets all the funny stories?
Example 1:
Input:
2
Output:
2
Explanation:
Person 1 sends a message to
Person 2, Person 2 sends
message to Person 1.
A total of 2 messages are sent.
Example 2:
Input:
1
Output:
0
Explanation:
No messages are sent.
Your Task:
You don't need to read input or print anything. Your task is to complete the function minimumMessages() which takes an integer N and returns the minimum number of messages they need to send to guarantee that every one of them gets all the funny stories.
Expected Time Complexity: O(1)
Expected Auxiliary Space: O(1)
Constraints:
1<=N<=10^{5}
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def minimumMessages (ob,N):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def minimumMessages(ob, N):
if N == 1:
return 0
if N == 2:
return 2
if N > 2:
i = 0
a = 2
while a <= N:
a = a + 1
i = i + 2
return i
``` | vfc_137946 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/message-spreading4258/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2",
"output": "2",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1",
"output": "0",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/PBK22020/problems/ITGUY23 | Solve the following coding problem using the programming language python:
The chef was not happy with the binary number system, so he designed a new machine which is having 6 different states, i.e. in binary there is a total of 2 states as 0 and 1. Now, the chef is confused about how to correlate this machine to get an interaction with Integer numbers, when N(Integer number) is provided to the system, what will be the Nth number that system will return(in Integer form), help the chef to design this system.
-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains a single line of input, $N$.
-----Output:-----
For each test case, output in a single line answer given by the system.
-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 10^5$
-----Sample Input:-----
2
3
5
-----Sample Output:-----
7
37
-----EXPLANATION:-----
Initial numbers for system = [1, 6, 7, 36, 37, 42, 43, 216, …..
For 1) 3rd Number for the system will be 7.
For 2) 5th Number for the system will be 37.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from sys import stdin, stdout
l = [1, 6, 7]
c = 1
for x in range(3, 100001):
if x % 2 == 1:
a = l[c] * 6
l.append(a)
else:
l.append(a + 1)
c += 1
n = int(stdin.readline())
for _ in range(n):
s = int(stdin.readline())
print(l[s - 1])
``` | vfc_137947 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/PBK22020/problems/ITGUY23",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n3\n5\n",
"output": "7\n37\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/withdrawing-money5323/1 | Solve the following coding problem using the programming language python:
Geek has N dollars in his bank account. He wants to withdraw all of it but the bank only allows withdrawal of an amount that is a divisor of the current amount in the bank and is less than the current amount.
If Geek withdraws the maximum possible amount each day, how many days does he need to take out all of his money from the bank?
Note: If the remaining amount is 1, he can withdraw it.
Example 1:
Input: N = 12
Output: 5
Explanation: N = 12
Withdraws 6, Remaining = 6
Withdraws 3, Remaining = 3
Withdraws 1, Remaining = 2
Withdraws 1, Remaining = 1
Withdraws 1, Remaining = 0
Example 2:
Input: N = 21
Output: 7
Explanation: N = 21
Withdraws 7, Remaining = 14
Withdraws 7, Remaining = 7
Withdraws 1, Remaining = 6
Withdraws 3, Remaining = 3
Withdraws 1, Remaining = 2
Withdraws 1, Remaining = 1
Withdraws 1, Remaining = 0
Your Task:
You don't need to read input or print anything. Your task is to complete the function numberOfDays() which takes an integer N as input parameter and returns the number of days Geek needs to withdraw all of his money.
Expected Time Complexity: O(sqrt(N))
Expected Auxiliary Space: O(1)
Constraints :
1 <= N <= 10^{12}
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def numberOfDays(self, N):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def numberOfDays(self, N):
ans = 0
while N > 0:
check = 0
for i in range(2, int(N ** 0.5) + 1):
if N % i == 0:
N -= N / i
ans += 1
check = 1
break
if check == 0:
N -= 1
ans += 1
return ans
``` | vfc_137951 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/withdrawing-money5323/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "N = 12",
"output": "5",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "N = 21",
"output": "7",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/adjacents-are-not-allowed3528/1 | Solve the following coding problem using the programming language python:
You have a rectangular grid mat of dimension 2 x N. You need to find out the maximum sum such that no two chosen numbers are adjacent, vertically, diagonally or horizontally.
Example 1:
Input: N = 3
mat = {{1, 4, 5},
{2, 0, 0}}
Output: 7
Explaination: Optimal choice is (2, 5).
Example 2:
Input: N = 2
mat = {{1, 2},
{3, 4}}
Output: 4
Explaination: Optimal choice is (4).
Your Task:
You do not need to read input or print anything. Your task is to complete the function maxSum() which takes the value N and grid mat as input parameters and returns the maximum sum.
Expected Time Complexity: O(N)
Expected Auxiliary Space: O(N)
Constraints:
1 ≤ N ≤ 10000
1 ≤ mat[i][j] ≤ 70
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def maxSum(self, N, mat):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def maxSum(self, N, mat):
dp = [-1] * N
if N == 1:
return max(mat[0][0], mat[1][0])
dp[0] = max(0, mat[0][0], mat[1][0])
dp[1] = max(dp[0], mat[0][1], mat[1][1])
for i in range(2, N):
dp[i] = max(max(mat[0][i], mat[1][i]) + dp[i - 2], dp[i - 1])
return dp[N - 1]
``` | vfc_137952 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/adjacents-are-not-allowed3528/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "N = 3\nmat = {{1, 4, 5}, \n {2, 0, 0}}",
"output": "7",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "N = 2\nmat = {{1, 2}, \n {3, 4}}",
"output": "4",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/find-the-sequence1346/1 | Solve the following coding problem using the programming language python:
Adobe is weak in the concepts of string. He is given a number N and has to find N terms of that series. The series is 1, 2, 5, 8,15. . .
Example 1:
Input:
N = 8
Output:
1 2 5 8 15 28 51 94
Explanation:
For N = 8, series comes out to be:
1 2 5 8 15 28 51 94
Example 2:
Input:
N = 3
Output:
1 2 5
Explanation:
For N = 3, series comes out to be:
1 2 5
Your Task:
You don't need to read input or print anything. Your task is to complete the function printSeries() which takes an integer N as input parameter and return the list of the first N term of the series.
Expected Time Complexity: O(N)
Expected Auxiliary Space: O(1)
Constraints:
1 <= N <= 50
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def printSeries(self, N):
#code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def printSeries(self, n):
a = 1
b = 2
c = 5
arr = []
i = 0
while i < n:
d = a + b + c
arr.append(a)
a = b
b = c
c = d
i += 1
return arr
``` | vfc_137957 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/find-the-sequence1346/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "N = 8",
"output": "1 2 5 8 15 28 51 94",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "N = 3",
"output": "1 2 5",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
The Antique Comedians of Malidinesia prefer comedies to tragedies. Unfortunately, most of the
ancient plays are tragedies. Therefore the dramatic advisor of ACM has decided to transfigure some
tragedies into comedies. Obviously, this work is very hard because the basic sense of the play must be
kept intact, although all the things change to their opposites. For example the numbers: if any number
appears in the tragedy, it must be converted to its reversed form before being accepted into the comedy
play.
Reversed number is a number written in arabic numerals but the order of digits is reversed. The first
digit becomes last and vice versa. For example, if the main hero had 1245 strawberries in the tragedy,
he has 5421 of them now. Note that all the leading zeros are omitted. That means if the number ends
with a zero, the zero is lost by reversing (e.g. 1200 gives 21). Also note that the reversed number never
has any trailing zeros.
ACM needs to calculate with reversed numbers. Your task is to add two reversed numbers and output
their reversed sum. Of course, the result is not unique because any particular number is a reversed
form of several numbers (e.g. 21 could be 12, 120 or 1200 before reversing). Thus we must assume
that no zeros were lost by reversing (e.g. assume that the original number was 12).
Input
The input consists of N cases (equal to about 1000000). The first line of the input contains only positive
integer N. Then follow the cases. Each case consists of exactly one line with two positive integers
separated by space. These are the numbers you are to add.
long long int will work for C/C++
Output
For each case, print exactly one line containing only one integer - the reversed sum of two reversed
numbers. Omit any leading zeros in the output.
SAMPLE INPUT
3
24 1
4358 754
305 794
SAMPLE OUTPUT
34
1998
1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
t = eval(input())
def rev1(n, m):
ns = str(n)
ns = int(ns[::-1])
ms = str(m)
ms = int(ms[::-1])
return ns + ms
def rev(n):
while(n%10 == 0):
n /= 10
return int(str(n)[::-1])
for i in range(t):
arr = list(map(int, list(input().strip().split(' '))))
a = arr[0]
b = arr[1]
print(rev(rev1(a,b)))
``` | vfc_137958 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
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"output": 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"output": 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"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/linked-list-insertion-1587115620/1 | Solve the following coding problem using the programming language python:
Create a link list of size N according to the given input literals. Each integer input is accompanied by an indicator which can either be 0 or 1. If it is 0, insert the integer in the beginning of the link list. If it is 1, insert the integer at the end of the link list.
Hint: When inserting at the end, make sure that you handle NULL explicitly.
Example 1:
Input:
LinkedList: 9->0->5->1->6->1->2->0->5->0
Output: 5 2 9 5 6
Explanation:
Length of Link List = N = 5
9 0 indicated that 9 should be
inserted in the beginning. Modified
Link List = 9.
5 1 indicated that 5 should be
inserted in the end. Modified Link
List = 9,5.
6 1 indicated that 6 should be
inserted in the end. Modified Link
List = 9,5,6.
2 0 indicated that 2 should be
inserted in the beginning. Modified
Link List = 2,9,5,6.
5 0 indicated that 5 should be
inserted in the beginning. Modified
Link List = 5,2,9,5,6.
Final linked list = 5, 2, 9, 5, 6.
Example 2:
Input:
LinkedList: 5->1->6->1->9->1
Output: 5 6 9
Your Task:
You only need to complete the functions insertAtBeginning() and insertAtEnd() that takes the head of link list and integer value of the data to be inserted as inputs and returns the head of the modified link list.
Expected Time Complexity: O(1) for insertAtBeginning() and O(N) for insertAtEnd().
Expected Auxiliary Space: O(1) for both.
Constraints:
1 <= N <= 10^{4}
Write your solution by modifying this code:
```python
'''
class Node:
def __init__(self,data):
self.data=data
self.next=None
'''
class Solution:
#Function to insert a node at the beginning of the linked list.
def insertAtBegining(self,head,x):
# code here
#Function to insert a node at the end of the linked list.
def insertAtEnd(self,head,x):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def insertAtBegining(self, head, x):
if not head:
return Node(x)
temp = Node(x)
temp.next = head
return temp
def insertAtEnd(self, head, x):
if head is None:
return Node(x)
temp = head
while temp.next:
temp = temp.next
temp.next = Node(x)
return head
``` | vfc_137962 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/linked-list-insertion-1587115620/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "LinkedList:9->0->5->1->6->1->2->0->5->0",
"output": "5 2 9 5 6",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "LinkedList:5->1->6->1->9->1",
"output": "5 6 9",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1440/C2 | Solve the following coding problem using the programming language python:
This is the hard version of the problem. The difference between the versions is in the number of possible operations that can be made. You can make hacks if and only if you solved both versions of the problem.
You are given a binary table of size n × m. This table consists of symbols 0 and 1.
You can make such operation: select 3 different cells that belong to one 2 × 2 square and change the symbols in these cells (change 0 to 1 and 1 to 0).
Your task is to make all symbols in the table equal to 0. You are allowed to make at most nm operations. You don't need to minimize the number of operations.
It can be proved, that it is always possible.
Input
The first line contains a single integer t (1 ≤ t ≤ 5000) — the number of test cases. The next lines contain descriptions of test cases.
The first line of the description of each test case contains two integers n, m (2 ≤ n, m ≤ 100).
Each of the next n lines contains a binary string of length m, describing the symbols of the next row of the table.
It is guaranteed, that the sum of nm for all test cases does not exceed 20000.
Output
For each test case print the integer k (0 ≤ k ≤ nm) — the number of operations.
In the each of the next k lines print 6 integers x_1, y_1, x_2, y_2, x_3, y_3 (1 ≤ x_1, x_2, x_3 ≤ n, 1 ≤ y_1, y_2, y_3 ≤ m) describing the next operation. This operation will be made with three cells (x_1, y_1), (x_2, y_2), (x_3, y_3). These three cells should be different. These three cells should belong to some 2 × 2 square.
Example
Input
5
2 2
10
11
3 3
011
101
110
4 4
1111
0110
0110
1111
5 5
01011
11001
00010
11011
10000
2 3
011
101
Output
1
1 1 2 1 2 2
2
2 1 3 1 3 2
1 2 1 3 2 3
4
1 1 1 2 2 2
1 3 1 4 2 3
3 2 4 1 4 2
3 3 4 3 4 4
4
1 2 2 1 2 2
1 4 1 5 2 5
4 1 4 2 5 1
4 4 4 5 3 4
2
1 3 2 2 2 3
1 2 2 1 2 2
Note
In the first test case, it is possible to make only one operation with cells (1, 1), (2, 1), (2, 2). After that, all symbols will be equal to 0.
In the second test case:
* operation with cells (2, 1), (3, 1), (3, 2). After it the table will be:
011
001
000
* operation with cells (1, 2), (1, 3), (2, 3). After it the table will be:
000
000
000
In the fifth test case:
* operation with cells (1, 3), (2, 2), (2, 3). After it the table will be:
010
110
* operation with cells (1, 2), (2, 1), (2, 2). After it the table will be:
000
000
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
input = sys.stdin.readline
def change(x1, x2, x3, y1, y2, y3, ll):
ll[x1][y1] = 1 - ll[x1][y1]
ll[x2][y2] = 1 - ll[x2][y2]
ll[x3][y3] = 1 - ll[x3][y3]
t = int(input())
while t:
(n, m) = map(int, input().split())
ll = []
for i in range(n):
l = list(map(int, input().strip()))
ll.append(l)
ans = []
for i in range(n - 1):
for j in range(m):
if i == n - 2 and j == m - 2:
break
if ll[i][j]:
if j + 1 < m:
ans.append((i + 1, i + 2, i + 2, j + 1, j + 1, j + 2))
change(i, i + 1, i + 1, j, j, j + 1, ll)
else:
ans.append((i + 1, i + 2, i + 2, j + 1, j + 1, j))
change(i, i + 1, i + 1, j, j, j - 1, ll)
for i in range(m - 1):
if ll[n - 1][i] and ll[n - 2][i]:
ans.append((n - 1, n, n, i + 1, i + 1, i + 2))
change(n - 2, n - 1, n - 1, i, i, i + 1, ll)
elif ll[n - 1][i]:
ans.append((n, n, n - 1, i + 1, i + 2, i + 2))
change(n - 1, n - 1, n - 2, i, i + 1, i + 1, ll)
elif ll[n - 2][i]:
ans.append((n - 1, n - 1, n, i + 1, i + 2, i + 2))
change(n - 2, n - 2, n - 1, i, i + 1, i + 1, ll)
if ll[n - 1][m - 1] and ll[n - 2][m - 1]:
ans.append((n, n - 1, n, m, m - 1, m - 1))
ans.append((n, n - 1, n - 1, m - 1, m - 1, m))
elif ll[n - 2][m - 1]:
ans.append((n - 1, n, n, m, m, m - 1))
change(n - 2, n - 1, n - 1, m - 1, m - 1, m - 2, ll)
ans.append((n, n - 1, n - 1, m, m - 1, m))
change(n - 1, n - 2, n - 2, m - 1, m - 2, m - 1, ll)
ans.append((n, n - 1, n - 1, m - 1, m, m - 1))
change(n - 1, n - 2, n - 2, m - 2, m - 1, m - 2, ll)
elif ll[n - 1][m - 1]:
ans.append((n, n, n - 1, m, m - 1, m - 1))
ans.append((n - 1, n - 1, n, m - 1, m, m))
ans.append((n, n, n - 1, m - 1, m, m))
print(len(ans))
for i in ans:
(x1, x2, x3, y1, y2, y3) = i
print(x1, y1, x2, y2, x3, y3)
t -= 1
``` | vfc_137963 | {
"difficulty": "hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1440/C2",
"time_limit": "1.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5\n2 2\n10\n11\n3 3\n011\n101\n110\n4 4\n1111\n0110\n0110\n1111\n5 5\n01011\n11001\n00010\n11011\n10000\n2 3\n011\n101\n",
"output": "1\n1 1 2 1 2 2 \n4\n1 2 1 3 2 2 \n2 1 3 1 2 2 \n2 2 3 2 3 3 \n2 2 2 3 3 3 \n8\n1 1 1 2 2 1 \n1 3 1 4 2 3 \n2 1 2 2 3 1 \n3 1 4 1 3 2 \n4 2 3 3 4 3 \n3 3 4 3 4 4 \n3 3 3 4 4 4 \n4 3 3 4 4 4 \n14\n1 2 1 3 2 2 \n1 3 1 4 2 3 \n1 5 2 4 2 5 \n2 1 2 2 3 1 \n2 2 2 3 3 2 \n2 4 3 4 3 5 \n3 1 3 2 4 1 \n3 5 4 4 4 5 \n5 1 4 2 5 2 \n5 2 4 3 5 3 \n4 3 5 3 4 4 \n4 4 5 4 4 5 \n4 4 5 4 5 5 \n4 4 4 5 5 5 \n2\n2 1 1 2 2 2 \n2 2 1 3 2 3 \n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5\n2 2\n10\n11\n3 3\n011\n101\n110\n4 4\n1111\n0110\n0110\n1111\n5 5\n01011\n11001\n00010\n01011\n10000\n2 3\n011\n101\n",
"output": "1\n1 1 2 1 2 2 \n4\n1 2 1 3 2 2 \n2 1 3 1 2 2 \n2 2 3 2 3 3 \n2 2 2 3 3 3 \n8\n1 1 1 2 2 1 \n1 3 1 4 2 3 \n2 1 2 2 3 1 \n3 1 4 1 3 2 \n4 2 3 3 4 3 \n3 3 4 3 4 4 \n3 3 3 4 4 4 \n4 3 3 4 4 4 \n9\n1 2 1 3 2 2 \n1 3 1 4 2 3 \n1 5 2 4 2 5 \n2 1 2 2 3 1 \n2 2 2 3 3 2 \n2 4 3 4 3 5 \n3 1 3 2 4 1 \n3 5 4 4 4 5 \n4 1 5 1 4 2 \n2\n2 1 1 2 2 2 \n2 2 1 3 2 3 \n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/617/C | Solve the following coding problem using the programming language python:
A flowerbed has many flowers and two fountains.
You can adjust the water pressure and set any values r_1(r_1 ≥ 0) and r_2(r_2 ≥ 0), giving the distances at which the water is spread from the first and second fountain respectively. You have to set such r_1 and r_2 that all the flowers are watered, that is, for each flower, the distance between the flower and the first fountain doesn't exceed r_1, or the distance to the second fountain doesn't exceed r_2. It's OK if some flowers are watered by both fountains.
You need to decrease the amount of water you need, that is set such r_1 and r_2 that all the flowers are watered and the r_1^2 + r_2^2 is minimum possible. Find this minimum value.
-----Input-----
The first line of the input contains integers n, x_1, y_1, x_2, y_2 (1 ≤ n ≤ 2000, - 10^7 ≤ x_1, y_1, x_2, y_2 ≤ 10^7) — the number of flowers, the coordinates of the first and the second fountain.
Next follow n lines. The i-th of these lines contains integers x_{i} and y_{i} ( - 10^7 ≤ x_{i}, y_{i} ≤ 10^7) — the coordinates of the i-th flower.
It is guaranteed that all n + 2 points in the input are distinct.
-----Output-----
Print the minimum possible value r_1^2 + r_2^2. Note, that in this problem optimal answer is always integer.
-----Examples-----
Input
2 -1 0 5 3
0 2
5 2
Output
6
Input
4 0 0 5 0
9 4
8 3
-1 0
1 4
Output
33
-----Note-----
The first sample is (r_1^2 = 5, r_2^2 = 1): $0^{\circ}$ The second sample is (r_1^2 = 1, r_2^2 = 32): [Image]
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import os
import sys
from math import *
from collections import *
from fractions import *
from bisect import *
from heapq import *
from io import BytesIO, IOBase
def vsInput():
sys.stdin = open('input.txt', 'r')
sys.stdout = open('output.txt', 'w')
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in file.mode or 'r' not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b'\n') + (not b)
ptr = self.buffer.tell()
(self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr))
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
(self.buffer.truncate(0), self.buffer.seek(0))
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode('ascii'))
self.read = lambda : self.buffer.read().decode('ascii')
self.readline = lambda : self.buffer.readline().decode('ascii')
(sys.stdin, sys.stdout) = (IOWrapper(sys.stdin), IOWrapper(sys.stdout))
input = lambda : sys.stdin.readline().rstrip('\r\n')
ALPHA = 'abcdefghijklmnopqrstuvwxyz'
M = 10 ** 9 + 7
EPS = 1e-06
def value():
return tuple(map(int, input().split()))
def array():
return [int(i) for i in input().split()]
def Int():
return int(input())
def Str():
return input()
def arrayS():
return [i for i in input().split()]
def Dist(p1, p2):
return (p2[1] - p1[1]) ** 2 + (p2[0] - p1[0]) ** 2
(n, x1, y1, x2, y2) = value()
f1 = (x1, y1)
f2 = (x2, y2)
dist_f2 = [0]
points = []
for i in range(n):
p = value()
dist_f2.append(Dist(p, f2))
points.append((Dist(p, f1), dist_f2[-1]))
points.sort()
dist_f2.sort()
ans = min(max(dist_f2), points[-1][0])
for i in range(n):
r1 = points[i][0]
r_need = 0
for j in range(i + 1, n):
if points[j][1] > r_need:
r_need = points[j][1]
ind = bisect_left(dist_f2, r_need)
r2 = dist_f2[ind]
ans = min(r1 + r2, ans)
print(ans)
``` | vfc_137967 | {
"difficulty": "medium_hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/617/C",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2 -1 0 5 3\n0 2\n5 2\n",
"output": "6\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4 0 0 5 0\n9 4\n8 3\n-1 0\n1 4\n",
"output": "33\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5 -6 -4 0 10\n-7 6\n-9 7\n-5 -1\n-2 1\n-8 10\n",
"output": "100\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "10 -68 10 87 22\n30 89\n82 -97\n-52 25\n76 -22\n-20 95\n21 25\n2 -3\n45 -7\n-98 -56\n-15 16\n",
"output": "22034\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1 -10000000 -10000000 -10000000 -9999999\n10000000 10000000\n",
"output": "799999960000001\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "10 -68 10 87 22\n30 89\n82 -97\n-52 25\n76 -22\n-20 95\n21 25\n2 -3\n45 -7\n-98 -56\n-15 16\n",
"output": "22034\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1534/E | Solve the following coding problem using the programming language python:
This is an interactive problem.
Note: the XOR-sum of an array a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) is defined as a_1 ⊕ a_2 ⊕ … ⊕ a_n, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
Little Dormi received an array of n integers a_1, a_2, …, a_n for Christmas. However, while playing with it over the winter break, he accidentally dropped it into his XOR machine, and the array got lost.
The XOR machine is currently configured with a query size of k (which you cannot change), and allows you to perform the following type of query: by giving the machine k distinct indices x_1, x_2, …, x_k, it will output a_{x_1} ⊕ a_{x_2} ⊕ … ⊕ a_{x_k}.
As Little Dormi's older brother, you would like to help him recover the XOR-sum of his array a_1, a_2, …, a_n by querying the XOR machine.
Little Dormi isn't very patient, so to be as fast as possible, you must query the XOR machine the minimum number of times to find the XOR-sum of his array. Formally, let d be the minimum number of queries needed to find the XOR-sum of any array of length n with a query size of k. Your program will be accepted if you find the correct XOR-sum in at most d queries.
Lastly, you also noticed that with certain configurations of the machine k and values of n, it may not be possible to recover the XOR-sum of Little Dormi's lost array. If that is the case, you should report it as well.
The array a_1, a_2, …, a_n is fixed before you start querying the XOR machine and does not change with the queries.
Input
The only line of input contains the integers n and k (1 ≤ n ≤ 500, 1 ≤ k ≤ n), the length of the lost array and the configured query size of the XOR machine.
Elements of the original array satisfy 1 ≤ a_i ≤ 10^9.
It can be proven that that if it is possible to recover the XOR sum under the given constraints, it can be done in at most 500 queries. That is, d ≤ 500.
After taking n and k, begin interaction.
Output
If it is impossible to recover the XOR-sum of the array, output -1 immediately after taking n and k. Do not begin interaction.
Otherwise, when your program finds the XOR-sum of the lost array a_1, a_2, …, a_n, report the answer in the following format: "! x", where x is the XOR sum of the array a_1, a_2, …, a_n, and terminate your program normally immediately after flushing the output stream.
Note that answering does not count as a query.
Interaction
Each query is made in the format "? b", where b is an array of exactly k distinct integers from 1 to n denoting the indices of the elements in the lost array that you want to query the XOR sum of.
You will then receive an integer x, the XOR sum of the queried elements. It can be proven that 0 ≤ x ≤ 2 ⋅ 10^9 will always be true.
After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
* fflush(stdout) or cout.flush() in C++;
* System.out.flush() in Java;
* flush(output) in Pascal;
* stdout.flush() in Python;
* see documentation for other languages.
If at any point you make an invalid query or try to make more than 500 queries (which is the hard limit), the interaction will terminate immediately and give you a Wrong Answer verdict. Note that if you exceed d queries, the interaction will continue normally unless you also exceed the 500 query hard limit, though you will still receive a Wrong Answer verdict either way.
Hacks
To hack a solution, use the following format.
The first line contains the integers n and k (1 ≤ n ≤ 500, 1 ≤ k ≤ n).
The second line contains the the array a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9).
Examples
Input
5 3
4
0
1
Output
? 1 2 3
? 2 3 5
? 4 1 5
! 7
Input
3 2
Output
-1
Note
In the first example interaction, the array a_1, a_2, …, a_n is 2, 1, 7, 5, 6 and its XOR-sum is 7.
The first query made asks for indices 1,2,3, so the response is a_1 ⊕ a_2 ⊕ a_3 = 2 ⊕ 1 ⊕ 7 = 4.
The second query made asks for indices 2,3,5, so the response is a_2 ⊕ a_3 ⊕ a_5 = 1 ⊕ 7 ⊕ 6 = 0.
The third query made asks for indices 4,1,5, so the response is a_4 ⊕ a_1 ⊕ a_5 = 5 ⊕ 2 ⊕ 6 = 1. Note that the indices may be output in any order.
Additionally, even though three queries were made in the example interaction, it is just meant to demonstrate the interaction format and does not necessarily represent an optimal strategy.
In the second example interaction, there is no way to recover the XOR-sum of Little Dormi's array no matter what is queried, so the program immediately outputs -1 and exits.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from sys import stdout
def reverse(n, req):
return [x for x in range(1, n + 1) if x not in req]
def solve():
(n, k) = (int(x) for x in input().split())
if n % 2 == 1 and k % 2 == 0:
print(-1)
stdout.flush()
return
elif n % k == 0:
xor = 0
curr_idx = 1
while curr_idx <= n:
next_idx = curr_idx + k
print('?', ' '.join((str(x) for x in range(curr_idx, next_idx))))
stdout.flush()
xor ^= int(input())
curr_idx = next_idx
print('!', xor)
stdout.flush()
return
elif n % 2 != k % 2 and n < 2 * k:
xor = 0
curr_idx = 1
kk = n - k
while True:
next_idx = curr_idx + kk
curr_arr = reverse(n, set(range(curr_idx, next_idx)))
print('?', ' '.join((str(x) for x in curr_arr)))
stdout.flush()
xor ^= int(input())
curr_idx = next_idx
if n - curr_idx + 1 < 2 * kk and (n - curr_idx + 1) % 2 == 0:
break
if curr_idx < n:
arr = list(range(1, kk + 1))
next_idx = curr_idx + (n - curr_idx + 1) // 2
curr_arr = list(range(curr_idx, next_idx)) + arr
curr_arr = reverse(n, set(curr_arr[:kk]))
print('?', ' '.join((str(x) for x in curr_arr)))
stdout.flush()
xor ^= int(input())
curr_arr = list(range(next_idx, n + 1)) + arr
curr_arr = reverse(n, set(curr_arr[:kk]))
print('?', ' '.join((str(x) for x in curr_arr)))
stdout.flush()
xor ^= int(input())
print('!', xor)
stdout.flush()
return
else:
xor = 0
curr_idx = 1
while True:
next_idx = curr_idx + k
print('?', ' '.join((str(x) for x in range(curr_idx, next_idx))))
stdout.flush()
xor ^= int(input())
curr_idx = next_idx
if n - curr_idx + 1 < 2 * k and (n - curr_idx + 1) % 2 == 0:
break
if curr_idx < n:
arr = list(range(1, k + 1))
next_idx = curr_idx + (n - curr_idx + 1) // 2
curr_arr = list(range(curr_idx, next_idx)) + arr
print('?', ' '.join((str(x) for x in curr_arr[:k])))
stdout.flush()
xor ^= int(input())
curr_arr = list(range(next_idx, n + 1)) + arr
print('?', ' '.join((str(x) for x in curr_arr[:k])))
stdout.flush()
xor ^= int(input())
print('!', xor)
stdout.flush()
return
solve()
``` | vfc_137971 | {
"difficulty": "unknown_difficulty",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1534/E",
"time_limit": "1.5 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3 1\n949490681 476940754 49124973\n",
"output": "3 639110214\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3 2\n1 2 3\n",
"output": "-1 -1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/EQPAIR | Solve the following coding problem using the programming language python:
You are given an array A of length N.
A pair (i, j) (1≤ i< j ≤ N) is said to be *good* if gcd(A_{i}, A_{j}) = lcm(A_{i}, A_{j}). Here gcd denotes the [greatest common divisor] and lcm denotes [least common multiple].
Find the total number of *good* pairs present in the given array.
------ Input Format ------
- The first line of input will contain a single integer T, denoting the number of test cases.
- The first line of each test case contains an integer N - the length of the array A.
- The second line of each test case contains N space-separated integers A_{1},A_{2},\ldots,A_{N}.
------ Output Format ------
For each test case, output on a new line the total number of such *good* pairs possible in the given array.
------ Constraints ------
$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{5}$
$1 ≤ A_{i} ≤ 10^{9}$
- The sum of $N$ over all test cases won't exceed $3 \cdot 10^{5}$.
----- Sample Input 1 ------
5
2
5 9
5
1 5 5 5 9
8
2 5 5 2 9 9 9 12
4
12 12 18 18
5
12 15 10 5 9
----- Sample Output 1 ------
0
3
5
2
0
----- explanation 1 ------
Test case $1$: No *good* pair is present.
Test case $2$: The *good* pairs $(i, j)$ are: $(2, 3), (3, 4),$ and $(2, 4)$. To elaborate, $gcd(A_{2}, A_{3}) = lcm(A_{2}, A_{3}) = 5$.
Test case $3$: The *good* pairs $(i, j)$ are: $(1, 4), (2, 3), (5, 6), (6, 7),$ and $(5, 7)$. To elaborate, $gcd(A_{1}, A_{4}) = lcm(A_{1}, A_{4}) = 2$.
Test case $4$: The *good* pair $(i, j)$ are: $(1, 2),$ and $(3, 4)$. To elaborate, $gcd(A_{3}, A_{4}) = lcm(A_{3}, A_{4}) = 18$.
Test case $5$: No *good* pair is present.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for _ in range(int(input())):
n = int(input())
lis = list(map(int, input().split()))
lis.sort()
ans = 0
cou = 1
for i in range(1, n):
if lis[i] == lis[i - 1]:
cou += 1
else:
ans = ans + cou * (cou - 1) / 2
cou = 1
ans = ans + cou * (cou - 1) // 2
print(int(ans))
``` | vfc_137979 | {
"difficulty": "easy",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/EQPAIR",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5\n2\n5 9\n5\n1 5 5 5 9\n8\n2 5 5 2 9 9 9 12\n4\n12 12 18 18\n5\n12 15 10 5 9\n",
"output": "0\n3\n5\n2\n0",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/java-strings-set-15112/1 | Solve the following coding problem using the programming language python:
Given two strings S1 and S2 as input. Your task is to concatenate two strings and then reverse the string. Finally print the reversed string.
Example 1:
Input: S1 = "Geeks" , S2 = "forGeeks"
Output: "skeeGrofskeeG"
Explanation: Concatenating S1 and S2 to
get "GeeksforGeeks" then reversing it to
"skeeGrofskeeG".
Example 2:
Input: S1 = "Practice" , S2 = "Geeks"
Output: "skeeGecitcarP"
Explanation: Concatenating S1 and S2 to
get "PracticeGeeks" then reversing it to
"skeegecitcarP".
Your Task:
You dont need to read input or print anything. Complete the function conRevstr() which takes S1 and S2 as input parameter and returns the sting final_s after concatenating and reversing.
Expected Time Complexity: O(|S1| + |S2|)
Expected Auxiliary Space: O(|S1| + |S2|)
Constraints:
1<= |S1| <=1000
1<= |S2| <=1000
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def conRevstr (ob, S1, S2):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def conRevstr(ob, S1, S2):
addedString = S1 + S2
reversedString = addedString[::-1]
return reversedString
``` | vfc_137988 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/java-strings-set-15112/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "S1 = \"Geeks\" , S2 = \"forGeeks\"",
"output": "\"skeeGrofskeeG\"",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "S1 = \"Practice\" , S2 = \"Geeks\"",
"output": "\"skeeGecitcarP\"",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/STICKS | Solve the following coding problem using the programming language python:
Read problems statements in Mandarin Chinese, Russian and Vietnamese as well.
Chef and his little brother are playing with sticks. They have total N sticks. Length of i-th stick is A_{i}.
Chef asks his brother to choose any four sticks and to make a rectangle with those sticks its sides. Chef warns his brother to not to break any of the sticks, he has to use sticks as a whole. Also, he wants that the rectangle formed should have the maximum possible area among all the rectangles that Chef's brother can make.
Chef's little brother takes this challenge up and overcomes it. Can you also do so? That is, you have to tell whether it is even possible to create a rectangle? If yes, then you have to tell the maximum possible area of rectangle.
------ Input ------
The first line contains a single integer T denoting the number of test-cases. T test cases follow.
The first line of each test case contains a single integer N denoting the number of sticks.
The second line of each test case contains N space-separated integers A_{1}, A_{2}, ..., A_{N} denoting the lengths of sticks.
------ Output ------
For each test case, output a single line containing an integer representing the maximum possible area for rectangle or -1 if it's impossible to form any rectangle using the available sticks.
------ Constraints ------
$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{3}$
$1 ≤ sum of N's over all test-cases in a single test file ≤ 10^{3}$
$1 ≤ A_{i} ≤ 10^{3}$
----- Sample Input 1 ------
2
5
1 2 3 1 2
4
1 2 2 3
----- Sample Output 1 ------
2
-1
----- explanation 1 ------
Example case 1. Chef's brother can choose sticks of lengths 1, 2, 1, 2. He can create a rectangle with area 1 * 2 = 2.
Example case 2. It's impossible to choose 4 sticks so that they form a rectangle.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
t = int(input())
for ni in range(t):
n = int(input())
l = [int(i) for i in input().split()]
s = list(set(l))
s = s[-1::-1]
x = 0
s1 = list()
for i in s:
c = l.count(i)
if c >= 2:
x = x + c // 2 * 2
s1.append(i)
if x >= 4:
break
if len(s1) == 0 or x < 4:
print(-1)
elif len(s1) == 1:
print(s1[0] * s1[0])
else:
print(s1[0] * s1[1])
``` | vfc_137989 | {
"difficulty": "easy",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/STICKS",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n5\n1 2 3 1 2\n4\n1 2 2 3",
"output": "2\n-1",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n5\n1 2 3 1 1\n4\n1 2 2 3",
"output": "-1\n-1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n5\n1 2 3 1 2\n4\n1 3 2 3",
"output": "2\n-1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1096/F | Solve the following coding problem using the programming language python:
A permutation of size $n$ is an array of size $n$ such that each integer from $1$ to $n$ occurs exactly once in this array. An inversion in a permutation $p$ is a pair of indices $(i, j)$ such that $i > j$ and $a_i < a_j$. For example, a permutation $[4, 1, 3, 2]$ contains $4$ inversions: $(2, 1)$, $(3, 1)$, $(4, 1)$, $(4, 3)$.
You are given a permutation $p$ of size $n$. However, the numbers on some positions are replaced by $-1$. Let the valid permutation be such a replacement of $-1$ in this sequence back to numbers from $1$ to $n$ in such a way that the resulting sequence is a permutation of size $n$.
The given sequence was turned into a valid permutation randomly with the equal probability of getting each valid permutation.
Calculate the expected total number of inversions in the resulting valid permutation.
It can be shown that it is in the form of $\frac{P}{Q}$ where $P$ and $Q$ are non-negative integers and $Q \ne 0$. Report the value of $P \cdot Q^{-1} \pmod {998244353}$.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the sequence.
The second line contains $n$ integers $p_1, p_2, \dots, p_n$ ($-1 \le p_i \le n$, $p_i \ne 0$) — the initial sequence.
It is guaranteed that all elements not equal to $-1$ are pairwise distinct.
-----Output-----
Print a single integer — the expected total number of inversions in the resulting valid permutation.
It can be shown that it is in the form of $\frac{P}{Q}$ where $P$ and $Q$ are non-negative integers and $Q \ne 0$. Report the value of $P \cdot Q^{-1} \pmod {998244353}$.
-----Examples-----
Input
3
3 -1 -1
Output
499122179
Input
2
1 2
Output
0
Input
2
-1 -1
Output
499122177
-----Note-----
In the first example two resulting valid permutations are possible:
$[3, 1, 2]$ — $2$ inversions; $[3, 2, 1]$ — $3$ inversions.
The expected value is $\frac{2 \cdot 1 + 3 \cdot 1}{2} = 2.5$.
In the second example no $-1$ are present, thus the only valid permutation is possible — the given one. It has $0$ inversions.
In the third example there are two resulting valid permutations — one with $0$ inversions and one with $1$ inversion.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def divisors(M):
d = []
i = 1
while M >= i ** 2:
if M % i == 0:
d.append(i)
if i ** 2 != M:
d.append(M // i)
i = i + 1
return d
def popcount(x):
x = x - (x >> 1 & 1431655765)
x = (x & 858993459) + (x >> 2 & 858993459)
x = x + (x >> 4) & 252645135
x = x + (x >> 8)
x = x + (x >> 16)
return x & 127
def eratosthenes(n):
res = [0 for i in range(n + 1)]
prime = set([])
for i in range(2, n + 1):
if not res[i]:
prime.add(i)
for j in range(1, n // i + 1):
res[i * j] = 1
return prime
def factorization(n):
res = []
for p in prime:
if n % p == 0:
while n % p == 0:
n //= p
res.append(p)
if n != 1:
res.append(n)
return res
def euler_phi(n):
res = n
for x in range(2, n + 1):
if x ** 2 > n:
break
if n % x == 0:
res = res // x * (x - 1)
while n % x == 0:
n //= x
if n != 1:
res = res // n * (n - 1)
return res
def ind(b, n):
res = 0
while n % b == 0:
res += 1
n //= b
return res
def isPrimeMR(n):
if n == 1:
return 0
d = n - 1
d = d // (d & -d)
L = [2, 3, 5, 7, 11, 13, 17]
for a in L:
t = d
y = pow(a, t, n)
if y == 1:
continue
while y != n - 1:
y = y * y % n
if y == 1 or t == n - 1:
return 0
t <<= 1
return 1
def findFactorRho(n):
from math import gcd
m = 1 << n.bit_length() // 8
for c in range(1, 99):
f = lambda x: (x * x + c) % n
(y, r, q, g) = (2, 1, 1, 1)
while g == 1:
x = y
for i in range(r):
y = f(y)
k = 0
while k < r and g == 1:
ys = y
for i in range(min(m, r - k)):
y = f(y)
q = q * abs(x - y) % n
g = gcd(q, n)
k += m
r <<= 1
if g == n:
g = 1
while g == 1:
ys = f(ys)
g = gcd(abs(x - ys), n)
if g < n:
if isPrimeMR(g):
return g
elif isPrimeMR(n // g):
return n // g
return findFactorRho(g)
def primeFactor(n):
i = 2
ret = {}
rhoFlg = 0
while i * i <= n:
k = 0
while n % i == 0:
n //= i
k += 1
if k:
ret[i] = k
i += 1 + i % 2
if i == 101 and n >= 2 ** 20:
while n > 1:
if isPrimeMR(n):
(ret[n], n) = (1, 1)
else:
rhoFlg = 1
j = findFactorRho(n)
k = 0
while n % j == 0:
n //= j
k += 1
ret[j] = k
if n > 1:
ret[n] = 1
if rhoFlg:
ret = {x: ret[x] for x in sorted(ret)}
return ret
def divisors(n):
res = [1]
prime = primeFactor(n)
for p in prime:
newres = []
for d in res:
for j in range(prime[p] + 1):
newres.append(d * p ** j)
res = newres
res.sort()
return res
def xorfactorial(num):
if num == 0:
return 0
elif num == 1:
return 1
elif num == 2:
return 3
elif num == 3:
return 0
else:
x = baseorder(num)
return 2 ** x * ((num - 2 ** x + 1) % 2) + function(num - 2 ** x)
def xorconv(n, X, Y):
if n == 0:
res = [X[0] * Y[0] % mod]
return res
x = [X[i] + X[i + 2 ** (n - 1)] for i in range(2 ** (n - 1))]
y = [Y[i] + Y[i + 2 ** (n - 1)] for i in range(2 ** (n - 1))]
z = [X[i] - X[i + 2 ** (n - 1)] for i in range(2 ** (n - 1))]
w = [Y[i] - Y[i + 2 ** (n - 1)] for i in range(2 ** (n - 1))]
res1 = xorconv(n - 1, x, y)
res2 = xorconv(n - 1, z, w)
former = [(res1[i] + res2[i]) * inv for i in range(2 ** (n - 1))]
latter = [(res1[i] - res2[i]) * inv for i in range(2 ** (n - 1))]
former = list(map(lambda x: x % mod, former))
latter = list(map(lambda x: x % mod, latter))
return former + latter
def merge_sort(A, B):
(pos_A, pos_B) = (0, 0)
(n, m) = (len(A), len(B))
res = []
while pos_A < n and pos_B < m:
(a, b) = (A[pos_A], B[pos_B])
if a < b:
res.append(a)
pos_A += 1
else:
res.append(b)
pos_B += 1
res += A[pos_A:]
res += B[pos_B:]
return res
class UnionFindVerSize:
def __init__(self, N):
self._parent = [n for n in range(0, N)]
self._size = [1] * N
self.group = N
def find_root(self, x):
if self._parent[x] == x:
return x
self._parent[x] = self.find_root(self._parent[x])
stack = [x]
while self._parent[stack[-1]] != stack[-1]:
stack.append(self._parent[stack[-1]])
for v in stack:
self._parent[v] = stack[-1]
return self._parent[x]
def unite(self, x, y):
gx = self.find_root(x)
gy = self.find_root(y)
if gx == gy:
return
self.group -= 1
if self._size[gx] < self._size[gy]:
self._parent[gx] = gy
self._size[gy] += self._size[gx]
else:
self._parent[gy] = gx
self._size[gx] += self._size[gy]
def get_size(self, x):
return self._size[self.find_root(x)]
def is_same_group(self, x, y):
return self.find_root(x) == self.find_root(y)
class WeightedUnionFind:
def __init__(self, N):
self.parent = [i for i in range(N)]
self.size = [1 for i in range(N)]
self.val = [0 for i in range(N)]
self.flag = True
self.edge = [[] for i in range(N)]
def dfs(self, v, pv):
stack = [(v, pv)]
new_parent = self.parent[pv]
while stack:
(v, pv) = stack.pop()
self.parent[v] = new_parent
for (nv, w) in self.edge[v]:
if nv != pv:
self.val[nv] = self.val[v] + w
stack.append((nv, v))
def unite(self, x, y, w):
if not self.flag:
return
if self.parent[x] == self.parent[y]:
self.flag = self.val[x] - self.val[y] == w
return
if self.size[self.parent[x]] > self.size[self.parent[y]]:
self.edge[x].append((y, -w))
self.edge[y].append((x, w))
self.size[x] += self.size[y]
self.val[y] = self.val[x] - w
self.dfs(y, x)
else:
self.edge[x].append((y, -w))
self.edge[y].append((x, w))
self.size[y] += self.size[x]
self.val[x] = self.val[y] + w
self.dfs(x, y)
class Dijkstra:
class Edge:
def __init__(self, _to, _cost):
self.to = _to
self.cost = _cost
def __init__(self, V):
self.G = [[] for i in range(V)]
self._E = 0
self._V = V
@property
def E(self):
return self._E
@property
def V(self):
return self._V
def add_edge(self, _from, _to, _cost):
self.G[_from].append(self.Edge(_to, _cost))
self._E += 1
def shortest_path(self, s):
import heapq
que = []
d = [10 ** 15] * self.V
d[s] = 0
heapq.heappush(que, (0, s))
while len(que) != 0:
(cost, v) = heapq.heappop(que)
if d[v] < cost:
continue
for i in range(len(self.G[v])):
e = self.G[v][i]
if d[e.to] > d[v] + e.cost:
d[e.to] = d[v] + e.cost
heapq.heappush(que, (d[e.to], e.to))
return d
def Z_algorithm(s):
N = len(s)
Z_alg = [0] * N
Z_alg[0] = N
i = 1
j = 0
while i < N:
while i + j < N and s[j] == s[i + j]:
j += 1
Z_alg[i] = j
if j == 0:
i += 1
continue
k = 1
while i + k < N and k + Z_alg[k] < j:
Z_alg[i + k] = Z_alg[k]
k += 1
i += k
j -= k
return Z_alg
class BIT:
def __init__(self, n, mod=None):
self.BIT = [0] * (n + 1)
self.num = n
self.mod = mod
def query(self, idx):
res_sum = 0
mod = self.mod
while idx > 0:
res_sum += self.BIT[idx]
if mod:
res_sum %= mod
idx -= idx & -idx
return res_sum
def update(self, idx, x):
mod = self.mod
while idx <= self.num:
self.BIT[idx] += x
if mod:
self.BIT[idx] %= mod
idx += idx & -idx
return
class dancinglink:
def __init__(self, n, debug=False):
self.n = n
self.debug = debug
self._left = [i - 1 for i in range(n)]
self._right = [i + 1 for i in range(n)]
self.exist = [True for i in range(n)]
def pop(self, k):
if self.debug:
assert self.exist[k]
L = self._left[k]
R = self._right[k]
if L != -1:
if R != self.n:
(self._right[L], self._left[R]) = (R, L)
else:
self._right[L] = self.n
elif R != self.n:
self._left[R] = -1
self.exist[k] = False
def left(self, idx, k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._left[res]
if res == -1:
break
k -= 1
return res
def right(self, idx, k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._right[res]
if res == self.n:
break
k -= 1
return res
class SparseTable:
def __init__(self, A, merge_func, ide_ele):
N = len(A)
n = N.bit_length()
self.table = [[ide_ele for i in range(n)] for i in range(N)]
self.merge_func = merge_func
for i in range(N):
self.table[i][0] = A[i]
for j in range(1, n):
for i in range(0, N - 2 ** j + 1):
f = self.table[i][j - 1]
s = self.table[i + 2 ** (j - 1)][j - 1]
self.table[i][j] = self.merge_func(f, s)
def query(self, s, t):
b = t - s + 1
m = b.bit_length() - 1
return self.merge_func(self.table[s][m], self.table[t - 2 ** m + 1][m])
class BinaryTrie:
class node:
def __init__(self, val):
self.left = None
self.right = None
self.max = val
def __init__(self):
self.root = self.node(-10 ** 15)
def append(self, key, val):
pos = self.root
for i in range(29, -1, -1):
pos.max = max(pos.max, val)
if key >> i & 1:
if pos.right is None:
pos.right = self.node(val)
pos = pos.right
else:
pos = pos.right
elif pos.left is None:
pos.left = self.node(val)
pos = pos.left
else:
pos = pos.left
pos.max = max(pos.max, val)
def search(self, M, xor):
res = -10 ** 15
pos = self.root
for i in range(29, -1, -1):
if pos is None:
break
if M >> i & 1:
if xor >> i & 1:
if pos.right:
res = max(res, pos.right.max)
pos = pos.left
else:
if pos.left:
res = max(res, pos.left.max)
pos = pos.right
elif xor >> i & 1:
pos = pos.right
else:
pos = pos.left
if pos:
res = max(res, pos.max)
return res
def solveequation(edge, ans, n, m):
x = [0] * m
used = [False] * n
for v in range(n):
if used[v]:
continue
y = dfs(v)
if y != 0:
return False
return x
def dfs(v):
used[v] = True
r = ans[v]
for (to, dire, id) in edge[v]:
if used[to]:
continue
y = dfs(to)
if dire == -1:
x[id] = y
else:
x[id] = -y
r += y
return r
class Matrix:
mod = 10 ** 9 + 7
def set_mod(m):
Matrix.mod = m
def __init__(self, L):
self.row = len(L)
self.column = len(L[0])
self._matrix = L
for i in range(self.row):
for j in range(self.column):
self._matrix[i][j] %= Matrix.mod
def __getitem__(self, item):
if type(item) == int:
raise IndexError('you must specific row and column')
elif len(item) != 2:
raise IndexError('you must specific row and column')
(i, j) = item
return self._matrix[i][j]
def __setitem__(self, item, val):
if type(item) == int:
raise IndexError('you must specific row and column')
elif len(item) != 2:
raise IndexError('you must specific row and column')
(i, j) = item
self._matrix[i][j] = val
def __add__(self, other):
if (self.row, self.column) != (other.row, other.column):
raise SizeError('sizes of matrixes are different')
res = [[0 for j in range(self.column)] for i in range(self.row)]
for i in range(self.row):
for j in range(self.column):
res[i][j] = self._matrix[i][j] + other._matrix[i][j]
res[i][j] %= Matrix.mod
return Matrix(res)
def __sub__(self, other):
if (self.row, self.column) != (other.row, other.column):
raise SizeError('sizes of matrixes are different')
res = [[0 for j in range(self.column)] for i in range(self.row)]
for i in range(self.row):
for j in range(self.column):
res[i][j] = self._matrix[i][j] - other._matrix[i][j]
res[i][j] %= Matrix.mod
return Matrix(res)
def __mul__(self, other):
if type(other) != int:
if self.column != other.row:
raise SizeError('sizes of matrixes are different')
res = [[0 for j in range(other.column)] for i in range(self.row)]
for i in range(self.row):
for j in range(other.column):
temp = 0
for k in range(self.column):
temp += self._matrix[i][k] * other._matrix[k][j]
res[i][j] = temp % Matrix.mod
return Matrix(res)
else:
n = other
res = [[n * self._matrix[i][j] % Matrix.mod for j in range(self.column)] for i in range(self.row)]
return Matrix(res)
def __pow__(self, m):
if self.column != self.row:
raise MatrixPowError('the size of row must be the same as that of column')
n = self.row
res = Matrix([[int(i == j) for i in range(n)] for j in range(n)])
while m:
if m % 2 == 1:
res = res * self
self = self * self
m //= 2
return res
def __str__(self):
res = []
for i in range(self.row):
for j in range(self.column):
res.append(str(self._matrix[i][j]))
res.append(' ')
res.append('\n')
res = res[:len(res) - 1]
return ''.join(res)
class SegmentTree:
def __init__(self, init_val, segfunc, ide_ele):
n = len(init_val)
self.segfunc = segfunc
self.ide_ele = ide_ele
self.num = 1 << (n - 1).bit_length()
self.tree = [ide_ele] * 2 * self.num
for i in range(n):
self.tree[self.num + i] = init_val[i]
for i in range(self.num - 1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])
def update(self, k, x):
k += self.num
self.tree[k] = x
while k > 1:
self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
k >>= 1
def query(self, l, r):
res = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
res = self.segfunc(res, self.tree[r - 1])
l >>= 1
r >>= 1
return res
def bisect_l(self, l, r, x):
l += self.num
r += self.num
Lmin = -1
Rmin = -1
while l < r:
if l & 1:
if self.tree[l] <= x and Lmin == -1:
Lmin = l
l += 1
if r & 1:
if self.tree[r - 1] <= x:
Rmin = r - 1
l >>= 1
r >>= 1
if Lmin != -1:
pos = Lmin
while pos < self.num:
if self.tree[2 * pos] <= x:
pos = 2 * pos
else:
pos = 2 * pos + 1
return pos - self.num
elif Rmin != -1:
pos = Rmin
while pos < self.num:
if self.tree[2 * pos] <= x:
pos = 2 * pos
else:
pos = 2 * pos + 1
return pos - self.num
else:
return -1
def cmb(n, r, mod):
if r < 0 or r > n:
return 0
r = min(r, n - r)
return g1[n] * g2[r] % mod * g2[n - r] % mod
mod = 998244353
N = 2 * 10 ** 5
g1 = [1] * (N + 1)
g2 = [1] * (N + 1)
inverse = [1] * (N + 1)
for i in range(2, N + 1):
g1[i] = g1[i - 1] * i % mod
inverse[i] = -inverse[mod % i] * (mod // i) % mod
g2[i] = g2[i - 1] * inverse[i] % mod
inverse[0] = 0
import sys, random, bisect
from collections import deque, defaultdict
from heapq import heapify, heappop, heappush
from itertools import permutations
from math import log, gcd
input = lambda : sys.stdin.readline().rstrip()
mi = lambda : map(int, input().split())
li = lambda : list(mi())
n = int(input())
p = li()
val = set([p[i] for i in range(n)])
fw = BIT(n)
cnt = 0
for i in range(1, n + 1):
if i not in val:
fw.update(i, 1)
cnt += 1
res = 0
tmp = 0
for i in range(n):
if p[i] != -1:
tmp += fw.query(p[i])
else:
res += tmp * inverse[cnt]
res %= mod
tmp = 0
for i in range(n - 1, -1, -1):
if p[i] != -1:
tmp += cnt - fw.query(p[i])
else:
res += tmp * inverse[cnt]
res %= mod
res += cnt * (cnt - 1) * inverse[4]
res %= mod
fw = BIT(n)
cnt = 0
for i in range(n):
if p[i] != -1:
res += cnt - fw.query(p[i])
cnt += 1
fw.update(p[i], 1)
print(res % mod)
``` | vfc_137994 | {
"difficulty": "hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1096/F",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n3 -1 -1\n",
"output": "499122179\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n1 2\n",
"output": "0\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
Summer vacation ended at last and the second semester has begun. You, a Kyoto University student, came to university and heard a rumor that somebody will barricade the entrance of your classroom. The barricade will be built just before the start of the A-th class and removed by Kyoto University students just before the start of the B-th class. All the classes conducted when the barricade is blocking the entrance will be cancelled and you will not be able to attend them. Today you take N classes and class i is conducted in the t_i-th period. You take at most one class in each period. Find the number of classes you can attend.
Constraints
* 1 \leq N \leq 1000
* 1 \leq A < B \leq 10^9
* 1 \leq t_i \leq 10^9
* All t_i values are distinct.
Input
N, A and B are given on the first line and t_i is given on the (i+1)-th line.
N A B
t1
:
tN
Output
Print the number of classes you can attend.
Examples
Input
5 5 9
4
3
6
9
1
Output
4
Input
5 4 9
5
6
7
8
9
Output
1
Input
4 3 6
9
6
8
1
Output
4
Input
2 1 2
1
2
Output
1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
(N, A, B) = map(int, input().split())
t = [int(input()) for i in range(N)]
ans = 0
for i in range(N):
if A <= t[i] < B:
continue
else:
ans += 1
print(ans)
``` | vfc_137998 | {
"difficulty": "unknown_difficulty",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "1.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "4 1 6\n9\n6\n8\n1",
"output": "3\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2 1 2\n2\n2",
"output": "2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5 5 5\n5\n6\n11\n8\n9",
"output": "5\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4 1 11\n7\n6\n0\n1",
"output": "1\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | Solve the following coding problem using the programming language python:
You are given N non-overlapping circles in xy-plane. The radius of each circle varies, but the radius of the largest circle is not double longer than that of the smallest.
<image>
Figure 1: The Sample Input
The distance between two circles C1 and C2 is given by the usual formula
<image>
where (xi, yi ) is the coordinates of the center of the circle Ci, and ri is the radius of Ci, for i = 1, 2.
Your task is to write a program that finds the closest pair of circles and print their distance.
Input
The input consists of a series of test cases, followed by a single line only containing a single zero, which indicates the end of input.
Each test case begins with a line containing an integer N (2 ≤ N ≤ 100000), which indicates the number of circles in the test case. N lines describing the circles follow. Each of the N lines has three decimal numbers R, X, and Y. R represents the radius of the circle. X and Y represent the x- and y-coordinates of the center of the circle, respectively.
Output
For each test case, print the distance between the closest circles. You may print any number of digits after the decimal point, but the error must not exceed 0.00001.
Example
Input
4
1.0 0.0 0.0
1.5 0.0 3.0
2.0 4.0 0.0
1.0 3.0 4.0
0
Output
0.5
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def _get_distance(c1, c2):
return ((c1[1] - c2[1]) ** 2 + (c1[2] - c2[2]) ** 2) ** 0.5 - c1[0] - c2[0]
from itertools import combinations
def _get_min_distance(circles):
min_d = float('inf')
for (c1, c2) in combinations(circles, 2):
min_d = min(min_d, _get_distance(c1, c2))
return min_d
def closest_pair_distance(circles, axis=1):
n = len(circles)
if n <= 3:
return _get_min_distance(circles)
else:
mid = n // 2
(r, x, y) = zip(*circles)
if len(set(x)) > len(set(y)):
if axis == 2:
circles.sort(key=lambda c: c[1] - c[0])
axis1 = 1
axis2 = 2
else:
if axis == 1:
circles.sort(key=lambda c: c[2] - c[0])
axis1 = 2
axis2 = 1
A_circles = circles[:mid]
B_circles = circles[mid:]
d_Amin = closest_pair_distance(A_circles.copy(), axis1)
d_Bmin = closest_pair_distance(B_circles.copy(), axis1)
dist = min(d_Amin, d_Bmin)
min_d = dist
A_circles.sort(key=lambda c: c[axis] + c[0])
B_edge = B_circles[0][axis1] - B_circles[0][0]
for ac in A_circles[::-1]:
ac_r = ac[0]
ac_edge = ac[axis1] + ac_r
if B_edge - ac_edge >= dist:
break
for bc in B_circles:
bc_r = bc[0]
if bc[axis1] - bc_r - ac_edge >= dist:
break
if abs(ac[axis2] - bc[axis2]) - ac_r - bc_r < dist:
min_d = min(min_d, _get_distance(ac, bc))
return min_d
def solve():
import sys
input_lines = sys.stdin.readlines()
while True:
N = int(input_lines[0])
if N == 0:
break
circles = [tuple(map(float, l.split())) for l in input_lines[1:N + 1]]
print('{:.8f}'.format(closest_pair_distance(circles)))
del input_lines[:N + 1]
solve()
``` | vfc_138006 | {
"difficulty": "unknown_difficulty",
"memory_limit": "134.217728 megabytes",
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "8.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "4\n1.0 0.0 0.0\n1.5 0.0 3.0\n2.4193437752467455 4.0 0.0\n1.0 3.0 4.0\n0",
"output": "0.500000000000\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n1.0 0.0 0.5226161732400485\n1.5 0.0 3.0\n2.4193437752467455 4.0 0.0\n1.0 3.0 4.0\n0",
"output": "-0.022616173240\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://codeforces.com/problemset/problem/1594/D | Solve the following coding problem using the programming language python:
Theofanis started playing the new online game called "Among them". However, he always plays with Cypriot players, and they all have the same name: "Andreas" (the most common name in Cyprus).
In each game, Theofanis plays with $n$ other players. Since they all have the same name, they are numbered from $1$ to $n$.
The players write $m$ comments in the chat. A comment has the structure of "$i$ $j$ $c$" where $i$ and $j$ are two distinct integers and $c$ is a string ($1 \le i, j \le n$; $i \neq j$; $c$ is either imposter or crewmate). The comment means that player $i$ said that player $j$ has the role $c$.
An imposter always lies, and a crewmate always tells the truth.
Help Theofanis find the maximum possible number of imposters among all the other Cypriot players, or determine that the comments contradict each other (see the notes for further explanation).
Note that each player has exactly one role: either imposter or crewmate.
-----Input-----
The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Description of each test case follows.
The first line of each test case contains two integers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5$; $0 \le m \le 5 \cdot 10^5$) — the number of players except Theofanis and the number of comments.
Each of the next $m$ lines contains a comment made by the players of the structure "$i$ $j$ $c$" where $i$ and $j$ are two distinct integers and $c$ is a string ($1 \le i, j \le n$; $i \neq j$; $c$ is either imposter or crewmate).
There can be multiple comments for the same pair of $(i, j)$.
It is guaranteed that the sum of all $n$ does not exceed $2 \cdot 10^5$ and the sum of all $m$ does not exceed $5 \cdot 10^5$.
-----Output-----
For each test case, print one integer — the maximum possible number of imposters. If the comments contradict each other, print $-1$.
-----Examples-----
Input
5
3 2
1 2 imposter
2 3 crewmate
5 4
1 3 crewmate
2 5 crewmate
2 4 imposter
3 4 imposter
2 2
1 2 imposter
2 1 crewmate
3 5
1 2 imposter
1 2 imposter
3 2 crewmate
3 2 crewmate
1 3 imposter
5 0
Output
2
4
-1
2
5
-----Note-----
In the first test case, imposters can be Andreas $2$ and $3$.
In the second test case, imposters can be Andreas $1$, $2$, $3$ and $5$.
In the third test case, comments contradict each other. This is because player $1$ says that player $2$ is an imposter, and player $2$ says that player $1$ is a crewmate. If player $1$ is a crewmate, then he must be telling the truth, so player $2$ must be an imposter. But if player $2$ is an imposter then he must be lying, so player $1$ can't be a crewmate. Contradiction.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from sys import stdin, setrecursionlimit
from collections import defaultdict
from threading import Thread, stack_size
input = stdin.readline
def work():
def dfs(curr):
nonlocal c1, c2, ok
if color[curr] == 0:
c1 += 1
else:
c2 += 1
for node in graph[curr]:
if color[node[0]] == -1:
color[node[0]] = color[curr] ^ node[1]
dfs(node[0])
elif color[node[0]] != color[curr] ^ node[1]:
ok = False
setrecursionlimit(2 * 10 ** 5 + 10)
for _ in range(int(input())):
(n, m) = map(int, input().split())
graph = defaultdict(list)
for __ in range(m):
(a, b, c) = input().split()
(a, b) = (int(a), int(b))
if c == 'imposter':
graph[a].append((b, 1))
graph[b].append((a, 1))
else:
graph[a].append((b, 0))
graph[b].append((a, 0))
color = [-1 for __ in range(n + 1)]
ans = 0
ok = True
for i in range(1, n + 1):
if color[i] == -1:
c1 = c2 = 0
color[i] = 0
dfs(i)
ans += max(c1, c2)
print(ans if ok else -1)
stack_size(10 ** 8)
Thread(target=work).start()
``` | vfc_138010 | {
"difficulty": "medium_hard",
"memory_limit": "256 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1594/D",
"time_limit": "3 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n",
"output": "2\n4\n-1\n2\n5\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 3 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 2 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n",
"output": "2\n4\n1\n2\n5\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 5 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n",
"output": "2\n4\n-1\n2\n5\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5\n3 2\n1 2 imposter\n2 3 crewmate\n5 4\n1 4 crewmate\n2 5 crewmate\n2 4 imposter\n3 4 imposter\n2 2\n1 2 imposter\n2 1 crewmate\n3 5\n1 2 imposter\n1 2 imposter\n3 2 crewmate\n3 2 crewmate\n1 3 imposter\n5 0\n",
"output": "2\n3\n-1\n2\n5\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
There are N temples in a straight line and K monks who want to spread their enlightening power to the entire road of temples. All the monks have an enlightenment value, which denotes the range of enlightenment which they can spread in both the directions. Since, they do not want to waste their efficiency on trivial things of the world, they want to keep their range minimum.
Also, when we say that the N temples are in a straight line, we mean that that all the temples lie on something like an X-axis in a graph.
Find the minimum enlightenment value such that all the temples can receive it.
Input Format:
The first line contains two integers, N and K - denoting the number of temples and number of monks. The next line contains N integers denoting the position of the temples in the straight line.
Output format:
Print the answer in a new line.
Constraints:
1 ≤ N ≤ 10^5
1 ≤ K < N
1 ≤ Positioni ≤ 10^7
Update:
The enlightenment value is an integer.
SAMPLE INPUT
3 2
1 5 20
SAMPLE OUTPUT
2
Explanation
The optimal answer is 2.
A monk positioned at 3, can serve temples at 1 and 5.
The other monk can be placed at 18, to serve temple at 20.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def is_enlightenment_possible(ar, n, k, dist):
#Checks if all n temples in list ar is possible to be enlightened by k monks with range dist
pos = ar[0] + dist
for i in ar:
if abs(pos - i) > dist:
k = k - 1
pos = i + dist
k = k - 1
if k >= 0: return True
return False
N, K = list(map(int, input().split()))
ar = list(map(int, input().split()))
ar.sort()
lo, hi = 1, 10000000
ans = 0
while lo<=hi:
mid = (lo + hi) >> 1
#print '%d .. %d .. %d' %(lo, mid, hi)
if is_enlightenment_possible(ar, N, K, mid):
ans = mid
hi = mid - 1
else:
lo = mid + 1
print(ans)
``` | vfc_138014 | {
"difficulty": "medium",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "100000 18\n3613051 6968776 8617651 5250945 2605599 4947993 6694873 2683281 1357358 5004417 4382640 7891512 7072189 6155695 8139750 8956961 6020969 2570586 8586683 3051843 3804421 6223742 857575 6081732 6800031 3601841 7021065 4549376 9668771 7611655 8030181 8775517 632210 6585213 8896733 6122773 1395361 4773148 9068549 4504535 150426 3487563 452115 3937026 7264486 4159041 5224876 6093860 3453825 8883257 9768961 3879813 2527489 9400714 2728829 1133801 5494184 6743565 9182991 8060757 9397672 6561156 5306395 636141 2233833 9947331 5930909 385327 125979 3110792 8028894 3324197 810051 1529466 1557879 2468983 1249384 4903589 8765896 6036145 8384119 3045551 4380207 2337073 9769971 9627033 2744781 7328506 6695251 8826689 7438461 798769 7674893 3343348 9893379 3998566 6465133 5092363 8990089 5567931 408282 8152865 5388559 2005073 613079 7628386 4394275 4229553 3748173 682732 5229576 743211 1516785 5773755 311129 6966071 1961562 284971 6847596 9285431 6001131 6752690 7834055 647452 347465 591323 6361319 5819569 2676389 7580349 664649 1617006 6906681 4588183 4943364 9839465 1826253 152761 2689272 8994441 1210174 7513801 806657 7959886 1211857 8485505 2821019 1949493 1828895 6159868 9649273 5274913 6561125 4449147 747178 6546734 8611539 7006610 7840180 4618041 9307659 3109041 6515169 7778143 9255851 3788857 7057096 1647806 2667404 3761321 3757931 8699841 8752490 2200511 9429628 1549884 1333494 8927923 2437874 9600243 1874141 8066591 3664325 3908811 3532365 8377014 9276830 3175901 7070433 2255985 8577363 7914776 3065058 4968505 7342361 6204977 9213279 7413697 1488067 8504131 6132319 8159953 3398171 8702036 8719113 6009303 2080497 874777 3491961 362056 94901 4363547 2872849 4867851 2103577 4392067 9610442 5496737 4934706 562701 6145009 7542929 6294834 6354480 2654201 6463681 5628785 8685619 7494121 1492301 7239315 1881457 7755685 1204801 219009 7412836 9083262 3395739 4162996 8684969 5863496 5852263 3880385 4765431 948313 598681 5844805 6864481 9546600 2189073 9297801 5880993 9242703 901281 7695401 9648832 9877377 4732545 5130466 3172956 1675853 610537 1986266 9189886 5575961 7098281 4175985 4216373 9980577 3062105 4386502 2925443 4282369 7207757 3597997 5646301 8837476 4372171 5257261 1546939 119901 1371609 1393783 284997 8528523 9300097 8543046 5663617 3753693 1352468 6412753 2621382 5257601 1647131 4783399 9420141 2893037 2840359 7994529 5176932 5736726 9202289 1342196 2869980 5648975 4444116 3300468 4093741 6451513 583633 727681 1706788 2139477 8009145 1170021 6121574 7140581 7771681 5478143 4340801 4148905 2079731 940214 2840693 1072601 1754449 5407417 2877200 7081856 4632833 1377907 2279645 2325612 468869 1251452 712221 8796919 7026521 1659871 7438627 339421 4523500 932492 9468577 5062435 2083181 345321 3986551 8044071 9823001 5957903 8539815 4990001 1274502 399361 6686591 4011847 9983651 546561 3890776 3237069 4337060 4189379 39031 8361170 5585722 5317248 7001481 6510285 2037301 7614298 9917571 8115085 2193799 9254021 7468761 7002043 1291440 3505573 4656126 9636777 9483557 1867023 1700741 7554955 3124761 2089467 2680177 2937389 2868815 5072341 4125651 818605 6931385 3801101 2002945 3434521 4116121 3832541 4391881 2753549 8539268 6605781 4577603 6554155 7870626 5997598 9945963 7690696 307165 3115872 1784924 3546196 5391621 7207985 6672488 3817665 1090401 3078981 6867901 461071 9532153 9321083 382589 969331 9700621 9694937 9501924 6728218 3373013 5094772 7836829 8637947 8493273 1333313 1958387 9878688 7646173 434593 3545748 9836024 9954443 3085305 1712935 1284826 9037789 3912917 3438102 1440161 937809 4075089 2983665 1715679 4019745 2006911 3727786 3298921 9926745 6962758 3693979 5529451 4612418 7871617 2000407 2655761 6628081 1062329 912321 1580516 6354386 1101739 5257931 4554076 310977 3203713 9369366 4462975 40935 4004641 4397851 6739197 4163293 578161 312025 8394181 8695967 6803711 4564083 7135817 1369089 9185221 9869355 8163974 5108776 3062716 1257341 45769 1714811 4324421 8350219 504660 8305092 7906841 2159819 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"output": "118\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
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"output": "3\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
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"output": "2\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/the-modulo-task1736/1 | Solve the following coding problem using the programming language python:
Given an integer N. FInd an integer K for which N%K is the largest ( 1 <= K < N).
Example 1:
Input:
N = 3
Output:
2
Explanation:
3%1 = 0
3%2 = 1
So, the modulo is highest for 2.
Example 2:
Input:
N = 4
Output:
3
Explanation:
4%1 = 0
4%2 = 0
4%3 = 1
So, the modulo is highest for 3.
Your Task:
You don't need to read input or print anything. Your task is to complete the function modTask() which takes a Integer N as input and returns an integer K(1 <= K < N) for which N%K is largest.
Expected Time Complexity: O(1)
Expected Auxiliary Space: O(1)
Constraints:
1 <= N <= 10^{18}
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def modTask(self, N):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def modTask(self, N):
if N % 2 == 1:
return (N + 1) // 2
else:
return N // 2 + 1
``` | vfc_138018 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/the-modulo-task1736/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "N = 3",
"output": "2",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "N = 4",
"output": "3",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/jumping-numbers3805/1 | Solve the following coding problem using the programming language python:
Given a positive number X. Find the largest Jumping Number which is smaller than or equal to X.
Jumping Number: A number is called Jumping Number if all adjacent digits in it differ by only 1. All single-digit numbers are considered as Jumping Numbers. For example 7, 8987 and 4343456 are Jumping numbers but 796, 677 and 89098 are not.
Example 1:
Input:
X = 10
Output:
10
Explanation:
10 is the largest Jumping Number
possible for X = 10.
Example 2:
Input:
X = 50
Output:
45
Explanation:
45 is the largest Jumping Number
possible for X = 50.
Your Task:
You don't need to read input or print anything. Your task is to complete the function jumpingNums() which takes an Integer X as input and returns the largest Jumping Number less than or equal to X.
Expected Time Complexity: O(k), where k is no of jumping numbers
Expected Auxiliary Space: O(k), where k is no of jumping numbers
Constraints:
1 <= X <= 10^{9}
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def jumpingNums(self, X):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from collections import deque
class Solution:
def generate_all_jumping_nums(self, X, i):
J = deque()
J.append(i)
while J:
num = J.popleft()
if num <= X:
self.ans = max(self.ans, num)
last_dig = num % 10
if last_dig != 9:
J.append(num * 10 + last_dig + 1)
if last_dig != 0:
J.append(num * 10 + last_dig - 1)
def jumpingNums(self, X):
self.ans = 0
for i in range(1, 10):
if i <= X:
self.generate_all_jumping_nums(X, i)
return self.ans
``` | vfc_138019 | {
"difficulty": "medium",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/jumping-numbers3805/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "X = 10",
"output": "10",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "X = 50",
"output": "45",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/GCDMOD | Solve the following coding problem using the programming language python:
------Read problems statements in Hindi,
Mandarin chinese
, Russian and Vietnamese as well. ------
At ShareChat, there are are plenty of interesting problems to solve. Here is one of them.
Given integers $A$, $B$ and $N$, you should calculate the [GCD] of $A^{N} + B^{N}$ and $|A - B|$. (Assume that $GCD(0, a) = a$ for any positive integer $a$). Since this number could be very large, compute it modulo $1000000007$ ($10^{9} + 7$).
------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first and only line of each test case contains three space-separated integers $A$, $B$ and $N$.
------ Output ------
For each test case, print a single line containing one integer — the required GCD modulo $10^{9} + 7$.
------ Constraints ------
$1 ≤ T ≤ 10$
$1 ≤ A, B, N ≤ 10^{12}$
$B ≤ A$
------ Subtasks ------
Subtask #1 (10 points): $1 ≤ A, B, N ≤ 10$
Subtask #2 (40 points): $1 ≤ A, B, N ≤ 10^{9}$
Subtask #3 (50 points): original constraints
----- Sample Input 1 ------
2
10 1 1
9 1 5
----- Sample Output 1 ------
1
2
----- explanation 1 ------
Example case 1: $GCD(10^{1} + 1^{1}, 10 - 1) = GCD(11, 9) = 1$
Example case 2: $GCD(9^{5} + 1^{5}, 9 - 1) = GCD(59050, 8) = 2$
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import math
def power(a, n, mod):
res = 1
while n > 0:
if n & 1 == 1:
res = res % mod * a % mod % mod
n -= 1
a = a % mod * a % mod % mod
n = n // 2
return res
def gcd(a, b, n, mod):
if a == b:
return (power(a, n, mod) + power(b, n, mod)) % mod
possible = 1
total = a - b
for i in range(1, int(math.sqrt(total)) + 1):
if total % i == 0:
temp = (power(a, n, i) + power(b, n, i)) % i
if temp == 0:
possible = max(possible, i)
temp = (power(a, n, total // i) + power(b, n, total // i)) % (total // i)
if temp == 0:
possible = max(possible, total // i)
return possible % mod
case = int(input())
for _ in range(case):
(a, b, n) = map(int, input().split(' '))
mod = 1000000007
res = gcd(a, b, n, mod)
print(res)
``` | vfc_138020 | {
"difficulty": "medium_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/GCDMOD",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n10 1 1\n9 1 5",
"output": "1\n2",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/PRIGAME | Solve the following coding problem using the programming language python:
Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.
Chef and Divyam are playing a game with the following rules:
First, an integer $X!$ is written on a board.
Chef and Divyam alternate turns; Chef plays first.
In each move, the current player should choose a positive integer $D$ which is divisible by up to $Y$ distinct primes and does not exceed the integer currently written on the board. Note that $1$ is not a prime.
$D$ is then subtracted from the integer on the board, i.e. if the integer written on the board before this move was $A$, it is erased and replaced by $A-D$.
When one player writes $0$ on the board, the game ends and this player wins.
Given $X$ and $Y$, determine the winner of the game.
------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first and only line of each test case contains two space-separated integers $X$ and $Y$.
------ Output ------
For each test case, print a single line containing the string "Chef" if Chef wins the game or "Divyam" if Divyam wins (without quotes).
------ Constraints ------
$1 ≤ T ≤ 10^{6}$
$1 ≤ X,Y ≤ 10^{6}$
------ Subtasks ------
Subtask #1 (5 points): $Y=1$
Subtask #2 (10 points):
$1 ≤ T ≤ 10^{2}$
$1 ≤ X ≤ 6$
Subtask #3 (85 points): original constraints
----- Sample Input 1 ------
3
1 2
3 1
2021 42
----- Sample Output 1 ------
Chef
Divyam
Divyam
----- explanation 1 ------
Example case 1: Since $D = 1$ is divisible by $0$ primes, Chef will write $0$ and win the game in the first move.
Example case 2: Chef must choose $D$ between $1$ and $5$ inclusive, since $D = 6$ is divisible by more than one prime. Then, Divyam can always choose $6-D$, write $0$ on the board and win the game.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
def solve(x, y):
if primes[x] > y:
return 'Divyam'
return 'Chef'
def prime(n):
primes = ['a' for i in range(n + 1)]
primes[0] = 0
primes[1] = 0
for i in range(2, n + 1):
if primes[i] == 'a':
primes[i] = 1 + primes[i - 1]
j = 2
while j * i < n:
primes[j * i] = 0
j += 1
elif primes[i] < primes[i - 1]:
primes[i] = primes[i - 1]
return primes
primes = prime(1000001)
for _ in range(int(sys.stdin.readline())):
print(solve(*map(int, sys.stdin.readline().split())))
``` | vfc_138028 | {
"difficulty": "medium_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/PRIGAME",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n1 2\n3 1\n2021 42",
"output": "Chef\nDivyam \nDivyam",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/cousins-of-a-given-node/1 | Solve the following coding problem using the programming language python:
Given a binary tree and a node, print all cousins of given node in order of their appearance. Note that siblings should not be printed.
Example 1:
Input :
1
/ \
2 3
/ \ / \
4 5 6 7
Given node : 5
Output : 6 7
Explanation :
Nodes 6 and 7 are on the same level
as 5 and have different parents.
Example 2 :
Input :
9
/
5
Given node : 5
Output : -1
Explanation :
There no other nodes than 5 in the same level.
Your task :
You don't have to read input or print anything. Your task is to complete the function printCousins() which takes the root node of the tree and the node whose cousins need to be found, as input and returns a list containing the cousins of the given node in order of their appearance in the tree. If there is no cousin of the given node, return -1 as the first element of the list.
Expected Time Complexity : O(n)
Expected Auxiliary Space : O(n)
Constraints :
1 <= n <=10^5
Write your solution by modifying this code:
```python
#User function Template for python3
'''
# Tree Node
class Node:
def __init__(self, val):
self.right = None
self.data = val
self.left = None
'''
class Solution:
def printCousins(self, root, node_to_find):
#code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def printCousins(self, root, node_to_find):
q = [root]
flag = 0
while len(q) > 0:
l = len(q)
for i in range(l):
temp = q[0]
q.pop(0)
if temp.left != None and temp.left == node_to_find:
flag = 1
continue
elif temp.right != None and temp.right == node_to_find:
flag = 1
continue
if temp.left != None:
q.append(temp.left)
if temp.right != None:
q.append(temp.right)
if flag == 1:
break
for i in range(len(q)):
q[i] = q[i].data
if len(q) == 0:
return [-1]
return q
``` | vfc_138032 | {
"difficulty": "medium",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/cousins-of-a-given-node/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "1\r\n / \\\r\n 2 3\r\n / \\ / \\\r\n 4 5 6 7\r\n\r\nGiven node:5",
"output": "6 7",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "9\r\n /\r\n 5\r\nGiven node:5",
"output": "-1",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/CMPRSS | Solve the following coding problem using the programming language python:
Read problem statements in [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.
You are given a strictly increasing sequence of integers $A_{1}, A_{2}, \ldots, A_{N}$. Your task is to compress this sequence.
The *compressed form* of this sequence is a sequence of ranges separated by commas (characters ','). A *range* is either an integer or a pair of integers separated by three dots (the string "..."). When each range a...b in the compressed form is decompressed into the subsequence $(a, a+1, \ldots, b)$, we should obtain the (comma-separated) sequence $A$ again.
For each maximal contiguous subsequence $(a, a+1, \ldots, b)$ of $A$ such that $b ≥ a+2$, the compressed form of $A$ must contain the range a...b; if $b ≤ a+1$, such a sequence should not be compressed into a range. A contiguous subsequence is maximal if it cannot be extended by at least one element of $A$ next to it. It can be proved that the compressed form of any sequence is unique (i.e. well-defined).
------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
The second line contains $N$ space-separated integers $A_{1}, A_{2}, \ldots, A_{N}$.
------ Output ------
For each test case, print a single line containing one string ― the compressed form of the given sequence.
------ Constraints ------
$1 ≤ T ≤ 100$
$1 ≤ N ≤ 100$
$1 ≤ A_{i} ≤ 1,000$ for each valid $i$
$A_{1} < A_{2} < \ldots < A_{N}$
------ Subtasks ------
Subtask #1 (100 points): original constraints
----- Sample Input 1 ------
3
12
1 2 3 5 6 8 9 10 11 12 15 17
4
4 5 7 8
1
4
----- Sample Output 1 ------
1...3,5,6,8...12,15,17
4,5,7,8
4
----- explanation 1 ------
Example case 1:
- $(1, 2, 3)$ is a contiguous subsequence with length $3$, so it is replaced by the string "1...3"
- $(5, 6)$ is a contiguous subsequence, but only with length $2$, so it is not compressed into a range
- $(8, 9, 10, 11, 12)$ is a contiguous subsequence with length $5$, so it is replaced by "8...12"
- the elements $15$, $17$ are unaffected
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
t = int(input())
for z in range(t):
n = int(input())
l = list(map(int, input().split()))
i = 0
s = str(l[0])
while i < n - 1:
j = i + 1
c = 1
while j < n:
if l[i] + j - i == l[j]:
c += 1
j += 1
else:
break
if c >= 3:
i = i + c
if i < n:
s = s + '...' + str(l[i - 1]) + ',' + str(l[i])
else:
s = s + '...' + str(l[i - 1])
else:
i = i + 1
s = s + ',' + str(l[i])
print(s)
``` | vfc_138033 | {
"difficulty": "medium",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/CMPRSS",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n12\n1 2 3 5 6 8 9 10 11 12 15 17\n4\n4 5 7 8\n1\n4",
"output": "1...3,5,6,8...12,15,17\n4,5,7,8\n4",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/TMSLT | Solve the following coding problem using the programming language python:
Read problems statements in Mandarin Chinese and Russian.
Chef wants to split a team of new chef into two teams to play a game. In order to make the split, he first designates two team captains who take alternate turns selecting players for their teams. During each turn, the captain selects a single player for his team. Since each captain wants to make the strongest possible team, he will always select the best available player. The players have strengths as integer number, where higher strength indicate better players. After all the players have been selected, the team strength is computed as the sum of the strengths of the players on that team.
For example, if strengths of 5 players are 5,7,8,4 and 2, then the first captain selects the player with strength 8 for his team, the second captain gets the player with strength 7, the first gets the one with strength 5, the second the one with strength 4, and the last one (strength 2) goes to the first team. The first team now has a total strength 8+5+2=15, and the second team has strength 7+4=11.
Now Chef wants to find the absolute strength difference between the two teams. For the example above the answer is 4(=|15-11|).
But Chef does not know exact strengths of each player. He knows some parameter a, b, c and d and a formula to find the strength of each player. The formula is
S_{0} = d,
S_{i} = (a * S_{i-1}^{2} + b * S_{i-1} + c) mod 1000000, for i = 1 to N - 1
There are N players numbering 0 to N-1 and S_{i} is the strength of player i.
------ Input ------
First line of the input contains an integer T, number of test cases to follow. Each test consist of single line containing five integers N, a, b, c and d.
------ Output ------
For each test case, you have to print a single line containing the absolute strength difference between the two teams.
------ Constraints ------
1 ≤ T ≤ 50
1 ≤ N ≤ 3000000
0 ≤ a, b, c, d ≤ 100
----- Sample Input 1 ------
4
1 1 1 1 1
2 1 1 1 1
3 1 2 3 4
4 2 3 4 1
----- Sample Output 1 ------
1
2
763
74896
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
mdl = 1000000
for _ in range(int(input())):
z = input().split()
(n, a, b, c, d) = map(int, z[:5])
sqd = dict()
sqd[d] = 0
r = d
for e in range(1, n):
r = ((a * r + b) * r + c) % mdl
try:
sqd[r] *= 1
break
except KeyError:
sqd[r] = e
if len(sqd) == n:
picks = list(sqd.keys())
else:
inrun = list(sqd.items())
inrun.sort(key=lambda x: x[1])
nunq = len(sqd)
repst = sqd[r]
picks = [inrun[e][0] for e in range(0, repst)]
reprun = [inrun[e][0] for e in range(repst, nunq)]
cyc = (n - len(picks)) // len(reprun)
runout = (n - len(picks)) % len(reprun)
if 0 == cyc % 2:
picks.extend(reprun[:runout])
else:
picks.extend(reprun[runout:])
picks.sort(reverse=True)
np = len(picks)
sth = sum(picks[0:np:2]) - sum(picks[1:np:2])
print(sth)
``` | vfc_138041 | {
"difficulty": "medium_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/TMSLT",
"time_limit": "5 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "4\n1 1 1 1 1\n2 1 1 1 1\n3 1 2 3 4\n4 2 3 4 1",
"output": "1\n2\n763\n74896",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/342/E | Solve the following coding problem using the programming language python:
Xenia the programmer has a tree consisting of n nodes. We will consider the tree nodes indexed from 1 to n. We will also consider the first node to be initially painted red, and the other nodes — to be painted blue.
The distance between two tree nodes v and u is the number of edges in the shortest path between v and u.
Xenia needs to learn how to quickly execute queries of two types:
1. paint a specified blue node in red;
2. calculate which red node is the closest to the given one and print the shortest distance to the closest red node.
Your task is to write a program which will execute the described queries.
Input
The first line contains two integers n and m (2 ≤ n ≤ 105, 1 ≤ m ≤ 105) — the number of nodes in the tree and the number of queries. Next n - 1 lines contain the tree edges, the i-th line contains a pair of integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi) — an edge of the tree.
Next m lines contain queries. Each query is specified as a pair of integers ti, vi (1 ≤ ti ≤ 2, 1 ≤ vi ≤ n). If ti = 1, then as a reply to the query we need to paint a blue node vi in red. If ti = 2, then we should reply to the query by printing the shortest distance from some red node to node vi.
It is guaranteed that the given graph is a tree and that all queries are correct.
Output
For each second type query print the reply in a single line.
Examples
Input
5 4
1 2
2 3
2 4
4 5
2 1
2 5
1 2
2 5
Output
0
3
2
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class CentroidDecomposition:
def __init__(self, g):
self.g = g
self.n = len(g)
self.parent = [-1] * self.n
self.size = [1] * self.n
self.cdparent = [-1] * self.n
self.cddepth = [0] * self.n
self.cdorder = [-1] * self.n
self.cdused = [0] * self.n
cnt = 0
stack = [0]
while stack:
v = stack.pop()
p = self.cdparent[v]
c = self.get_centroid(v)
self.cdused[c] = True
self.cdparent[c] = p
self.cddepth[c] = self.cddepth[v]
self.cdorder[c] = cnt
cnt += 1
for u in self.g[c]:
if self.cdused[u]:
continue
self.cdparent[u] = c
self.cddepth[u] = self.cddepth[c] + 1
stack.append(u)
def get_centroid(self, root):
self.parent[root] = -1
self.size[root] = 1
stack = [root]
order = []
while stack:
v = stack.pop()
order.append(v)
for u in g[v]:
if self.parent[v] == u or self.cdused[u]:
continue
self.size[u] = 1
self.parent[u] = v
stack.append(u)
if len(order) <= 2:
return root
for v in reversed(order):
if self.parent[v] == -1:
continue
self.size[self.parent[v]] += self.size[v]
total = self.size[root]
v = root
while True:
for u in self.g[v]:
if self.parent[v] == u or self.cdused[u]:
continue
if self.size[u] > total // 2:
v = u
break
else:
return v
class HLD:
def __init__(self, g):
self.g = g
self.n = len(g)
self.parent = [-1] * self.n
self.size = [1] * self.n
self.head = [0] * self.n
self.preorder = [0] * self.n
self.k = 0
self.depth = [0] * self.n
for v in range(self.n):
if self.parent[v] == -1:
self.dfs_pre(v)
self.dfs_hld(v)
def dfs_pre(self, v):
g = self.g
stack = [v]
order = [v]
while stack:
v = stack.pop()
for u in g[v]:
if self.parent[v] == u:
continue
self.parent[u] = v
self.depth[u] = self.depth[v] + 1
stack.append(u)
order.append(u)
while order:
v = order.pop()
child_v = g[v]
if len(child_v) and child_v[0] == self.parent[v]:
(child_v[0], child_v[-1]) = (child_v[-1], child_v[0])
for (i, u) in enumerate(child_v):
if u == self.parent[v]:
continue
self.size[v] += self.size[u]
if self.size[u] > self.size[child_v[0]]:
(child_v[i], child_v[0]) = (child_v[0], child_v[i])
def dfs_hld(self, v):
stack = [v]
while stack:
v = stack.pop()
self.preorder[v] = self.k
self.k += 1
top = self.g[v][0]
for u in reversed(self.g[v]):
if u == self.parent[v]:
continue
if u == top:
self.head[u] = self.head[v]
else:
self.head[u] = u
stack.append(u)
def for_each(self, u, v):
while True:
if self.preorder[u] > self.preorder[v]:
(u, v) = (v, u)
l = max(self.preorder[self.head[v]], self.preorder[u])
r = self.preorder[v]
yield (l, r)
if self.head[u] != self.head[v]:
v = self.parent[self.head[v]]
else:
return
def for_each_edge(self, u, v):
while True:
if self.preorder[u] > self.preorder[v]:
(u, v) = (v, u)
if self.head[u] != self.head[v]:
yield (self.preorder[self.head[v]], self.preorder[v])
v = self.parent[self.head[v]]
else:
if u != v:
yield (self.preorder[u] + 1, self.preorder[v])
break
def subtree(self, v):
l = self.preorder[v]
r = self.preorder[v] + self.size[v]
return (l, r)
def lca(self, u, v):
while True:
if self.preorder[u] > self.preorder[v]:
(u, v) = (v, u)
if self.head[u] == self.head[v]:
return u
v = self.parent[self.head[v]]
import sys
import io, os
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
(n, m) = map(int, input().split())
g = [[] for i in range(n)]
for i in range(n - 1):
(a, b) = map(int, input().split())
(a, b) = (a - 1, b - 1)
g[a].append(b)
g[b].append(a)
cd = CentroidDecomposition(g)
hld = HLD(g)
min_dist = [0] * n
for i in range(n):
min_dist[i] = hld.depth[i]
for i in range(m):
(t, v) = map(int, input().split())
v -= 1
if t == 1:
cur = v
while cur != -1:
l = hld.lca(cur, v)
d = hld.depth[cur] + hld.depth[v] - 2 * hld.depth[l]
min_dist[cur] = min(min_dist[cur], d)
cur = cd.cdparent[cur]
else:
ans = n
cur = v
while cur != -1:
l = hld.lca(cur, v)
d = hld.depth[cur] + hld.depth[v] - 2 * hld.depth[l]
ans = min(ans, d + min_dist[cur])
cur = cd.cdparent[cur]
print(ans)
``` | vfc_138049 | {
"difficulty": "very_hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/342/E",
"time_limit": "5.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 5\n1 2\n2 1\n",
"output": "0\n3\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 1\n1 2\n2 1\n",
"output": "0\n0\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5 4\n1 2\n2 3\n2 4\n1 5\n2 1\n2 5\n1 2\n2 5\n",
"output": "0\n1\n1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/WORLDCUP | Solve the following coding problem using the programming language python:
Read problems statements in Mandarin Chinese and Russian as well.
Captain Dehatti from Bawanian village is making strategy to win the Fake Cricket World Cup organised in his village.
He want his team to score runs only in 4's and 6's because he believes that scoring any runs by running will make them tired.
He also wants that the team does not loose more than L wickets.
He now wonders in how many ways his team can score exactly R runs in B balls. Ofcourse, he assumes that the opponent bowling is awesome and will not concede any extra runs.
Formally, He wonders how many ways can his team score exactly R runs in B balls, given that each ball can result in 4, 6, 0 , or W(wicket wont add anything to score). Atmost L wicktes are allowed [i.e. Atmost L 'W' can be there in B balls ].
Note: His batting order is fixed i.e. After each wicket , next player to come is fixed.
------ Input ------
First line contains T, the number of test cases.
Each test case contains 3 space separated integers, R, B and L
------ Output ------
For each test cases output the number of ways modulo 1e9+7 (i.e. 1000000007)
------ Constraints ------
$1 ≤ T ≤ 25000$
$0 ≤ R ≤ 10^{9}$
$1 ≤ B ≤ 300$
$0 ≤ L ≤ 9$
Note that the answer to R = 0 , B = 2 , W =1 is 3 [ 00 , 0W , W0 ]
----- Sample Input 1 ------
6
10 2 9
6 2 9
6 1 9
4 1 9
5 1 9
10 3 9
----- Sample Output 1 ------
2
4
1
1
0
12
----- explanation 1 ------
Explanation for the sample input 1:
All possible ways to face 2 deliveries:
00
04
06
0W
W0
W4
W6
WW
40
44
46
4W
60
64
66
6W
Only possible ways to win the match are 46 and 64. Hence answer is 2.
You need to consider all sample space i.e. 4^{B}
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def solve(r, b, l):
if b == 0:
if r == 0 and l >= 0:
return 1
return 0
if l < 0 or r < 0:
return 0
if arr[r][b][l] != -1:
return arr[r][b][l]
ans = 0
ans += solve(r - 0, b - 1, l)
ans %= mod
ans += solve(r - 0, b - 1, l - 1)
ans %= mod
ans += solve(r - 4, b - 1, l)
ans %= mod
ans += solve(r - 6, b - 1, l)
ans %= mod
arr[r][b][l] = ans
return ans
mod = int(1000000000.0 + 7)
arr = [[[-1 for k in range(10)] for j in range(301)] for i in range(1801)]
for _ in range(int(input())):
(r, b, l) = map(int, input().split())
if r > 1800 or r & 1:
print(0)
else:
print(solve(r, b, l))
``` | vfc_138053 | {
"difficulty": "hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/WORLDCUP",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "6\n10 2 9\n6 2 9\n6 1 9\n4 1 9\n5 1 9\n10 3 9",
"output": "2\n4\n1\n1\n0\n12",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/760/A | Solve the following coding problem using the programming language python:
Petr wants to make a calendar for current month. For this purpose he draws a table in which columns correspond to weeks (a week is seven consequent days from Monday to Sunday), rows correspond to weekdays, and cells contain dates. For example, a calendar for January 2017 should look like on the picture: $\left. \begin{array}{|r|r|r|r|r|r|} \hline & {2} & {9} & {16} & {23} & {30} \\ \hline & {3} & {10} & {17} & {24} & {31} \\ \hline & {4} & {11} & {18} & {25} & {} \\ \hline & {5} & {12} & {19} & {26} & {} \\ \hline & {6} & {13} & {20} & {27} & {} \\ \hline & {7} & {14} & {21} & {28} & {} \\ \hline 1 & {8} & {15} & {22} & {29} & {} \\ \hline \end{array} \right.$
Petr wants to know how many columns his table should have given the month and the weekday of the first date of that month? Assume that the year is non-leap.
-----Input-----
The only line contain two integers m and d (1 ≤ m ≤ 12, 1 ≤ d ≤ 7) — the number of month (January is the first month, December is the twelfth) and the weekday of the first date of this month (1 is Monday, 7 is Sunday).
-----Output-----
Print single integer: the number of columns the table should have.
-----Examples-----
Input
1 7
Output
6
Input
1 1
Output
5
Input
11 6
Output
5
-----Note-----
The first example corresponds to the January 2017 shown on the picture in the statements.
In the second example 1-st January is Monday, so the whole month fits into 5 columns.
In the third example 1-st November is Saturday and 5 columns is enough.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
(x, y) = map(int, input().split())
z = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
k = (z[x - 1] - (abs(y - 7) + 1)) / 7
j = (z[x - 1] - (abs(y - 7) + 1)) % 7
if j == 0:
print(int(k + 1))
else:
print(int(k + 2))
``` | vfc_138070 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/760/A",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "1 7\n",
"output": "6\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1 1\n",
"output": "5\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/340/A | Solve the following coding problem using the programming language python:
Iahub and his friend Floyd have started painting a wall. Iahub is painting the wall red and Floyd is painting it pink. You can consider the wall being made of a very large number of bricks, numbered 1, 2, 3 and so on.
Iahub has the following scheme of painting: he skips x - 1 consecutive bricks, then he paints the x-th one. That is, he'll paint bricks x, 2·x, 3·x and so on red. Similarly, Floyd skips y - 1 consecutive bricks, then he paints the y-th one. Hence he'll paint bricks y, 2·y, 3·y and so on pink.
After painting the wall all day, the boys observed that some bricks are painted both red and pink. Iahub has a lucky number a and Floyd has a lucky number b. Boys wonder how many bricks numbered no less than a and no greater than b are painted both red and pink. This is exactly your task: compute and print the answer to the question.
-----Input-----
The input will have a single line containing four integers in this order: x, y, a, b. (1 ≤ x, y ≤ 1000, 1 ≤ a, b ≤ 2·10^9, a ≤ b).
-----Output-----
Output a single integer — the number of bricks numbered no less than a and no greater than b that are painted both red and pink.
-----Examples-----
Input
2 3 6 18
Output
3
-----Note-----
Let's look at the bricks from a to b (a = 6, b = 18). The bricks colored in red are numbered 6, 8, 10, 12, 14, 16, 18. The bricks colored in pink are numbered 6, 9, 12, 15, 18. The bricks colored in both red and pink are numbered with 6, 12 and 18.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def gcd(x, y):
if y % x == 0:
return x
else:
return gcd(y % x, x)
inp = input()
arr = inp.split(' ')
x = int(arr[0])
y = int(arr[1])
a = int(arr[2])
b = int(arr[3])
g = gcd(min(x, y), max(x, y))
l = x * y // g
i = 0
for i in range(a, a + l + 1):
if i > b:
break
if i % l == 0:
break
ans = 0
if b >= i:
ans = (b - i) // l + 1
print(ans)
``` | vfc_138075 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/340/A",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2 3 6 18\n",
"output": "3",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
Naruto is a fan of numbers, he likes to play with them. This time he decided to multiply numbers and produce output. After every k elements he decides to find x^m, where x is the multiplication till k elements and m is a random number that naruto takes. Help naruto find the output.
As answer could be large, help him, calculate value modulo w.
Input
T=number of test case
N=number of elements he will enter
K=every kth element
M=Random number
W=Modulo
A[i]=n elements to be entered.
Output
Output answer of each test case in one line.
Constraint:
0<t<100
0<a[i]<10000000
1<n<101
k<100000
m<100000
w<100000
SAMPLE INPUT
2
5 2 2 5
1 2 3 4 5
5 2 2 5
1 2 3 4 6
SAMPLE OUTPUT
0
4
Explanation
In first case n=5,k=2,m=2,w=5;
Step 1
1
Step 2: 12=2
since k=2 therefore 2^m=2^2=4;
Step 3: 43=12
Step 4: 124=48
since k=2,therefore 48^m=48^2
step 5: 23045=11520
step 6: 11520%5=0
2nd Test case
Step 1
1
Step 2: 12=2
since k=2 therefore 2^m=2^2=4;
Step 3: 43=12
Step 4: 124=48
since k=2,therefore 48^m=48^2
step 5: 23046=13824
step 6: 13824%5=4
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def power1(x,n,MOD):
if(n==0):
return 1
ret=1
while(n):
if(n&1):
ret*=x
ret%=MOD
x*=x
x%=MOD
n>>=1
return ret
T=eval(input())
while(T):
T-=1
N,K,M,W=list(map(int,input().split()))
L=list(map(int,input().split()))
prod=1
for x in range(N):
prod=prod*L[x]%W
if((x+1)%K==0):
prod=power1(prod,M,W)
prod%=W
if(prod==0):
break
print(prod%W)
``` | vfc_138079 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n3 2 5 5\n8 4 9\n4 9 7 13\n9 4 77 85\n6 4 8 17\n5 98 74 23 65 45",
"output": "1",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/c239059f6d110e6778cc2f2a1ab58ffd0a3d64ca/1 | Solve the following coding problem using the programming language python:
Given two integers N and K, the task is to count the number of ways to divide N into groups of positive integers. Such that each group shall have K elements and their sum is N. Also the number of elements in the groups follows a non-decreasing order (i.e. group[i] <= group[i+1]). Find the number of such groups
Example 1:
Input:
N = 8
K = 4
Output:
5
Explanation:
There are 5 groups such that their sum is 8
and the number of positive integers in each
group is 4. The 5 groups are [1, 1, 1, 5],
[1, 1, 2, 4], [1, 1, 3, 3], [1, 2, 2, 3] and
[2, 2, 2, 2].
Example 2:
Input:
N = 4
K = 3
Output:
1
Explanation:
The only possible grouping is {1, 1, 2}. Hence,
the answer is 1 in this case.
Your Task:
Complete the function countWaystoDivide() which takes the integers N and K as the input parameters, and returns the number of ways to divide the sum N into K groups.
Expected Time Complexity: O(N^{2}*K)
Expected Auxiliary Space: O(N^{2}*K)
Constraints:
1 ≤ K ≤ N ≤ 100
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def countWaystoDivide(self, N, K):
# Code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
class Solution:
def countWaystoDivide(self, N, K):
dp = [[[0 for _ in range(K + 1)] for _ in range(N + 1)] for _ in range(N + 1)]
for i in range(1, N + 1):
dp[i][0][0] = 1
for max_value in range(1, N + 1):
for remaining_sum in range(1, N + 1):
for remaining_groups in range(1, K + 1):
dp[max_value][remaining_sum][remaining_groups] = dp[max_value - 1][remaining_sum][remaining_groups]
if remaining_sum >= max_value:
dp[max_value][remaining_sum][remaining_groups] += dp[max_value][remaining_sum - max_value][remaining_groups - 1]
ans = 0
for i in range(1, N + 1):
ans += dp[i][N - i][K - 1]
return ans
``` | vfc_138084 | {
"difficulty": "medium_hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/c239059f6d110e6778cc2f2a1ab58ffd0a3d64ca/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "N = 8\r\nK = 4",
"output": "5",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "N = 4\r\nK = 3",
"output": "1",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/33af95e5935f1f2a0c3f5083c4b9d0db68e97bd4/1 | Solve the following coding problem using the programming language python:
Samwell laid out N bowls in a straight line and put a few marbles randomly in each bowl, i^{th} bowl has A[i] marbles. A bowl can never have more than 9 marbles at a time. A bowl can have zero marbles. Now Samwells friend adds one more marble to the last bowl, after this addition all the bowls must still be aligned with the rules mentioned above. Adding a marble follows the same rules as of addition with carryover. You are given the initial list of the number of marbles in each bowl find the position of the bowl which was last modified. It is guaranteed that there is at least one bowl which has at least one space left.
Note: Consider one-based indexing.
Input:
N = 4
A[] = {3, 1, 4, 5}
Output:
4
Explanation:
The last bowl has 5 marbels, we can just
add the marbel here.
Example 2:
Input:
N = 3
A[] = {1, 9, 9}
Output:
1
Explanation:
When we add the marbel to last bowl we
have to move one marbel to 2nd bowl,
to add the marbel in 2nd bowl we have
to move one marbel to 1st bowl.
Hence the last modified bowl is 1.
Your Task:
You don't need to read input or print anything. Your task is to complete the function solve( ) which takes N and A[ ] as input parameters and returns the position of the last modified bowl.
Constraints:
1 ≤ N ≤ 10^{5}
0^{ }≤ A[i] ≤ 9
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution():
def solve(self, N, A):
#your code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def solve(self, n, a):
for i in range(n - 1, 0, -1):
if a[i] < 9:
return i + 1
``` | vfc_138085 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/33af95e5935f1f2a0c3f5083c4b9d0db68e97bd4/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "N = 3\r\nA[] = {1, 9, 9}",
"output": "1",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/CLRL | Solve the following coding problem using the programming language python:
Read problems statements in Mandarin chinese, Russian and Vietnamese as well.
Chef is at a Code Expo where many coders are present discussing, solving, sharing, and eavesdropping on solutions :P
He recently learnt that a former HackerPlant employee, Reziba, who is now working at KodeKarma stole some questions for their KoolKontest. Chef wants to find Reziba, but the only data he has on him, and everyone else present, are their CodeXP ratings, which are distinct.
Chef decides to find Reziba through his rating by asking different people present at the expo. Everyone present are arranged in such a way that, assuming a person with rating X, every person with a rating higher than X are on the person's right, while every person with a rating lower than X are on the person's left.
Everyone present there knows Reziba's rating, except Chef, who now asks people where he could find Reziba.
Chef initially asks an arbitrary person, who replies by giving information on whether Reziba is to the person's left or the person's right, depending on whether this person has a higher or lower rating than Reziba.
Chef proceeds in that direction for an arbitrary distance and stops and asks the next person encountered, and repeats this procedure.
However, Chef will never go beyond a person whose rating Chef has asked before. For example, if Chef was walking to the left and finds a person who already told him to walk to the right then he will not continue going to the person's left.
Chef finally finds Reziba when he finally stops in front of Reziba.
During Chef's search for Reziba, he wrote the sequence of ratings of the people Chef asked in the exact same order, including Reziba's rating, which is the last integer in the sequence.
Towards the end, Chef feels he might've made a mistake while writing this sequence.
Given the sequence that Chef wrote and Reziba's rating, find out whether this sequence is possible or has mistakes.
------ Input ------
First line contains number of test cases T.
The first line of each test case contains the number of people Chef meets, N and Reziba's rating R seperated by a space.
Second line of each test case contains N number of space separated ratings from A_{1} to A_{N} where A_{N} is always equal to R.
------ Output ------
For each test case, output a singe line with either "YES" if the sequence is correct, or print "NO" if the sequence has mistakes, without quotes.
------ Constraints ------
1 ≤ T ≤ 50
1 ≤ N ≤ 10^{6}
1 ≤ sum of N in all test-cases ≤ 1.5*10^{6}
1 ≤ A_{i} ≤ 10^{9}
Integers in A are distinct
A_{N} = R
------ Subtasks ------
Subtask #1: N ≤ 20
Subtask #2: Original Constraints
----- Sample Input 1 ------
2
5 200
600 300 100 350 200
5 890
5123 3300 783 1111 890
----- Sample Output 1 ------
NO
YES
----- explanation 1 ------
Example case 1.The first person that Chef asked has a rating of 600, which is more than 200 so he tells Chef to go to his left. The second person Chef meets has a rating of 300, also tells Chef to go to the left. The third person that chef asked has a rating of 100 so he tells Chef to go to the right. Then Chef asked a person with rating 350, that means Chef went beyond the person with rating of 300, which should never happen, so Chef must have made a mistake while writing this sequence.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
t = int(input())
for jhj in range(t):
(n, r) = map(int, input().split())
a = list(map(int, input().split()))
if n < 3:
print('YES')
continue
b = a[0:n - 1]
mini = min(b)
maxi = max(b)
ans = 'YES'
for i in b:
if i > r and i <= maxi:
maxi = i
elif i < r and i >= mini:
mini = i
else:
ans = 'NO'
print(ans)
``` | vfc_138086 | {
"difficulty": "medium",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/CLRL",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n5 200\n600 300 100 350 200\n5 890\n5123 3300 783 1111 890\n",
"output": "NO\nYES",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
You are situated in an N dimensional grid at position (x1,x2,...,xN). The dimensions of the grid are (D1,D2,...DN). In one step, you can walk one step ahead or behind in any one of the N dimensions. (So there are always 2×N possible different moves). In how many ways can you take M steps such that you do not leave the grid at any point? You leave the grid if at any point xi, either xi≤0 or xi>Di.
Input Format
The first line contains the number of test cases T. T test cases follow. For each test case, the first line contains N and M, the second line contains x1,x2,…,xN and the 3rd line contains D1,D2,…,DN.
Output Format
Output T lines, one corresponding to each test case. Since the answer can be really huge, output it modulo 1000000007.
Constraints
1≤T≤10
1≤N≤10
1≤M≤300
1≤Di≤100
1≤xi≤Di
SAMPLE INPUT
5
1 287
44
78
1 236
25
87
1 122
41
63
1 260
7
64
1 127
3
73
SAMPLE OUTPUT
38753340
587915072
644474045
423479916
320130104
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
mod = 1000000007
def solve(x, d, n, m):
mat = [[0 for i in range(n + 1)] for j in range(m + 1)]
for i in range(n):
mat1 = [[0 for j in range(m + 1)] for k in range(d[i] + 1)]
D = d[i]
for j in range(1, D + 1):
mat1[j][0] = 1
for j in range(1, m + 1):
for k in range(1, D + 1):
mat1[k][j] = 0
if k - 1 > 0:
mat1[k][j] = (mat1[k][j] + mat1[k - 1][j - 1]) % mod
if k + 1 <= D:
mat1[k][j] = (mat1[k][j] + mat1[k + 1][j - 1]) % mod
mat[0][i + 1] = 1
for j in range(1, m + 1):
mat[j][i + 1] = mat1[x[i]][j]
comb = [[0 for i in range(m + 1)] for j in range(m + 1)]
for i in range(0, m + 1):
comb[i][0] = 1
comb[i][i] = 1
for i in range(1, m + 1):
for j in range(1, i):
comb[i][j] = (comb[i - 1][j] + comb[i - 1][j - 1]) % mod
res = [[0 for i in range(n + 1)] for j in range(m + 1)]
for i in range(0, m + 1):
res[i][1] = mat[i][1]
for i in range(0, n + 1):
res[0][i] = 1
for i in range(2, n + 1):
for j in range(1, m + 1):
res[j][i] = 0
for k in range(0, j + 1):
res[j][i] = (res[j][i] + ((comb[j][j - k] * ((res[k][i - 1] * mat[j - k][i]) % mod)) % mod)) % mod;
print(res[m][n])
t = eval(input())
for i in range(t):
n, m = list(map(int, input().split()))
ar = [int(x) for x in input().split()]
dim_len = [int(x) for x in input().split()]
solve(ar, dim_len, n, m)
``` | vfc_138090 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5\n1 287\n44\n78\n1 236\n25\n87\n1 122\n41\n63\n1 260\n7\n64\n1 127\n3\n73",
"output": "38753340\n587915072\n644474045\n423479916\n320130104",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5\n1 287\n44\n78\n1 236\n25\n87\n1 122\n41\n63\n1 260\n7\n64\n1 127\n3\n73",
"output": "38753340\n587915072\n644474045\n423479916\n320130104",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "10\n1 285\n37\n73\n5 41\n57 65 44 4 15\n84 99 64 51 74\n10 223\n45 24 11 4 22 23 3 31 29 21\n48 83 33 55 99 41 60 63 42 24\n3 223\n11 12 58\n55 22 66\n2 177\n9 2\n70 2\n4 234\n8 29 73 9\n8 29 98 85\n5 299\n9 78 9 90 5\n92 99 53 90 7\n7 125\n10 1 4 29 30 8 8\n10 1 10 82 39 27 48\n8 132\n21 2 50 15 43 8 32 56\n33 82 51 91 51 14 95 82\n1 234\n35\n83",
"output": "38753340\n587915072\n644474045\n423479916\n320130104\n792930663\n846814121\n385120933\n60306396\n306773532",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "10\n1 287\n44\n78\n1 236\n25\n87\n1 122\n41\n63\n1 260\n7\n64\n1 127\n3\n73\n1 69\n6\n68\n1 231\n14\n63\n1 236\n13\n30\n1 259\n38\n70\n1 257\n11\n12",
"output": "667210458\n863578060\n625582833\n41130742\n316799627\n587789824\n93300685\n25887465\n185596283\n958238361",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://codeforces.com/problemset/problem/1043/E | Solve the following coding problem using the programming language python:
Zibi is a competitive programming coach. There are $n$ competitors who want to be prepared well. The training contests are quite unusual – there are two people in a team, two problems, and each competitor will code exactly one of them. Of course, people in one team will code different problems.
Rules of scoring also aren't typical. The first problem is always an implementation problem: you have to implement some well-known algorithm very fast and the time of your typing is rated. The second one is an awful geometry task and you just have to get it accepted in reasonable time. Here the length and difficulty of your code are important. After that, Zibi will give some penalty points (possibly negative) for each solution and the final score of the team is the sum of them (the less the score is, the better).
We know that the $i$-th competitor will always have score $x_i$ when he codes the first task and $y_i$ when he codes the second task. We can assume, that all competitors know each other's skills and during the contest distribute the problems in the way that minimizes their final score. Remember that each person codes exactly one problem in a contest.
Zibi wants all competitors to write a contest with each other. However, there are $m$ pairs of people who really don't like to cooperate and they definitely won't write a contest together. Still, the coach is going to conduct trainings for all possible pairs of people, such that the people in pair don't hate each other. The coach is interested for each participant, what will be his or her sum of scores of all teams he trained in?
-----Input-----
The first line contains two integers $n$ and $m$ ($2 \le n \le 300\,000$, $0 \le m \le 300\,000$) — the number of participants and the number of pairs of people who will not write a contest together.
Each of the next $n$ lines contains two integers $x_i$ and $y_i$ ($-10^9 \le x_i, y_i \le 10^9$) — the scores which will the $i$-th competitor get on the first problem and on the second problem. It is guaranteed that there are no two people having both $x_i$ and $y_i$ same.
Each of the next $m$ lines contain two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$, $u_i \ne v_i$) — indices of people who don't want to write a contest in one team. Each unordered pair of indices will appear at most once.
-----Output-----
Output $n$ integers — the sum of scores for all participants in the same order as they appear in the input.
-----Examples-----
Input
3 2
1 2
2 3
1 3
1 2
2 3
Output
3 0 3
Input
3 3
1 2
2 3
1 3
1 2
2 3
1 3
Output
0 0 0
Input
5 3
-1 3
2 4
1 1
3 5
2 2
1 4
2 3
3 5
Output
4 14 4 16 10
-----Note-----
In the first example, there will be only one team consisting of persons $1$ and $3$. The optimal strategy for them is to assign the first task to the $3$-rd person and the second task to the $1$-st person, this will lead to score equal to $1 + 2 = 3$.
In the second example, nobody likes anyone, so there won't be any trainings. It seems that Zibi won't be titled coach in that case...
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from __future__ import division, print_function
import io
import os
import sys
if sys.version_info[0] < 3:
from __builtin__ import xrange as range
from cStringIO import StringIO
from future_builtins import ascii, filter, hex, map, oct, zip
else:
from io import BytesIO as StringIO
(sys.stdout, stream) = (io.IOBase(), StringIO())
sys.stdout.flush = lambda : os.write(1, stream.getvalue()) and (not stream.truncate(0)) and stream.seek(0)
sys.stdout.write = stream.write if sys.version_info[0] < 3 else lambda s: stream.write(s.encode())
(input, flush) = (sys.stdin.readline, sys.stdout.flush)
numbers = []
(num, sign) = (0, True)
for char in os.read(0, os.fstat(0).st_size):
if char >= 48:
num = 10 * num + char - 48
elif char == 45:
sign = False
elif char != 13:
numbers.append(num if sign else -num)
(num, sign) = (0, True)
if char >= 48:
numbers.append(num if sign else -num)
getnum = iter(numbers).__next__
def main():
(n, m) = (getnum(), getnum())
c = [0] * n
a = [[getnum(), getnum(), i] for i in range(n)]
for _ in range(m):
(x, y) = (getnum(), getnum())
s = min(a[x - 1][0] + a[y - 1][1], a[x - 1][1] + a[y - 1][0])
c[x - 1] -= s
c[y - 1] -= s
a.sort(key=lambda x: x[1] - x[0])
sum_x = sum((i[0] for i in a))
sum_y = 0
for i in range(n):
sum_x -= a[i][0]
c[a[i][2]] += sum_x + (n - i - 1) * a[i][1] + sum_y + i * a[i][0]
sum_y += a[i][1]
print(*c)
main()
``` | vfc_138094 | {
"difficulty": "hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1043/E",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3 2\n1 2\n2 3\n1 3\n1 2\n2 3\n",
"output": "3 0 3 ",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3 3\n1 2\n2 3\n1 3\n1 2\n2 3\n1 3\n",
"output": "0 0 0 ",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5 3\n-1 3\n2 4\n1 1\n3 5\n2 2\n1 4\n2 3\n3 5\n",
"output": "4 14 4 16 10 ",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/316/E1 | Solve the following coding problem using the programming language python:
By the age of three Smart Beaver mastered all arithmetic operations and got this summer homework from the amazed teacher:
You are given a sequence of integers a_1, a_2, ..., a_{n}. Your task is to perform on it m consecutive operations of the following type: For given numbers x_{i} and v_{i} assign value v_{i} to element a_{x}_{i}. For given numbers l_{i} and r_{i} you've got to calculate sum $\sum_{x = 0}^{r_{i} - l_{i}}(f_{x} \cdot a_{l_{i} + x})$, where f_0 = f_1 = 1 and at i ≥ 2: f_{i} = f_{i} - 1 + f_{i} - 2. For a group of three numbers l_{i} r_{i} d_{i} you should increase value a_{x} by d_{i} for all x (l_{i} ≤ x ≤ r_{i}).
Smart Beaver planned a tour around great Canadian lakes, so he asked you to help him solve the given problem.
-----Input-----
The first line contains two integers n and m (1 ≤ n, m ≤ 2·10^5) — the number of integers in the sequence and the number of operations, correspondingly. The second line contains n integers a_1, a_2, ..., a_{n} (0 ≤ a_{i} ≤ 10^5). Then follow m lines, each describes an operation. Each line starts with an integer t_{i} (1 ≤ t_{i} ≤ 3) — the operation type: if t_{i} = 1, then next follow two integers x_{i} v_{i} (1 ≤ x_{i} ≤ n, 0 ≤ v_{i} ≤ 10^5); if t_{i} = 2, then next follow two integers l_{i} r_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n); if t_{i} = 3, then next follow three integers l_{i} r_{i} d_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n, 0 ≤ d_{i} ≤ 10^5).
The input limits for scoring 30 points are (subproblem E1): It is guaranteed that n does not exceed 100, m does not exceed 10000 and there will be no queries of the 3-rd type.
The input limits for scoring 70 points are (subproblems E1+E2): It is guaranteed that there will be queries of the 1-st and 2-nd type only.
The input limits for scoring 100 points are (subproblems E1+E2+E3): No extra limitations.
-----Output-----
For each query print the calculated sum modulo 1000000000 (10^9).
-----Examples-----
Input
5 5
1 3 1 2 4
2 1 4
2 1 5
2 2 4
1 3 10
2 1 5
Output
12
32
8
50
Input
5 4
1 3 1 2 4
3 1 4 1
2 2 4
1 2 10
2 1 5
Output
12
45
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
(n, m) = list(map(int, input().split()))
a = list(map(int, input().split()))
for i in range(m):
(t, l, r) = list(map(int, input().split()))
if t == 1:
a[l - 1] = r
else:
s = 0
fiba = fibb = 1
for i in range(l - 1, r):
s += fiba * a[i]
(fiba, fibb) = (fibb, fiba + fibb)
print(s % 1000000000)
``` | vfc_138098 | {
"difficulty": "medium",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/316/E1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5 5\n1 3 1 2 4\n2 1 4\n2 1 5\n2 2 4\n1 3 10\n2 1 5\n",
"output": "12\n32\n8\n50\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1 3\n2\n2 1 1\n1 1 3\n2 1 1\n",
"output": "2\n3\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "11 11\n6 1 9 0 2 9 1 6 2 8 0\n2 9 9\n1 9 0\n1 1 8\n2 2 5\n2 7 11\n2 2 8\n1 3 2\n1 10 0\n2 1 8\n2 9 11\n1 9 7\n",
"output": "2\n16\n31\n147\n234\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "11 18\n14 13 18 17 14 17 13 3 0 3 21\n2 6 9\n2 1 6\n2 5 7\n2 1 3\n2 1 9\n2 3 9\n2 2 5\n2 7 10\n2 1 5\n2 4 6\n2 10 11\n2 4 5\n2 2 8\n2 3 9\n2 1 5\n2 2 3\n2 2 6\n1 4 19\n",
"output": "36\n320\n57\n63\n552\n203\n107\n25\n184\n65\n24\n31\n335\n203\n184\n31\n192\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "12 26\n18 5 13 38 33 11 30 24 6 34 11 30\n2 1 12\n2 1 12\n2 1 11\n1 3 15\n1 11 5\n2 1 11\n2 2 10\n2 3 12\n2 2 11\n2 3 11\n2 3 10\n2 3 11\n1 9 37\n1 2 37\n2 1 11\n1 3 30\n2 2 12\n1 4 42\n2 3 10\n2 1 11\n1 11 26\n1 7 37\n2 3 11\n1 7 30\n1 6 40\n1 7 13\n",
"output": "8683\n8683\n4363\n3833\n2084\n3106\n2359\n1456\n1286\n1456\n4919\n5727\n1708\n4961\n2627\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
Write a program that extracts n different numbers from the numbers 0 to 9 and outputs the number of combinations that add up to s. Each n number is from 0 to 9, and the same number cannot be used in one combination. For example, if n is 3 and s is 6, the combination of the three numbers totaling 6 is
1 + 2 + 3 = 6
0 + 1 + 5 = 6
0 + 2 + 4 = 6
There are three ways.
Input
Given multiple datasets. For each dataset, n (1 ≤ n ≤ 9) and s (0 ≤ s ≤ 100) are given on one line, separated by a single space. When both n and s are 0, it is the end of the input (in this case, the program is terminated without processing).
The number of datasets does not exceed 50.
Output
For each dataset, output the number of combinations in which the sum of n integers is s on one line.
Example
Input
3 6
3 1
0 0
Output
3
0
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def dfs(depth, prev, sum):
if depth == n:
return sum == s
ret = 0
for i in range(prev + 1, 10):
ret += dfs(depth + 1, i, sum + i)
return ret
while True:
(n, s) = map(int, input().split())
if n == 0:
break
print(dfs(0, -1, 0))
``` | vfc_138102 | {
"difficulty": "unknown_difficulty",
"memory_limit": "134.217728 megabytes",
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "1.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3 5\n3 1\n0 0",
"output": "2\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3 0\n5 1\n0 0",
"output": "0\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1 0\n5 1\n0 0",
"output": "1\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3 6\n3 0\n0 0",
"output": "3\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2 5\n1 1\n0 0",
"output": "3\n1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2 0\n1 1\n0 0",
"output": "0\n1\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://codeforces.com/problemset/problem/1130/D2 | Solve the following coding problem using the programming language python:
Alice received a set of Toy Train™ from Bob. It consists of one train and a connected railway network of n stations, enumerated from 1 through n. The train occupies one station at a time and travels around the network of stations in a circular manner. More precisely, the immediate station that the train will visit after station i is station i+1 if 1 ≤ i < n or station 1 if i = n. It takes the train 1 second to travel to its next station as described.
Bob gave Alice a fun task before he left: to deliver m candies that are initially at some stations to their independent destinations using the train. The candies are enumerated from 1 through m. Candy i (1 ≤ i ≤ m), now at station a_i, should be delivered to station b_i (a_i ≠ b_i).
<image> The blue numbers on the candies correspond to b_i values. The image corresponds to the 1-st example.
The train has infinite capacity, and it is possible to load off any number of candies at a station. However, only at most one candy can be loaded from a station onto the train before it leaves the station. You can choose any candy at this station. The time it takes to move the candies is negligible.
Now, Alice wonders how much time is needed for the train to deliver all candies. Your task is to find, for each station, the minimum time the train would need to deliver all the candies were it to start from there.
Input
The first line contains two space-separated integers n and m (2 ≤ n ≤ 5 000; 1 ≤ m ≤ 20 000) — the number of stations and the number of candies, respectively.
The i-th of the following m lines contains two space-separated integers a_i and b_i (1 ≤ a_i, b_i ≤ n; a_i ≠ b_i) — the station that initially contains candy i and the destination station of the candy, respectively.
Output
In the first and only line, print n space-separated integers, the i-th of which is the minimum time, in seconds, the train would need to deliver all the candies were it to start from station i.
Examples
Input
5 7
2 4
5 1
2 3
3 4
4 1
5 3
3 5
Output
10 9 10 10 9
Input
2 3
1 2
1 2
1 2
Output
5 6
Note
Consider the second sample.
If the train started at station 1, the optimal strategy is as follows.
1. Load the first candy onto the train.
2. Proceed to station 2. This step takes 1 second.
3. Deliver the first candy.
4. Proceed to station 1. This step takes 1 second.
5. Load the second candy onto the train.
6. Proceed to station 2. This step takes 1 second.
7. Deliver the second candy.
8. Proceed to station 1. This step takes 1 second.
9. Load the third candy onto the train.
10. Proceed to station 2. This step takes 1 second.
11. Deliver the third candy.
Hence, the train needs 5 seconds to complete the tasks.
If the train were to start at station 2, however, it would need to move to station 1 before it could load the first candy, which would take one additional second. Thus, the answer in this scenario is 5+1 = 6 seconds.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
(n, m) = map(int, input().split())
def dist(a, b):
return (n + b - a) % n
def main():
inp1 = [0] * (n + 1)
inp2 = [n] * (n + 1)
for _ in range(m):
(a, b) = map(int, input().split())
inp1[a] += 1
inp2[a] = min(inp2[a], dist(a, b))
inp = tuple(((r1 - 1) * n + r2 for (r1, r2) in zip(inp1, inp2)))
last = max((i + inp[i] for i in range(1, n + 1) if inp[i])) - 1
res = [last]
for inp_i in inp[1:n]:
last -= 1
if inp_i:
last = max(last, inp_i + n - 1)
res.append(last)
print(*res)
main()
``` | vfc_138106 | {
"difficulty": "medium_hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1130/D2",
"time_limit": "2.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "10 8\n5 2\n6 5\n3 8\n9 10\n4 3\n9 5\n2 6\n9 10\n",
"output": "29 28 27 26 25 24 23 22 21 30 ",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/ZCOPREP | Solve the following coding problem using the programming language python:
ZCO is approaching, and you want to be well prepared!
There are $N$ topics to cover and the $i^{th}$ topic takes $H_i$ hours to prepare (where $1 \le i \le N$). You have only $M$ days left to prepare, and you want to utilise this time wisely. You know that you can't spend more than $S$ hours in a day preparing, as you get tired after that. You don't want to study more than one topic in a day, and also, don't want to spend more than two days on any topic, as you feel that this is inefficient.
Given these constraints, can you find the maximum number of topics you can prepare, if you choose the topics wisely?
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- The first line of each test case contains three space-separated integers: $N$, $M$ and $S$, denoting the number of topics, the number of days remaining and the number of hours you can study in a day.
- The second line of each test case contains $N$ space-separated integers $H_i$, denoting the number of hours needed to prepare for the $i^{th}$ topic.
-----Output:-----
For each testcase, output in a single line: the maximum number of topics you can prepare.
-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $1 \leq M \leq 10^5$
- $1 \leq S \leq 16$
- $1 \leq H_i \leq 50$
-----Subtasks-----
- 30 points : Every topic takes the same number of hours to prepare (i.e. all $H_i$ are equal).
- 70 points : Original constraints.
-----Sample Input:-----
2
5 4 10
10 24 30 19 40
5 4 16
7 16 35 10 15
-----Sample Output:-----
2
4
-----Explanation:-----
Testcase 1:
You can choose topics $1$ and $4$. Topic $1$ will consume a single day , while topic $4$ will consume two days. Thus, you'll be able to prepare these two topics within the 4 remaining days. But you can check that you cannot do any better.
Testcase 2:
You can choose topics $1$, $2$, $4$, and $5$. Each of them will consume one day each. Thus you'll be able to cover $4$ topics.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import math
T = int(input())
for i in range(T):
(N, M, S) = input().split()
N = int(N)
M = int(M)
S = int(S)
ls = list(map(int, input().split()))
maxx = max(ls)
if S < 17 and maxx <= 50:
ls.sort()
total_sum = M * S
count = 0
sum = 0
for i in ls:
if i / S > 2:
continue
else:
sum = sum + math.ceil(i / S) * S
if sum <= total_sum:
count = count + 1
print(count)
``` | vfc_138110 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/ZCOPREP",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n5 4 10\n10 24 30 19 40\n5 4 16\n7 16 35 10 15\n",
"output": "2\n4\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/XORNUBER | Solve the following coding problem using the programming language python:
Given an integer N, Chef wants to find the smallest positive integer M such that the bitwise XOR of M and M+1 is N. If no such M exists output -1.
-----Input-----
The first line of input contain an integer T denoting the number of test cases. Each of the following T lines contains an integer N for that test case.
-----Output-----
For each test case, output a single line containing the number M or -1 as described above.
-----Constraints-----
- 1 ≤ T ≤ 5000
- 1 ≤ N ≤ 230
-----Example-----
Input:
1
3
Output:
1
-----Explanation-----First Example : M desired in the problem would be 1. As bitwise XOR of 1 and 2 is equal to 3.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
a = [2 ** x - 1 for x in range(1, 31)]
for _ in range(int(input())):
n = int(input())
if n == 1:
print(2)
elif n in a:
print(n // 2)
else:
print('-1')
``` | vfc_138115 | {
"difficulty": "medium_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/XORNUBER",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "1\n3\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1\n1",
"output": "2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1\n2",
"output": "-1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1\n7",
"output": "3\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/67/A | Solve the following coding problem using the programming language python:
A teacher decides to give toffees to his students. He asks n students to stand in a queue. Since the teacher is very partial, he follows the following rule to distribute toffees.
He looks at the first two students and gives more toffees to the student having higher marks than the other one. If they have the same marks they get the same number of toffees. The same procedure is followed for each pair of adjacent students starting from the first one to the last one.
It is given that each student receives at least one toffee. You have to find the number of toffees given to each student by the teacher such that the total number of toffees is minimum.
Input
The first line of input contains the number of students n (2 ≤ n ≤ 1000). The second line gives (n - 1) characters consisting of "L", "R" and "=". For each pair of adjacent students "L" means that the left student has higher marks, "R" means that the right student has higher marks and "=" means that both have equal marks.
Output
Output consists of n integers separated by a space representing the number of toffees each student receives in the queue starting from the first one to the last one.
Examples
Input
5
LRLR
Output
2 1 2 1 2
Input
5
=RRR
Output
1 1 2 3 4
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from collections import deque
n = int(input())
s = input()
ans = [1] * n
for i in range(1, n):
if s[i - 1] == 'R':
ans[i] = ans[i - 1] + 1
elif s[i - 1] == '=':
ans[i] = ans[i - 1]
for i in range(n - 2, -1, -1):
if s[i] == 'L':
ans[i] = max(ans[i + 1] + 1, ans[i])
elif s[i] == '=':
ans[i] = max(ans[i], ans[i + 1])
print(*ans)
``` | vfc_138119 | {
"difficulty": "medium_hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/67/A",
"time_limit": "1.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "166\nR===RL=LRRR=RRRL=LRR=R=RR==L=R=R=RRR=RR=RLLRRL=LLRL==L=R==RLR==RL=RR=LR==R=R=LLRLRLR=RR=RLLRLR=RRLL==L=LR=RR=RRRL=RLLLR==L=RRLRLLLLLLLRL===LRLRLRLRRLL=LRLL===LRLRR==\n",
"output": "1 2 2 2 2 3 2 2 1 2 3 4 4 5 6 7 2 2 1 2 3 3 4 4 5 6 6 6 1 1 2 2 3 3 4 5 6 6 7 8 8 9 2 1 2 4 3 3 2 1 3 2 2 2 1 1 2 2 2 3 1 2 2 2 3 1 1 2 3 3 1 2 2 2 3 3 4 4 2 1 2 1 2 1 2 2 3 4 4 5 2 1 2 1 2 2 3 5 4 3 3 3 2 2 1 2 2 3 4 4 5 6 7 1 1 4 3 2 1 2 2 2 1 1 2 3 1 8 7 6 5 4 3 2 1 3 2 2 2 2 1 2 1 2 1 2 1 2 4 3 2 2 1 4 3 2 2 2 2 1 2 1 2 3 3 3 \n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3\nR=\n",
"output": "1 2 2 \n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "6\nRLRL=\n",
"output": "1 2 1 2 1 1 \n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "453\nR==LL==RRLLRRLR=L=LRLL=LRRR=R====L=RL======RR==RRRR=LRR=LLLRR=LLLLL===LL=LLL=LR=RLRL===L==R=LRL=L=R==RRLLR=L==LRR=RRLRLLRR=LL==RLRLLRRRL=RRL=R====L=RLRR=RR=RRRL=R=RL=LLR=LR=L=RR=RR====LRRLRRLLR==R==L==RRLLRLR=RLLLLR==L=L=L=RR==L=LRRRL=R==RRL=LRR=RRRRRL===RLRLR=RLRLRLRLRR=RL=LL=RLLRR=LL=RLL=L=LRLLLLLR==RRL=R=L===LRLLL=RRRLR=LR====RR=L===LLLL=R=LLLRRRLL=LL==RLRL=LRLRL=RR=RLR==LLR=LR=RLLRLRRLL==L=LL==L==RLRLRLL=L=RLLR==LLRRLRRL==L=R=RLLRLLLL====L=====\n",
"output": "1 3 3 3 2 1 1 1 2 3 2 1 2 3 1 3 3 2 2 1 4 3 2 2 1 2 3 4 4 5 5 5 5 5 1 1 2 1 1 1 1 1 1 1 2 3 3 3 4 5 6 7 7 1 2 4 4 3 2 1 2 12 12 11 10 9 8 7 7 7 7 6 5 5 4 3 2 2 1 2 2 3 1 3 2 2 2 2 1 1 1 2 2 1 3 2 2 1 1 2 2 2 3 4 2 1 3 3 2 2 2 1 2 3 3 4 5 1 3 2 1 2 3 3 2 1 1 1 2 1 3 2 1 2 3 4 1 1 2 3 1 1 2 2 2 2 2 1 1 2 1 2 3 3 4 5 5 6 7 8 1 1 2 2 4 3 3 2 1 2 2 1 2 2 1 1 2 3 3 4 5 5 5 5 5 1 2 3 1 2 3 2 1 2 2 2 3 3 3 1 1 1 2 3 2 1 2 1 2 2 5 4 3 2 1 4 4 4 3 3 2 2 1 1 2 3 3 3 2 2 1 2 3 4 1 1 2 2 2 3 4 2 2 1 2 3 3 4 5 6 7 8 1 1 1 1 2 1 2 1 2 2 3 1 2 1 2 1 2 1 2 3 3 4 3 3 2 1 1 3 2 1 2 3 3 2 1 1 5 4 3 3 2 2 1 6 5 4 3 2 1 2 2 2 3 4 1 1 3 3 2 2 2 2 1 4 3 2 1 1 2 3 4 1 2 2 1 2 2 2 2 2 3 6 6 5 5 5 5 4 3 2 1 1 4 4 3 2 1 2 3 5 4 3 3 2 1 1 1 2 1 3 2 2 1 2 1 2 1 1 2 3 3 4 1 3 3 3 2 1 2 2 1 2 2 3 2 1 2 1 2 7 6 5 5 5 4 4 3 2 2 2 1 1 1 2 1 2 1 4 3 2 2 1 1 3 2 1 3 3 3 2 1 2 3 1 2 3 2 2 2 1 1 2 2 3 2 1 6 5 4 3 2 2 2 2 2 1 1 1 1 1 1 \n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "438\nLR=RLLLRL=R==LLR=RRLRRR==RLRLRLLRRRRRLRL=RRRRLRR==RR=RR=LLRR=L=LLRRRLLR==RL=L=LLR=L=R==LLR=L=RR==LRL=LLL=RRR=R=LRLLRLLLR==LRRLLL=L==LLR=RL=LLLLR=RR=LR=RL==LRLRR=RRRRRLRLRR==RR=LLLRLR====LRRLL==LR==LL=LLRR=LRL=RRRRLR=RLLR=R=LLLRRRRR===R==LRLLRLR=LLL=L=L=R=RLLR=R=RR=RL=LLRRLLRR=LRRRR==LR==L==R=L=L=R===LLL=LL==L=L=LLLLL==RRRR==R=RLL=RLR=RRRR=R=L=RRRLLRRLRRRLLRLLRRRL=LR=R=LRLRL=R=RLRRLRRL==R=RRR=RLLR=RR=LL=RLR=R==R===RRLR=LLLR=L===LR=L=R\n",
"output": "2 1 2 2 4 3 2 1 2 1 1 3 3 3 2 1 2 2 3 4 1 2 3 4 4 4 5 1 2 1 3 2 1 2 3 4 5 6 1 2 1 1 2 3 4 5 1 2 3 3 3 4 5 5 6 7 7 2 1 2 4 4 3 3 2 1 2 3 4 2 1 2 2 2 5 4 4 3 3 2 1 2 2 1 1 3 3 3 2 1 2 2 1 1 2 3 3 3 1 5 4 4 3 2 1 1 2 3 4 4 5 5 1 3 2 1 4 3 2 1 2 2 2 1 2 7 6 5 4 4 3 3 3 2 1 2 2 6 5 5 4 3 2 1 2 2 3 4 4 1 2 2 3 2 2 2 1 2 1 2 3 3 4 5 6 7 8 1 2 1 2 3 3 3 4 5 5 3 2 1 2 1 2 2 2 2 2 1 2 4 3 2 2 2 1 5 5 5 4 3 3 2 1 2 3 3 1 2 1 1 2 3 4 5 1 2 2 3 2 1 2 2 4 4 3 2 1 2 3 4 5 6 6 6 6 7 7 7 1 3 2 1 2 1 6 6 5 4 3 3 2 2 1 1 2 2 3 2 1 2 2 3 3 4 5 5 6 3 3 2 1 2 3 2 1 2 3 3 1 2 3 4 5 5 5 1 2 2 2 1 1 1 3 3 2 2 1 1 13 13 13 13 12 11 10 10 9 8 8 8 7 7 6 6 5 4 3 2 1 1 1 2 3 4 5 5 5 6 6 7 2 1 1 2 1 2 2 3 4 5 6 6 7 7 1 1 2 3 4 2 1 2 3 1 2 3 4 2 1 3 2 1 2 3 4 2 2 1 2 2 3 3 1 2 1 2 1 1 2 2 3 1 2 3 1 2 3 1 1 1 2 2 3 4 5 5 6 2 1 2 2 3 4 4 2 1 1 2 1 2 2 3 3 3 4 4 4 4 5 6 1 4 4 3 2 1 3 3 2 2 2 2 1 2 2 1 1 2 \n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "198\nLLRRR=RRRRLRRLRR=R===R=RL==R=RLLLR=R=L=LR=R====RRL=RRR=LL=R=RR=RRRLRRLRRR==L=LRLLL====LR=RL==L===LRR=L=L==R==R==L=LLL===R=LLL=R=L=LLLLRLL=RL=LRRLR=RL==RR=R==RLR==R=R==RLRL=LL=RRR=R===LLLRRRRL=RLRLL\n",
"output": "3 2 1 2 3 4 4 5 6 7 8 1 2 3 1 2 3 3 4 4 4 4 5 5 6 1 1 1 2 2 4 3 2 1 2 2 3 3 2 2 1 2 2 3 3 3 3 3 4 5 1 1 2 3 4 4 2 1 1 2 2 3 4 4 5 6 7 1 2 3 1 2 3 4 4 4 2 2 1 5 4 3 2 2 2 2 2 1 2 2 4 3 3 3 2 2 2 2 1 2 3 3 2 2 1 1 1 2 2 2 5 5 5 4 4 3 2 1 1 1 1 4 4 3 2 1 1 6 6 5 5 4 3 2 1 3 2 1 1 3 2 2 1 2 3 1 2 2 3 1 1 1 2 3 3 4 4 4 5 1 2 2 2 3 3 4 4 4 5 1 4 3 3 2 1 1 2 3 4 4 5 5 5 5 3 2 1 2 3 4 5 1 1 2 1 3 2 1 \n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/create-your-own-calculator4308/1 | Solve the following coding problem using the programming language python:
Given the co-effecients of X,Y and Z in a system of simultaneous equations. Find the values of X,Y and Z.
a1X + b1Y + c1Z = d1
a2X + b2Y + c2Z = d2
a3X + b3Y + c3Z = d3
Example 1:
Input:
Arr = {{5, 4, 2, 0},
{1, 4, 2, 0},
{4, 2, 9, 0}}
Output: {0, 0, 0}
Explanation: After calculating with these
given coefficient the value of X, Y, Z is
0, 0, 0.
Example 2:
Input:
Arr = {{4.2, 6, 7, 10},
{1, 2, 3, 12},
{3, 2, 2, 20}}
Output: {3, 4, -1}
Explanation: After calculating with these
given coefficient the value of X, Y, Z is
3, 4, -1.
Your Task:
You dont need to read input or print anything. Complete the function myCalculator() which takes Arr as input parameter and returns 0 in case the system is inconsistent and 1 in case the system is consistent and has infinitely many solutions. In case the system is consistent and has a unique solution, return 3 space separated integers denoting the floor values of X, Y and Z respectively.
Expected Time Complexity: O(1)
Expected Auxiliary Space: O(1)
Constraints:
-100 <= Arr[i][j] <=100
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def myCalculator(self, Arr):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import math
class Solution:
def delta(self, Arr, i, j, k):
ans = Arr[0][i] * Arr[1][j] * Arr[2][k]
ans += Arr[0][j] * Arr[1][k] * Arr[2][i]
ans += Arr[0][k] * Arr[1][i] * Arr[2][j]
ans -= Arr[0][i] * Arr[1][k] * Arr[2][j]
ans -= Arr[0][j] * Arr[1][i] * Arr[2][k]
ans -= Arr[0][k] * Arr[1][j] * Arr[2][i]
return ans
def myCalculator(self, Arr):
d = self.delta(Arr, 0, 1, 2)
p = self.delta(Arr, 3, 1, 2)
q = self.delta(Arr, 0, 3, 2)
r = self.delta(Arr, 0, 1, 3)
if d == 0:
if p == 0 and r == 0 and (q == 0):
return [1]
else:
return [0]
return [int(p // d), int(q // d), int(r // d)]
``` | vfc_138124 | {
"difficulty": "medium_hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/create-your-own-calculator4308/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "Arr = {{5, 4, 2, 0},\r\n {1, 4, 2, 0},\r\n {4, 2, 9, 0}}",
"output": "{0, 0, 0}",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "Arr = {{4.2, 6, 7, 10},\r\n {1, 2, 3, 12},\r\n {3, 2, 2, 20}}",
"output": "{3, 4, -1}",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/CLOST | Solve the following coding problem using the programming language python:
Read problems statements in Mandarin Chinese , Russian and Vietnamese
Churu is taking the course called “Introduction to Data Structures”. Yesterday, he learned how to use a stack to check is a given parentheses expression is balanced or not. He finds it intriguing, and more importantly, he was given an assignment. The professor gave him a string S containing characters “(” and “)”, and asked him numerous queries of the form (x, y), i.e., if the substring S[x, y] represents a balanced parentheses expression or not. Here, S[x, y] refers to the substring of S from index x to y (both inclusive), assuming 0-based indexing. Diligently working through his assignment, our ace student Churu finds that all the queries given by the professor represented balanced substrings. Later, Churu lost his original string but he has all the queries.
Churu wants to restore his original string. As there can be many valid strings, print any one among them.
------ Input ------
First line of input contains an integer T denoting the number of test cases.
First line of each of test case contains two space-separated integers: N, K representing the length of the string and number of queries asked by professor, respectively.
Each of the next K lines contains a space-separated pair of integers: x and y, denoting a query.
------ Output ------
Print T lines, with the i^{th} one containing the solution string for the i^{th} test case.
------ Constraints ------
Subtask #1: 20 points
$1 ≤ T ≤ 5, 2 ≤ N ≤ 16, 1 ≤ K ≤ 20, x ≤ y$
Subtask #2: 80 points
$1 ≤ T ≤ 5, 2 ≤ N ≤ 2000, 1 ≤ K ≤ 30, x ≤ y$
----- Sample Input 1 ------
2
4 1
0 3
4 2
0 3
1 2
----- Sample Output 1 ------
()()
(())
----- explanation 1 ------
For the first sample case, "(())" are "()()" are two possible outputs. Printing anyone will do.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for _ in range(int(input())):
(n, k) = map(int, input().split())
ans = '00' * (n // 2) + '0' * (n % 2)
ans = list(ans)
qry = []
for i in range(k):
(x, y) = map(int, input().split())
qry.append([x, y])
qry.sort(key=lambda x: x[1] - x[0])
for i in range(k):
x = qry[i][0]
y = qry[i][1]
mauka = 0
for i in range(x, y + 1):
if mauka == 0 and ans[i] == '0':
ans[i] = '('
elif mauka == 1 and ans[i] == '0':
ans[i] = ')'
mauka = 1 - mauka
for i in range(n):
if ans[i] == '0' and i % 2:
ans[i] = ')'
elif ans[i] == '0' and i % 2 == 0:
ans[i] = '('
print(*ans, sep='')
``` | vfc_138125 | {
"difficulty": "hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/CLOST",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n4 1\n0 3\n4 2\n0 3\n1 2",
"output": "()()\n(())",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/REIGN | Solve the following coding problem using the programming language python:
Read problems statements in Mandarin Chinese and Russian.
The Baratheons have been ruling in the Seven Kingdoms for many years. They have seen a lot: prosperity and hunger, tranquility and rebellions, live and death. But nevertheless, they still hold the throne.
King Joffrey Baratheon's reign is running now. As a wise man, he honors the history of his family. So, he commanded to build up two monuments, that will remind about some historical periods of the Baratheons.
Formally, the Baratheons have been ruling for N years. Every year is described by an integer A_{i}, the level of prosperity in i-th year. If i-th year was a great year, then A_{i} might be a positive integer. Otherwise, if i-th year was a horrible year, then A_{i} might be a negative integer.
Each historical period can be described as two integers S and F, the start and the finish of the period respectively. Of course, S is not greater than F for each period, that we consider in this task.
You are to pick two historical periods, but there are some rules:
Two periods shouldn't have common years. I.e. a period [1, 5] has no common years with a period [6, 7];
The first period should start earlier than the second one. I.e. a period [1, 5] starts earlier than [6, 7];
Two periods shouldn't be too close to each other. There must be at least K years between the finish of the first period and the start of the second period. I.e. periods [1, 5] and [10, 10] can be chosen in case K equals to 4, while they can't in case K equals to 5.
The sum of the levels of prosperity in chosen years should be as big as possible.
Afterwards, you should report the sum of the levels of prosperity in chosen years to your King. Make everything right, otherwise King Joffrey won't be merciful!
------ Input ------
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains two integers N and K denoting the length of the Baratheons' reign and the minimal amount of years between two chosen periods.
The second line contains N space-separated integers A_{1}, A_{2}, ..., A_{N} denoting the levels of prosperity in corresponding years.
------ Output ------
For each test case, output a single line containing the required integer.
------ Constraints ------
$1 ≤ T ≤ 5;$
$2 ≤ N ≤ 10^{5};$
$0 ≤ K ≤ 10^{5};$
$-10^{9} ≤ A_{i} ≤ 10^{9} for every 1 ≤ i ≤ N;$
$K + 2 ≤ N$
----- Sample Input 1 ------
3
5 3
-1 1 2 3 -1
8 3
5 5 -1 -2 3 -1 2 -2
6 0
5 -1 5 0 -1 9
----- Sample Output 1 ------
-2
12
18
----- explanation 1 ------
There are T = 3 test cases the input.
The first test case: N equals to 5, K equals to 3, A[] equals to {-1, 1, 2, 3, -1}. There is the only option: we have to choose [1, 1] and [5, 5] periods.
The second test case: N equals to 8, K equals to 3, A[] equals to {5, 5, -1, -2, 3, -1, 2, -2}. It is optimal to choose [1, 2] and [7, 7] periods. That is the only optimal choice that you can make.
The second test case: N equals to 6, K equals to 0, A[] equals to {5, -1, 5, 0, -1, 9}. It is optimal to choose [1, 3] and [6, 6] periods. But that is not the only optimal choice that you can make.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def reign(arr, K):
subarr1 = kadanesmax(arr)
arr.reverse()
subarr2 = kadanesmax(arr)
subarr2.reverse()
prosperity = arr[0] + arr[-1]
for i in range(len(arr) - K - 1):
year = subarr2[i + (K + 1)] + subarr1[i]
prosperity = max(prosperity, year)
return prosperity
def kadanesmax(arr):
maxend = arr[0]
maxupto = arr[0]
lmax = [arr[0]]
for i in range(1, len(arr)):
if maxend < 0:
maxend = arr[i]
else:
maxend += arr[i]
maxupto = max(maxupto, maxend)
lmax.append(maxupto)
return lmax
T = int(input())
for t in range(T):
constraint = input()
(N, K) = [int(x) for x in constraint.split()]
line = input()
years = [int(x) for x in line.split()]
print(reign(years, K))
``` | vfc_138133 | {
"difficulty": "medium_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/REIGN",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n5 3\n-1 1 2 3 -1\n8 3\n5 5 -1 -2 3 -1 2 -2\n6 0\n5 -1 5 0 -1 9",
"output": "-2\n12\n18",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
Example
Input
crc
1
Output
crc
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from heapq import heappush, heappop
def solve():
S = input()
K = int(input())
L = len(S)
INF = 10 ** 9
cost = [[INF] * (L + 1) for i in range(L + 1)]
cost[0][L] = 0
ss = []
que = [(0, 0, L)]
while que:
(d, a, b) = heappop(que)
if cost[a][b] < d:
continue
ss.append((a, b))
if a + 1 == b:
if d + 1 < cost[a + 1][b]:
cost[a + 1][b] = d + 1
continue
if S[a] == S[b - 1]:
if d + 2 < cost[a + 1][b - 1]:
cost[a + 1][b - 1] = d + 2
if a + 1 < b - 1:
heappush(que, (d + 2, a + 1, b - 1))
else:
if d + 2 < cost[a + 1][b]:
cost[a + 1][b] = d + 2
if a + 1 < b:
heappush(que, (d + 2, a + 1, b))
if d + 2 < cost[a][b - 1]:
cost[a][b - 1] = d + 2
if a < b - 1:
heappush(que, (d + 2, a, b - 1))
ln = min((cost[i][i] for i in range(L + 1)))
ss.reverse()
dp = [[0] * (L + 1) for i in range(L + 1)]
for i in range(L + 1):
if cost[i][i] == ln:
dp[i][i] = 1
for (a, b) in ss:
d = cost[a][b]
r = 0
if a + 1 == b:
if d + 1 == cost[a + 1][b]:
r = dp[a + 1][b]
elif S[a] == S[b - 1]:
if d + 2 == cost[a + 1][b - 1]:
r = dp[a + 1][b - 1]
else:
if d + 2 == cost[a + 1][b]:
r += dp[a + 1][b]
if d + 2 == cost[a][b - 1]:
r += dp[a][b - 1]
dp[a][b] = r
if dp[a][b] < K:
print('NONE')
return True
SL = []
SR = []
a = 0
b = L
while a < b:
if a + 1 == b:
assert cost[a][b] + 1 == cost[a + 1][b]
SL.append(S[a])
a += 1
continue
if S[a] == S[b - 1]:
assert cost[a][b] + 2 == cost[a + 1][b - 1]
SL.append(S[a])
SR.append(S[b - 1])
a += 1
b -= 1
elif S[a] < S[b - 1]:
c = cost[a][b] + 2 == cost[a + 1][b]
if c and K <= dp[a + 1][b]:
SL.append(S[a])
SR.append(S[a])
a += 1
else:
if c:
K -= dp[a + 1][b]
SL.append(S[b - 1])
SR.append(S[b - 1])
b -= 1
else:
c = cost[a][b] + 2 == cost[a][b - 1]
if c and K <= dp[a][b - 1]:
SL.append(S[b - 1])
SR.append(S[b - 1])
b -= 1
else:
if c:
K -= dp[a][b - 1]
SL.append(S[a])
SR.append(S[a])
a += 1
SR.reverse()
SL.extend(SR)
print(''.join(SL))
solve()
``` | vfc_138137 | {
"difficulty": "unknown_difficulty",
"memory_limit": "268.435456 megabytes",
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "3.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "crb\n1",
"output": "bcrcb\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://www.codechef.com/problems/MNMX | Solve the following coding problem using the programming language python:
Chef loves to play with arrays by himself. Today, he has an array A consisting of N distinct integers. He wants to perform the following operation on his array A.
- Select a pair of adjacent integers and remove the larger one of these two. This decreases the array size by 1. Cost of this operation will be equal to the smaller of them.
Find out minimum sum of costs of operations needed to convert the array into a single element.
-----Input-----
First line of input contains a single integer T denoting the number of test cases. First line of each test case starts with an integer N denoting the size of the array A. Next line of input contains N space separated integers, where the ith integer denotes the value Ai.
-----Output-----
For each test case, print the minimum cost required for the transformation.
-----Constraints-----
- 1 ≤ T ≤ 10
- 2 ≤ N ≤ 50000
- 1 ≤ Ai ≤ 105
-----Subtasks-----
- Subtask 1 : 2 ≤ N ≤ 15 : 35 pts
- Subtask 2 : 2 ≤ N ≤ 100 : 25 pts
- Subtask 3 : 2 ≤ N ≤ 50000 : 40 pts
-----Example-----
Input
2
2
3 4
3
4 2 5
Output
3
4
-----Explanation-----Test 1 : Chef will make only 1 move: pick up both the elements (that is, 3 and 4), remove the larger one (4), incurring a cost equal to the smaller one (3).
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for _ in range(int(input())):
n = int(input())
list_a = list(map(int, input().split()))
if n == 2:
print(min(list_a))
else:
print(min(list_a) * (n - 1))
``` | vfc_138141 | {
"difficulty": "easy",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/MNMX",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n2\n3 4\n3\n4 2 5\n",
"output": "3\n4\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n2\n3 4\n3\n4 2 9",
"output": "3\n4\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n2\n3 4\n3\n0 2 5",
"output": "3\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n2\n0 4\n3\n4 0 9",
"output": "0\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n2\n0 4\n3\n7 2 9",
"output": "0\n4\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/249/B | Solve the following coding problem using the programming language python:
For he knew every Who down in Whoville beneath, Was busy now, hanging a mistletoe wreath. "And they're hanging their stockings!" he snarled with a sneer, "Tomorrow is Christmas! It's practically here!"
Dr. Suess, How The Grinch Stole Christmas
Christmas celebrations are coming to Whoville. Cindy Lou Who and her parents Lou Lou Who and Betty Lou Who decided to give sweets to all people in their street. They decided to give the residents of each house on the street, one kilogram of sweets. So they need as many kilos of sweets as there are homes on their street.
The street, where the Lou Who family lives can be represented as n consecutive sections of equal length. You can go from any section to a neighbouring one in one unit of time. Each of the sections is one of three types: an empty piece of land, a house or a shop. Cindy Lou and her family can buy sweets in a shop, but no more than one kilogram of sweets in one shop (the vendors care about the residents of Whoville not to overeat on sweets).
After the Lou Who family leave their home, they will be on the first section of the road. To get to this section of the road, they also require one unit of time. We can assume that Cindy and her mom and dad can carry an unlimited number of kilograms of sweets. Every time they are on a house section, they can give a kilogram of sweets to the inhabitants of the house, or they can simply move to another section. If the family have already given sweets to the residents of a house, they can't do it again. Similarly, if they are on the shop section, they can either buy a kilo of sweets in it or skip this shop. If they've bought a kilo of sweets in a shop, the seller of the shop remembered them and the won't sell them a single candy if they come again. The time to buy and give sweets can be neglected. The Lou Whos do not want the people of any house to remain without food.
The Lou Whos want to spend no more than t time units of time to give out sweets, as they really want to have enough time to prepare for the Christmas celebration. In order to have time to give all the sweets, they may have to initially bring additional k kilos of sweets.
Cindy Lou wants to know the minimum number of k kilos of sweets they need to take with them, to have time to give sweets to the residents of each house in their street.
Your task is to write a program that will determine the minimum possible value of k.
Input
The first line of the input contains two space-separated integers n and t (2 ≤ n ≤ 5·105, 1 ≤ t ≤ 109). The second line of the input contains n characters, the i-th of them equals "H" (if the i-th segment contains a house), "S" (if the i-th segment contains a shop) or "." (if the i-th segment doesn't contain a house or a shop).
It is guaranteed that there is at least one segment with a house.
Output
If there isn't a single value of k that makes it possible to give sweets to everybody in at most t units of time, print in a single line "-1" (without the quotes). Otherwise, print on a single line the minimum possible value of k.
Examples
Input
6 6
HSHSHS
Output
1
Input
14 100
...HHHSSS...SH
Output
0
Input
23 50
HHSS.......SSHHHHHHHHHH
Output
8
Note
In the first example, there are as many stores, as houses. If the family do not take a single kilo of sweets from home, in order to treat the inhabitants of the first house, they will need to make at least one step back, and they have absolutely no time for it. If they take one kilogram of sweets, they won't need to go back.
In the second example, the number of shops is equal to the number of houses and plenty of time. Available at all stores passing out candy in one direction and give them when passing in the opposite direction.
In the third example, the shops on the street are fewer than houses. The Lou Whos have to take the missing number of kilograms of sweets with them from home.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
def check(n, casas):
global T, N, street
current = n
time = T
need = 0
last_house = 0
for (ind, i) in enumerate(street):
time -= 1
if i == 'S':
current += 1
elif i == 'H':
need += 1
if need == 1:
last_house = ind
if need > 0 and current >= need:
current -= need
casas -= need
need = 0
if casas > 0:
if (ind - last_house) * 2 >= N - last_house - 1:
time -= N - last_house - 1 + N - ind - 1
return time >= 0
time -= (ind - last_house) * 2
else:
time -= ind - last_house
if casas == 0:
break
return time >= 0 and casas == 0
(N, T) = [int(i) for i in input().split()]
street = input().rstrip('.')
N = len(street)
C = street.count('H')
S = street.count('S')
l = max(C - S, 0)
r = 500005
while l < r:
mid = (l + r) // 2
if check(mid, C):
r = mid
else:
l = mid + 1
print(l if l < 500005 else -1)
``` | vfc_138145 | {
"difficulty": "hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/249/B",
"time_limit": "2.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "336 400\nHSSHHSSHHS..S..SS..H.S.H..SSH.H.H.H.S.H.S.S.H.S..SS..H.SS.H.SS.SS..SS.H...H.H.H.HSS..H...SS..SS.H..H.S.S....S.H.SS..HS..S.S.S.H.H.S..S.H.SS.SS..SS.SS.HS.SS.HSSSSHSSSSSS.H.SS..HHH.H.H.S..H.SS.S.H..SS.HS.SS.S.H.H.H..H.SS.HS.HHHSS.SS.S.SSS.S.S.SS.HS.H.S.SS.H.SS.H.S.SS.HS.SS..SS.H.S.H.SSH.HSSS.SS..SS.SS.HS.H.S.SS.SS..SS.HHHS.H.SS.SS.SS.SS\n",
"output": "0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "8 8\nHH.SSSS.\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "66 3\nHS................................................................\n",
"output": "0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "37 37\n..H..S..H..S..SSHHHHHSSSSSSSSSSSSS...\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "66 1\nHS................................................................\n",
"output": "1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/618/D | Solve the following coding problem using the programming language python:
A group of n cities is connected by a network of roads. There is an undirected road between every pair of cities, so there are $\frac{n \cdot(n - 1)}{2}$ roads in total. It takes exactly y seconds to traverse any single road.
A spanning tree is a set of roads containing exactly n - 1 roads such that it's possible to travel between any two cities using only these roads.
Some spanning tree of the initial network was chosen. For every road in this tree the time one needs to traverse this road was changed from y to x seconds. Note that it's not guaranteed that x is smaller than y.
You would like to travel through all the cities using the shortest path possible. Given n, x, y and a description of the spanning tree that was chosen, find the cost of the shortest path that starts in any city, ends in any city and visits all cities exactly once.
-----Input-----
The first line of the input contains three integers n, x and y (2 ≤ n ≤ 200 000, 1 ≤ x, y ≤ 10^9).
Each of the next n - 1 lines contains a description of a road in the spanning tree. The i-th of these lines contains two integers u_{i} and v_{i} (1 ≤ u_{i}, v_{i} ≤ n) — indices of the cities connected by the i-th road. It is guaranteed that these roads form a spanning tree.
-----Output-----
Print a single integer — the minimum number of seconds one needs to spend in order to visit all the cities exactly once.
-----Examples-----
Input
5 2 3
1 2
1 3
3 4
5 3
Output
9
Input
5 3 2
1 2
1 3
3 4
5 3
Output
8
-----Note-----
In the first sample, roads of the spanning tree have cost 2, while other roads have cost 3. One example of an optimal path is $5 \rightarrow 3 \rightarrow 4 \rightarrow 1 \rightarrow 2$.
In the second sample, we have the same spanning tree, but roads in the spanning tree cost 3, while other roads cost 2. One example of an optimal path is $1 \rightarrow 4 \rightarrow 5 \rightarrow 2 \rightarrow 3$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from collections import defaultdict
from collections import deque
from functools import reduce
(n, x, y) = [int(x) for x in input().split()]
E = defaultdict(set)
for i in range(n - 1):
(u, v) = [int(x) for x in input().split()]
E[u].add(v)
E[v].add(u)
if x > y:
for v in E:
if len(E[v]) == n - 1:
print((n - 2) * y + x)
break
elif len(E[v]) > 1:
print((n - 1) * y)
break
else:
visited = {v: False for v in E}
stack = [1]
topsorted = deque()
while stack:
v = stack.pop()
if visited[v]:
continue
visited[v] = True
topsorted.appendleft(v)
stack.extend(E[v])
chopped = set()
ans = 0
for v in topsorted:
ans += max(0, len(E[v]) - 2)
if len(E[v]) > 2:
S = E[v].intersection(chopped)
S1 = {S.pop(), S.pop()}
for u in E[v]:
if not u in S1:
E[u].remove(v)
E[v].clear()
E[v].update(S1)
chopped.add(v)
print(ans * y + (n - 1 - ans) * x)
``` | vfc_138149 | {
"difficulty": "hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/618/D",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5 2 3\n1 2\n1 3\n3 4\n5 3\n",
"output": "9\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5 3 2\n1 2\n1 3\n3 4\n5 3\n",
"output": "8\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "50 23129 410924\n18 28\n17 23\n21 15\n18 50\n50 11\n32 3\n44 41\n50 31\n50 34\n5 14\n36 13\n22 40\n20 9\n9 43\n19 47\n48 40\n20 22\n33 45\n35 22\n33 24\n9 6\n13 1\n13 24\n49 20\n1 20\n29 38\n10 35\n25 23\n49 30\n42 8\n20 18\n32 15\n32 1\n27 10\n20 47\n41 7\n20 14\n18 26\n4 20\n20 2\n46 37\n41 16\n46 41\n12 20\n8 40\n18 37\n29 3\n32 39\n23 37\n",
"output": "8113631\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2 3 4\n1 2\n",
"output": "3\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1520/G | Solve the following coding problem using the programming language python:
Dima overslept the alarm clock, which was supposed to raise him to school.
Dima wonders if he will have time to come to the first lesson. To do this, he needs to know the minimum time it will take him to get from home to school.
The city where Dima lives is a rectangular field of n × m size. Each cell (i, j) on this field is denoted by one number a_{ij}:
* The number -1 means that the passage through the cell is prohibited;
* The number 0 means that the cell is free and Dima can walk though it.
* The number x (1 ≤ x ≤ 10^9) means that the cell contains a portal with a cost of x. A cell with a portal is also considered free.
From any portal, Dima can go to any other portal, while the time of moving from the portal (i, j) to the portal (x, y) corresponds to the sum of their costs a_{ij} + a_{xy}.
In addition to moving between portals, Dima can also move between unoccupied cells adjacent to one side in time w. In particular, he can enter a cell with a portal and not use it.
Initially, Dima is in the upper-left cell (1, 1), and the school is in the lower right cell (n, m).
Input
The first line contains three integers n, m and w (2 ≤ n, m ≤ 2 ⋅ 10^3, 1 ≤ w ≤ 10^9), where n and m are city size, w is time during which Dima moves between unoccupied cells.
The next n lines each contain m numbers (-1 ≤ a_{ij} ≤ 10^9) — descriptions of cells.
It is guaranteed that the cells (1, 1) and (n, m) are free.
Output
Output the minimum time it will take for Dima to get to school. If he cannot get to school at all, then output "-1".
Example
Input
5 5 1
0 -1 0 1 -1
0 20 0 0 -1
-1 -1 -1 -1 -1
3 0 0 0 0
-1 0 0 0 0
Output
14
Note
Explanation for the first sample:
<image>
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import io
import os
from collections import deque
from math import inf
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
M9 = 10 ** 9 + 7
(yes, no) = ('YES', 'NO')
d4 = [(1, 0), (0, 1), (-1, 0), (0, -1)]
MAXINT = inf
def solve_(mrr, w, nrows, ncols):
size = nrows * ncols
def dfs(source, size):
stack = deque([source])
dist = [MAXINT] * size
dist[source] = 0
while stack:
loc = stack.popleft()
(x, y) = divmod(loc, ncols)
for (dx, dy) in d4:
xx = x + dx
yy = y + dy
new_loc = xx * ncols + yy
if 0 <= xx < nrows and 0 <= yy < ncols and (dist[new_loc] == MAXINT) and (mrr[new_loc] >= 0):
dist[new_loc] = dist[loc] + 1
stack.append(new_loc)
return dist
dist_from_start = dfs(0, size)
dist_from_dest = dfs(size - 1, size)
tele_from_start = inf
tele_from_dest = inf
for x in range(nrows):
for y in range(ncols):
loc = x * ncols + y
if mrr[loc] > 0:
tele_from_start = min(tele_from_start, mrr[loc] + w * dist_from_start[loc])
tele_from_dest = min(tele_from_dest, mrr[loc] + w * dist_from_dest[loc])
minres = min(dist_from_start[size - 1] * w, tele_from_start + tele_from_dest)
if minres == inf:
return -1
return minres
for case_num in [0]:
(n, m, w) = list(map(int, input().split()))
w = float(w)
mrr = [float(x) for i in range(n) for x in input().split()]
res = solve_(mrr, w, n, m)
print(int(res))
``` | vfc_138153 | {
"difficulty": "hard",
"memory_limit": "512.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1520/G",
"time_limit": "3.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2 3 1000000000\n0 0 0\n0 0 0\n",
"output": "3000000000",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "10 5 2\n0 3 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n-1 0 0 0 0\n0 0 0 6 0\n0 0 0 0 8\n0 0 5 6 0\n0 0 0 5 -1\n0 0 0 0 10\n0 0 0 0 0\n",
"output": "16",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "10 2 2\n0 -1\n0 10\n8 4\n0 0\n0 0\n-1 0\n0 0\n0 0\n0 0\n4 0\n",
"output": "16",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/BREAKBAL | Solve the following coding problem using the programming language python:
JJ found a balanced parenthesis sequence. He does not like balanced parentheses so he will make the parenthesis sequence unbalanced by swapping adjacent characters in the sequence.
JJ is lazy and wants to know minimum number of adjacent swaps required to make the given balanced parenthesis sequence unbalanced.
A parenthesis sequence is called balanced if one can turn it into a valid mathematical expression by adding characters + and 1. Sequences such as (())() and ()() are balanced whereas sequences such as ())( and )() are unbalanced.
------ Input Format ------
- The first line contains T - the number of test cases. Then the test cases follow.
- The first line of each test case contains S - a balanced parenthesis sequence.
------ Output Format ------
For each test case, output the minimum number of adjacent swaps required to make the parenthesis sequence unbalanced.
------ Constraints ------
$1 ≤ T ≤ 5\cdot10^{4}$
$2 ≤ |S| ≤ 10^{5}$
- Sum of $S$ does not exceeds $10^{6}$ over all test cases
$S$ is a balanced parentheses sequence
----- Sample Input 1 ------
4
()
(())
()()
((()))(())
----- Sample Output 1 ------
1
2
1
2
----- explanation 1 ------
- Test case $1$: Swap the first and second character to get the unbalanced sequence )(.
- Test case $2$: Swap the second and third character first to obtain the bracket sequence ()(). Now you can swap the first and second character to obtain the sequence )(() which is unbalanced.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from sys import stdin
input = stdin.readline
def answer():
ans = float('inf')
(o, c, ind) = (0, 0, 0)
for i in range(n):
req = o - c + 1
while dist[-1] < i + 1:
dist.pop()
ind += 1
if n // 2 - ind < req:
break
cal = prefix[ind + req] - prefix[ind] - req * i - req * (req + 1) // 2
ans = min(ans, cal)
if a[i] == '(':
o += 1
else:
c += 1
return ans
for T in range(int(input())):
a = input().strip()
n = len(a)
dist = []
for i in range(n):
if a[i] == ')':
dist.append(i + 1)
prefix = [0]
for i in range(len(dist)):
prefix.append(prefix[-1] + dist[i])
dist = dist[::-1]
print(answer())
``` | vfc_138157 | {
"difficulty": "very_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/BREAKBAL",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "4\n()\n(())\n()()\n((()))(())\n",
"output": "1\n2\n1\n2\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1354/D | Solve the following coding problem using the programming language python:
Note that the memory limit is unusual.
You are given a multiset consisting of n integers. You have to process queries of two types:
* add integer k into the multiset;
* find the k-th order statistics in the multiset and remove it.
k-th order statistics in the multiset is the k-th element in the sorted list of all elements of the multiset. For example, if the multiset contains elements 1, 4, 2, 1, 4, 5, 7, and k = 3, then you have to find the 3-rd element in [1, 1, 2, 4, 4, 5, 7], which is 2. If you try to delete an element which occurs multiple times in the multiset, only one occurence is removed.
After processing all queries, print any number belonging to the multiset, or say that it is empty.
Input
The first line contains two integers n and q (1 ≤ n, q ≤ 10^6) — the number of elements in the initial multiset and the number of queries, respectively.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_1 ≤ a_2 ≤ ... ≤ a_n ≤ n) — the elements of the multiset.
The third line contains q integers k_1, k_2, ..., k_q, each representing a query:
* if 1 ≤ k_i ≤ n, then the i-th query is "insert k_i into the multiset";
* if k_i < 0, then the i-th query is "remove the |k_i|-th order statistics from the multiset". For this query, it is guaranteed that |k_i| is not greater than the size of the multiset.
Output
If the multiset is empty after all queries, print 0.
Otherwise, print any integer that belongs to the resulting multiset.
Examples
Input
5 5
1 2 3 4 5
-1 -1 -1 -1 -1
Output
0
Input
5 4
1 2 3 4 5
-5 -1 -3 -1
Output
3
Input
6 2
1 1 1 2 3 4
5 6
Output
6
Note
In the first example, all elements of the multiset are deleted.
In the second example, the elements 5, 1, 4, 2 are deleted (they are listed in chronological order of their removal).
In the third example, 6 is not the only answer.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from collections import Counter
from collections import defaultdict
from collections import deque
import math
import os
import sys
input = sys.stdin.readline
ii = 0
_inp = b''
def getchar():
global ii, _inp
if ii >= len(_inp):
_inp = os.read(0, 4000)
ii = 0
if not _inp:
return b' '[0]
ii += 1
return _inp[ii - 1]
def input():
c = getchar()
if c == b'-'[0]:
x = 0
sign = 1
else:
x = c - b'0'[0]
sign = 0
c = getchar()
while c >= b'0'[0]:
x = 10 * x + c - b'0'[0]
c = getchar()
if c == b'\r'[0]:
getchar()
return -x if sign else x
import bisect
def find(k):
curr = 0
ans = 0
prevsum = 0
for i in range(19, -1, -1):
if curr + (1 << i) < n and fen[curr + (1 << i)] + prevsum < k:
ans = curr + (1 << i)
curr = ans
prevsum += fen[curr]
return ans + 1
def update(i, add):
while i < n:
fen[i] = fen[i] + add
i = i + (i & -i)
def sum(i):
s = 0
while i > 0:
s = s + fen[i]
i = i - (i & -i)
return s
def range_sum(i, j):
return sum(r) - sum(l - 1)
n = input()
q = input()
n = n + 1
fen = [0] * n
for i in range(n - 1):
update(input(), 1)
for i in range(q):
x = input()
if x > 0:
update(x, 1)
else:
x = x * -1
num = find(x)
update(num, -1)
ans = sum(n - 1)
if ans == 0:
os.write(1, b'0')
else:
for i in range(1, n):
if sum(i) > 0:
os.write(1, str(i).encode('ascii'))
break
``` | vfc_138161 | {
"difficulty": "hard",
"memory_limit": "28.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1354/D",
"time_limit": "1.5 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5 8\n1 1 1 1 1\n2 3 4 -1 -1 -1 -1 -1\n",
"output": "2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "6 2\n1 1 1 2 3 4\n5 6\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2 2\n1 2\n1 -1\n",
"output": "1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1292/F | Solve the following coding problem using the programming language python:
SIHanatsuka - EMber SIHanatsuka - ATONEMENT
Back in time, the seven-year-old Nora used to play lots of games with her creation ROBO_Head-02, both to have fun and enhance his abilities.
One day, Nora's adoptive father, Phoenix Wyle, brought Nora $n$ boxes of toys. Before unpacking, Nora decided to make a fun game for ROBO.
She labelled all $n$ boxes with $n$ distinct integers $a_1, a_2, \ldots, a_n$ and asked ROBO to do the following action several (possibly zero) times:
Pick three distinct indices $i$, $j$ and $k$, such that $a_i \mid a_j$ and $a_i \mid a_k$. In other words, $a_i$ divides both $a_j$ and $a_k$, that is $a_j \bmod a_i = 0$, $a_k \bmod a_i = 0$. After choosing, Nora will give the $k$-th box to ROBO, and he will place it on top of the box pile at his side. Initially, the pile is empty. After doing so, the box $k$ becomes unavailable for any further actions.
Being amused after nine different tries of the game, Nora asked ROBO to calculate the number of possible different piles having the largest amount of boxes in them. Two piles are considered different if there exists a position where those two piles have different boxes.
Since ROBO was still in his infant stages, and Nora was still too young to concentrate for a long time, both fell asleep before finding the final answer. Can you help them?
As the number of such piles can be very large, you should print the answer modulo $10^9 + 7$.
-----Input-----
The first line contains an integer $n$ ($3 \le n \le 60$), denoting the number of boxes.
The second line contains $n$ distinct integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 60$), where $a_i$ is the label of the $i$-th box.
-----Output-----
Print the number of distinct piles having the maximum number of boxes that ROBO_Head can have, modulo $10^9 + 7$.
-----Examples-----
Input
3
2 6 8
Output
2
Input
5
2 3 4 9 12
Output
4
Input
4
5 7 2 9
Output
1
-----Note-----
Let's illustrate the box pile as a sequence $b$, with the pile's bottommost box being at the leftmost position.
In the first example, there are $2$ distinct piles possible: $b = [6]$ ($[2, \mathbf{6}, 8] \xrightarrow{(1, 3, 2)} [2, 8]$) $b = [8]$ ($[2, 6, \mathbf{8}] \xrightarrow{(1, 2, 3)} [2, 6]$)
In the second example, there are $4$ distinct piles possible: $b = [9, 12]$ ($[2, 3, 4, \mathbf{9}, 12] \xrightarrow{(2, 5, 4)} [2, 3, 4, \mathbf{12}] \xrightarrow{(1, 3, 4)} [2, 3, 4]$) $b = [4, 12]$ ($[2, 3, \mathbf{4}, 9, 12] \xrightarrow{(1, 5, 3)} [2, 3, 9, \mathbf{12}] \xrightarrow{(2, 3, 4)} [2, 3, 9]$) $b = [4, 9]$ ($[2, 3, \mathbf{4}, 9, 12] \xrightarrow{(1, 5, 3)} [2, 3, \mathbf{9}, 12] \xrightarrow{(2, 4, 3)} [2, 3, 12]$) $b = [9, 4]$ ($[2, 3, 4, \mathbf{9}, 12] \xrightarrow{(2, 5, 4)} [2, 3, \mathbf{4}, 12] \xrightarrow{(1, 4, 3)} [2, 3, 12]$)
In the third sequence, ROBO can do nothing at all. Therefore, there is only $1$ valid pile, and that pile is empty.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
MOD = 1000000007
def isSubset(a, b):
return a & b == a
def isIntersect(a, b):
return a & b != 0
def cntOrder(s, t):
p = len(s)
m = len(t)
inMask = [0 for i in range(m)]
for x in range(p):
for i in range(m):
if t[i] % s[x] == 0:
inMask[i] |= 1 << x
cnt = [0 for mask in range(1 << p)]
for mask in range(1 << p):
for i in range(m):
if isSubset(inMask[i], mask):
cnt[mask] += 1
dp = [[0 for mask in range(1 << p)] for k in range(m + 1)]
for i in range(m):
dp[1][inMask[i]] += 1
for k in range(m):
for mask in range(1 << p):
for i in range(m):
if not isSubset(inMask[i], mask) and isIntersect(inMask[i], mask):
dp[k + 1][mask | inMask[i]] = (dp[k + 1][mask | inMask[i]] + dp[k][mask]) % MOD
dp[k + 1][mask] = (dp[k + 1][mask] + dp[k][mask] * (cnt[mask] - k)) % MOD
return dp[m][(1 << p) - 1]
def dfs(u):
global a, graph, degIn, visited, s, t
visited[u] = True
if degIn[u] == 0:
s.append(a[u])
else:
t.append(a[u])
for v in graph[u]:
if not visited[v]:
dfs(v)
def main():
global a, graph, degIn, visited, s, t
n = int(input())
a = list(map(int, input().split()))
c = [[0 for j in range(n)] for i in range(n)]
for i in range(n):
c[i][0] = 1
for j in range(1, i + 1):
c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % MOD
degIn = [0 for u in range(n)]
graph = [[] for u in range(n)]
for u in range(n):
for v in range(n):
if u != v and a[v] % a[u] == 0:
graph[u].append(v)
graph[v].append(u)
degIn[v] += 1
ans = 1
curLen = 0
visited = [False for u in range(n)]
for u in range(n):
if not visited[u]:
s = []
t = []
dfs(u)
if len(t) > 0:
sz = len(t) - 1
cnt = cntOrder(s, t)
ans = ans * cnt % MOD
ans = ans * c[curLen + sz][sz] % MOD
curLen += sz
print(ans)
main()
``` | vfc_138169 | {
"difficulty": "hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1292/F",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n2 6 8\n",
"output": "2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5\n2 3 4 9 12\n",
"output": "4\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n5 7 2 9\n",
"output": "1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
Given integer n, find length of n! (which is factorial of n) excluding trailing zeros.
Input
The first line of the standard input contains one integer t (t<10001) which is the number of test cases.
In each of the next t lines there is number n (0 ≤ n ≤ 5*10^9).
Output
For each test, print the length of n! (which is factorial of n).
Constraints
1 ≤ t ≤ 10
1 ≤ n ≤ 10^9
SAMPLE INPUT
3
5
7
10
SAMPLE OUTPUT
2
3
5
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from math import *
def Trailing_Zeroes(x):
fives = 0
i = 1
while 5**i <= x:
fives+=x/(5**i)
i+=1
return fives
t = int(input())
while t:
t-=1
n = int(input())
a = 0
#for i in xrange(1,n+1):
# a+=log(i)
print(int(ceil(lgamma(n+1)/log(10))) - Trailing_Zeroes(n))
``` | vfc_138173 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "4\n105\n78\n123\n79",
"output": "143\n378\n1426\n33149\n331869\n180622",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "6\n104\n224\n665\n9996\n78787\n45457",
"output": "144\n98\n178\n99",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n4568\n4545992\n9265642\n4592886",
"output": "13598\n27154740\n58212156\n27455323",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://www.hackerrank.com/challenges/stonegame/problem | Solve the following coding problem using the programming language python:
Alice and Bob are playing the game of Nim with $n$ piles of stones with sizes $p_0,p_1,\ldots,p_{n-1}$. If Alice plays first, she loses if and only if the 'xor sum' (or 'Nim sum') of the piles is zero, i.e., $p_0\oplus p_1\oplus...\oplus p_{n-1}=0$.
Since Bob already knows who will win (assuming optimal play), he decides to cheat by removing some stones in some piles before the game starts. However, to reduce the risk of suspicion, he must keep at least one pile unchanged. Your task is to count the number of ways Bob can remove the stones to force Alice into losing the game. Since the number can be very large, output the number of ways modulo $10^9+7$. Assume that both players will try to optimize their strategy and try to win the game.
Input Format
The first line of the input contains an integer $n$ denoting the number of piles. The next line contains $n$ space-separated integers $p_0,p_1,\ldots,p_{n-1}$ indicating the sizes of the stone piles.
Constraints
$3\leq n\leq100$
$0<p[i]<10^9$
Output Format
Print a single integer denoting the number of ways Bob can force Alice to lose the game, modulo $10^9+7$.
Sample Input 0
3
1 2 3
Sample Output 0
4
Explanation 0
The answer is $4$. The four possible resulting lists of piles is:
$[0,2,2]$
$[1,0,1]$
$[1,1,0]$
$[1,2,3]$
Note that $[0,1,1]$ is not allowed since he must keep one pile unchanged.
Sample Input 1
10
10 10 1 1 1 1 1 10 10 10
Sample Output 1
321616
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import operator as op
import functools as ft
from sys import stderr
MOD = 1000000007
def readcase():
npiles = int(input())
piles = [int(fld) for fld in input().split()]
assert npiles == len(piles)
return piles
def numsolns(piles):
return (numunrestrictedsolns(piles) - numunrestrictedsolns([pile - 1 for pile in piles if pile > 1])) % MOD
def numunrestrictedsolns(piles, MOD=MOD):
if len(piles) == 0:
return 1
xorall = ft.reduce(op.xor, piles)
leftmost = ft.reduce(op.or_, piles).bit_length() - 1
rightmost = max(0, xorall.bit_length() - 1)
ans = 0
for first1 in range(rightmost, leftmost + 1):
premult = 1
matchbit = 1 << first1
for (i, bigalt) in enumerate(piles):
if bigalt & matchbit != 0:
even = 1
odd = 0
for pile in piles[i + 1:]:
neweven = (1 + (pile & ~-matchbit)) * even
newodd = (1 + (pile & ~-matchbit)) * odd
if pile & matchbit != 0:
neweven += matchbit * odd
newodd += matchbit * even
(even, odd) = (neweven % MOD, newodd % MOD)
ans += (even if xorall & matchbit != 0 else odd) * premult % MOD
premult = premult * ((bigalt & ~-matchbit) + 1) % MOD
if xorall == 0:
ans += 1
return ans % MOD
print(numsolns(readcase()))
``` | vfc_138178 | {
"difficulty": "medium_hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://www.hackerrank.com/challenges/stonegame/problem",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n1 2 3\n",
"output": "4\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/divisible-by-82732/1 | Solve the following coding problem using the programming language python:
Given a number S, you need to check whether any permutation of the number S divisible by 8 or not.
Example 1:
Input: S = "80"
Output: "Divisible"
Explanation: 80 is divisible by 8
Example 2
Input: S = "101"
Output: "Not divisible"
Your Task :
Complete the function isDivisible8() that receives a string S denoting the number and returns 1 if any permutation of the number is divisible by 8 or else returns 0.
Expected Time Complexity : O(lS|^{3})
Expected Space Complexity : O(1)
Constraints:
1 ≤ lS| ≤ 10^{2}
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def isDivisible8(self, S):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def isDivisible8(self, S):
if len(S) == 1:
return int(not int(S) % 8)
elif len(S) == 2:
a = S[0]
b = S[1]
if int(a + b) % 8 == 0 or int(b + a) % 8 == 0:
return 1
return 0
for i in range(len(S)):
for j in range(i + 1, len(S)):
for k in range(j + 1, len(S)):
a = S[i]
b = S[j]
c = S[k]
if int(a + b + c) % 8 == 0:
return 1
return 0
``` | vfc_138183 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/divisible-by-82732/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "S = \"80\"",
"output": "\"Divisible\"",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/COVAXIN | Solve the following coding problem using the programming language python:
Read problem statements in [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.
There are two types of vaccines available: Covaxin and Covishield.
A black marketeer has X coins and wants to buy as many vaccines as possible. Due to the black marketing concerns, government has enforced the following policy:
i^{th} dose of Covaxin costs a + (i - 1)\cdot b coins for every i ≥ 1.
i^{th} dose of Covishield costs c + (i - 1)\cdot d coins for every i ≥ 1.
The values of the four parameters a, b, c and d, however isn't constant and might vary from query to query. In general the value of these four parameters for i^{th} query will be A_{i}, B_{i}, C_{i} and D_{i} respectively.
Let ans_{i} be the maximum total quantity of vaccines the black marketeer can buy corresponding to the i^{th} query. For each query, you have to find the value of ans_{i}.
You will be given integers A_{1}, B_{1}, C_{1}, D_{1}, P, Q, R, S, T and M which will define the queries to be followed.
For i ≥ 1 and i ≤ I - 1:
A_{i+1} = (A_{i} + ans_{i}\cdot T) \bmod M + P
B_{i+1} = (B_{i} + ans_{i}\cdot T) \bmod M + Q
C_{i+1} = (C_{i} + ans_{i}\cdot T) \bmod M + R
D_{i+1} = (D_{i} + ans_{i}\cdot T) \bmod M + S .
Note: Since the output is large, prefer using fast input-output methods.
------ Input Format ------
- First line contains of input contains an integer I denoting the number of queries.
- Second line of input contains five integers X, A_{1}, B_{1}, C_{1}, D_{1}.
- Third line of input contains six integers P, Q, R, S, T, M.
------ Output Format ------
For each query output the maximum quantity of vaccines the black marketeer can buy.
------ Constraints ------
$1 ≤ I ≤ 5 \cdot 10^{5}$
$1 ≤ X,A_{1},B_{1},C_{1},D_{1} ≤ 10^{18}$
$1 ≤ P,Q,R,S,M ≤ 10^{18}$
$1 ≤ T ≤ 10^{9}$
------ subtasks ------
Subtask #1 (10 points):
$1 ≤ I ≤ 10^{3}$
$1 ≤ X ≤ 10^{9}$
Time limit: $1$ sec
Subtask #2 (30 points):
$1 ≤ I ≤ 10^{3}$
$1 ≤ X ≤ 10^{15}$
$10^{9} ≤ A_{1} ≤ 10^{18}$
$10^{9} ≤ B_{1} ≤ 10^{18}$
$10^{9} ≤ P ≤ 10^{18}$
$10^{9} ≤ Q ≤ 10^{18}$
Time limit: $1$ sec
Subtask #3 (60 points):
Original constraints
Time limit: $3$ sec
----- Sample Input 1 ------
3
20 2 3 4 1
3 7 8 4 11 20
----- Sample Output 1 ------
4
1
2
----- explanation 1 ------
Test case $1$:
- For the first query, $[a, b, c, d] = [A_{1}, B_{1}, C_{1}, D_{1}] = [2, 3, 4, 1]$. It is optimal to buy $2$ doses of Covaxin $(2+5=7)$ and $2$ doses of Covishield $(4+5=9)$. So the total money spent is $7+9=16$ and now the black marketeer cannot buy any more doses. So the answer is 4.
- For the second query, $[a, b, c, d] = [A_{2}, B_{2}, C_{2}, D_{2}] = [(2 + 11\cdot 4)\bmod 20 + 3, (3 + 11\cdot 4) \bmod 20 + 7, (4 + 11\cdot 4) \bmod 20 + 8, (1 + 11\cdot 4) \bmod 20 + 4]=[9, 14, 16, 9]$.
- For the third and the last query, $[a, b, c, d] = [A_{3}, B_{3}, C_{3}, D_{3}] = [3, 12, 15, 4]$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import cmath
def find_total(x, y):
return B * x * x / 2 + j * x + D * y * y / 2 + k * y
def find_root(a, b, c):
dis = b ** 2 - 4 * a * c
r1 = (-b - cmath.sqrt(dis)) / (2 * a)
r2 = (-b + cmath.sqrt(dis)) / (2 * a)
return max(r1.real, r2.real)
q = int(input())
(X, A, B, C, D) = map(int, input().split())
(P, Q, R, S, T, M) = map(int, input().split())
for _ in range(q):
i = (2 * (A - C) + D - B) / (2 * D)
j = A - B / 2
k = C - D / 2
a = B / 2 * (B / D + 1)
b = j + B * k / D + B * i
c = i * k + D * i * i / 2 - X
r = find_root(a, b, c)
y = r * B / D + i
(r, y) = (int(r), int(y))
arr = [(r + i, y + j) for i in range(2) for j in range(2)]
cx = int(find_root(B / 2, j, -X))
remain = X - find_total(cx, 0)
arr.append((cx, int(find_root(D / 2, k, -remain))))
csd = int(find_root(D / 2, k, -X))
remain = X - find_total(0, csd)
arr.append((int(find_root(B / 2, j, -remain)), csd))
ans = max(map(lambda y: y[0] + y[1], filter(lambda x: x[0] >= 0 and x[1] >= 0 and (find_total(x[0], x[1]) <= X), arr)))
print(ans)
A = (A + ans * T) % M + P
B = (B + ans * T) % M + Q
C = (C + ans * T) % M + R
D = (D + ans * T) % M + S
``` | vfc_138184 | {
"difficulty": "very_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/COVAXIN",
"time_limit": "1 - 3 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n20 2 3 4 1\n3 7 8 4 11 20\n",
"output": "4\n1\n2\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/154/A | Solve the following coding problem using the programming language python:
Sergey attends lessons of the N-ish language. Each lesson he receives a hometask. This time the task is to translate some sentence to the N-ish language. Sentences of the N-ish language can be represented as strings consisting of lowercase Latin letters without spaces or punctuation marks.
Sergey totally forgot about the task until half an hour before the next lesson and hastily scribbled something down. But then he recollected that in the last lesson he learned the grammar of N-ish. The spelling rules state that N-ish contains some "forbidden" pairs of letters: such letters can never occur in a sentence next to each other. Also, the order of the letters doesn't matter (for example, if the pair of letters "ab" is forbidden, then any occurrences of substrings "ab" and "ba" are also forbidden). Also, each pair has different letters and each letter occurs in no more than one forbidden pair.
Now Sergey wants to correct his sentence so that it doesn't contain any "forbidden" pairs of letters that stand next to each other. However, he is running out of time, so he decided to simply cross out some letters from the sentence. What smallest number of letters will he have to cross out? When a letter is crossed out, it is "removed" so that the letters to its left and right (if they existed), become neighboring. For example, if we cross out the first letter from the string "aba", we get the string "ba", and if we cross out the second letter, we get "aa".
Input
The first line contains a non-empty string s, consisting of lowercase Latin letters — that's the initial sentence in N-ish, written by Sergey. The length of string s doesn't exceed 105.
The next line contains integer k (0 ≤ k ≤ 13) — the number of forbidden pairs of letters.
Next k lines contain descriptions of forbidden pairs of letters. Each line contains exactly two different lowercase Latin letters without separators that represent the forbidden pairs. It is guaranteed that each letter is included in no more than one pair.
Output
Print the single number — the smallest number of letters that need to be removed to get a string without any forbidden pairs of neighboring letters. Please note that the answer always exists as it is always possible to remove all letters.
Examples
Input
ababa
1
ab
Output
2
Input
codeforces
2
do
cs
Output
1
Note
In the first sample you should remove two letters b.
In the second sample you should remove the second or the third letter. The second restriction doesn't influence the solution.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
ans = 0
t = []
x = input()
y = int(input())
for i in range(y):
z = input()
t.append(z)
pt = -1
ln = len(x)
for i in t:
a = i[0]
b = i[1]
pt = 0
for j in range(ln):
ded1 = 0
ded2 = 0
if j >= pt:
if x[j] in [a, b]:
pt = j
while pt < ln and x[pt] in [a, b]:
if x[pt] == a:
ded1 += 1
else:
ded2 += 1
pt += 1
ans += min(ded1, ded2)
print(ans)
``` | vfc_138193 | {
"difficulty": "medium_hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/154/A",
"time_limit": "2.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "vefneyamdzoytemupniw\n13\nve\nfg\noi\nan\nck\nwx\npq\nml\nbt\nud\nrz\nsj\nhy\n",
"output": "1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/license-key-formatting/1 | Solve the following coding problem using the programming language python:
Given a string S that consists of only alphanumeric characters and dashes. The string is separated into N + 1 groups by N dashes. Also given an integer K.
We want to reformat the string S, such that each group contains exactly K characters, except for the first group, which could be shorter than K but still must contain at least one character. Furthermore, there must be a dash inserted between two groups, and you should convert all lowercase letters to uppercase.
Return the reformatted string.
Example 1:
Input:
S = "5F3Z-2e-9-w", K = 4
Output: "5F3Z-2E9W"
Explanation: The string S has been split into two
parts, each part has 4 characters. Note that two
extra dashes are not needed and can be removed.
Example 2:
Input:
S = "2-5g-3-J", K = 2
Output: "2-5G-3J"
Explanation: The string s has been split
into three parts, each part has 2 characters
except the first part as it could
be shorter as mentioned above.
Your Task:
You don't need to read input or print anything. Your task is to complete the function ReFormatString() which takes a string S and an integer K as input and returns the reformatted string.
Expected Time Complexity: O(N)
Expected Auxiliary Space: O(N)
Constraints:
1 ≤ S.length() ≤ 10^{5}
1 ≤ K ≤ 10^{4}
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def ReFormatString(self,S, K):
#code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def ReFormatString(self, S, K):
c = K
N = len(S)
size = 0
ans = []
for j in range(N - 1, -1, -1):
tmp = S[j]
if tmp >= 'a' and tmp <= 'z':
tmp = chr(65 + (ord(tmp) - 97))
if S[j] != '-' and c:
ans.append(tmp)
c -= 1
size += 1
elif c == 0:
c = K
ans.append('-')
size += 1
if S[j] != '-':
ans.append(tmp)
c -= 1
size += 1
if size == 0:
return ''
if ans[size - 1] == '-':
ans.pop()
ans = ans[::-1]
return ''.join(ans)
``` | vfc_138197 | {
"difficulty": "medium",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/license-key-formatting/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "S = \"5F3Z-2e-9-w\", K = 4",
"output": "\"5F3Z-2E9W\"",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "S = \"2-5g-3-J\", K = 2",
"output": "\"2-5G-3J\"",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1694/B | Solve the following coding problem using the programming language python:
Let's call a binary string $T$ of length $m$ indexed from $1$ to $m$ paranoid if we can obtain a string of length $1$ by performing the following two kinds of operations $m-1$ times in any order :
Select any substring of $T$ that is equal to 01, and then replace it with 1.
Select any substring of $T$ that is equal to 10, and then replace it with 0.
For example, if $T = $ 001, we can select the substring $[T_2T_3]$ and perform the first operation. So we obtain $T = $ 01.
You are given a binary string $S$ of length $n$ indexed from $1$ to $n$. Find the number of pairs of integers $(l, r)$ $1 \le l \le r \le n$ such that $S[l \ldots r]$ (the substring of $S$ from $l$ to $r$) is a paranoid string.
-----Input-----
The first line contains an integer $t$ ($1 \le t \le 1000$) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the size of $S$.
The second line of each test case contains a binary string $S$ of $n$ characters $S_1S_2 \ldots S_n$. ($S_i = $ 0 or $S_i = $ 1 for each $1 \le i \le n$)
It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
-----Output-----
For each test case, output the number of pairs of integers $(l, r)$ $1 \le l \le r \le n$ such that $S[l \ldots r]$ (the substring of $S$ from $l$ to $r$) is a paranoid string.
-----Examples-----
Input
5
1
1
2
01
3
100
4
1001
5
11111
Output
1
3
4
8
5
-----Note-----
In the first sample, $S$ already has length $1$ and doesn't need any operations.
In the second sample, all substrings of $S$ are paranoid. For the entire string, it's enough to perform the first operation.
In the third sample, all substrings of $S$ are paranoid except $[S_2S_3]$, because we can't perform any operations on it, and $[S_1S_2S_3]$ (the entire string).
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
input = sys.stdin.readline
def solve():
n = int(input())
s = input().strip()
ans = n
for i in range(1, n):
if s[i - 1] != s[i]:
ans += i
return ans
for _ in range(int(input())):
print(solve())
``` | vfc_138200 | {
"difficulty": "easy",
"memory_limit": "256 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1694/B",
"time_limit": "1 second"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5\n1\n1\n2\n01\n3\n100\n4\n1001\n5\n11111\n",
"output": "1\n3\n4\n8\n5\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/RC122020/problems/RECNDNUM | Solve the following coding problem using the programming language python:
Chef is playing a game on the non-negative x-axis. It takes him $1$ second to reach from $i^{th}$ position to $(i-1)^{th}$ position or $(i+1)^{th}$ position. The chef never goes to the negative x-axis. Also, Chef doesn't stop at any moment of time.
The movement of chef can be described as follows.
- At the start he is standing at $x=0$ at time $0$.
- In the first round, he moves towards $x=1$ and comes back to the $x=0$ position.
- In the second round, he moves towards the $x=2$ and comes back again to $x=0$.
- Generalizing, in the $k^{th}$ round, he moves from $x=0$ to $x=k$ and then returns back to $x=0$ at the end of the round. This goes on as the game progresses.
For Example, the path of Chef for $3^{rd}$ round is given below.
$0 - 1 - 2 - 3 - 2 - 1 - 0$
The overall path followed by Chef would look somewhat like this:
$0 - 1 - 0 - 1 - 2 - 1 - 0 - 1 - 2 - 3 - 2 - 1 - 0 - 1 - 2 - 3 - 4 - 3 - …$
You are given two non-negative integers $N$ and $K$. You have to tell the time at which Chef arrives at $x=N$ for the $K^{th}$ time.
Note - Chef can not skip a position while visiting the positions.
-----Input:-----
- The first line contains $T$ the number of test cases. Then the test cases follow.
- Each test case contains a single line of two integers $N$ and $K$.
-----Output:-----
For each test case, print a single line containing one integer -- the time taken by the chef to arrive at $x=N$ for the $K^{th}$ time by modulo $1,000,000,007$.
-----Constraints-----
- $1 \le T \le 10^5$
- $0 \le N \le 10^9$
- $1 \le K \le 10^9$
-----Sample Input:-----
5
0 1
1 1
2 1
1 3
4 6
-----Sample Output:-----
0
1
4
5
46
-----Explanation:-----
Test Case 1:
Chef starts the journey from the $N = 0$ at time $t = 0$ and it's the first time $(K = 1)$, he is here. So, the answer is $0$.
Test Case 2:
Chef starts the journey from the $N = 0$ at time $t = 0$ then goes to $N = 1$ at $t = 1$ and it's the first time $(K = 1)$, he is here. So, the answer is $1$.
Test Case 4:
The path followed by Chef to reach $1$ for the third time is given below.
$0 - 1 - 0 - 1 - 2 - 1$
He reaches $1$ for the third time at $t=5$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
from random import choice, randint
inp = sys.stdin.readline
out = sys.stdout.write
flsh = sys.stdout.flush
sys.setrecursionlimit(10 ** 9)
inf = 10 ** 20
eps = 1.0 / 10 ** 10
mod = 10 ** 9 + 7
dd = [(-1, 0), (0, 1), (1, 0), (0, -1)]
ddn = [(-1, 0), (-1, 1), (0, 1), (1, 1), (1, 0), (1, -1), (0, -1), (-1, -1)]
def MI():
return map(int, inp().strip().split())
def LI():
return list(map(int, inp().strip().split()))
def LLI():
return [list(map(int, l.split())) for l in sys.stdin.readlines().strip()]
def LI_():
return [int(x) - 1 for x in inp().strip().split()]
def LF():
return [float(x) for x in inp().strip().split()]
def LS():
return inp().strip().split()
def I():
return int(inp().strip())
def F():
return float(inp().strip())
def S():
return inp().strip()
def pf(s):
return out(s + '\n')
def JA(a, sep):
return sep.join(map(str, a))
def JAA(a, s, t):
return s.join((t.join(map(str, b)) for b in a))
def main():
from math import ceil
t = I()
l = []
for _ in range(t):
(n, k) = MI()
if n == 0:
k -= 1
ans = k * (k + 1) % mod
l.append(ans)
elif k % 2 != 0:
lr = k // 2
l.append((n * n % mod + lr * (2 * n % mod) % mod + lr * (lr + 1) % mod) % mod)
else:
lr = k // 2
l.append((n * n % mod + lr * (2 * n) % mod % mod + lr * (lr - 1) % mod) % mod)
for i in range(t):
pf(str(l[i]))
def __starting_point():
main()
__starting_point()
``` | vfc_138204 | {
"difficulty": "unknown_difficulty",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/RC122020/problems/RECNDNUM",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "5\n0 1\n1 1\n2 1\n1 3\n4 6\n",
"output": "0\n1\n4\n5\n46\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/CNCTCT | Solve the following coding problem using the programming language python:
The country of Berland initially has N isolated cities, the i-th city has a significance of A_{i}. The President of Berland wants to connect all the cities. He can construct a bidirectional road of length L (L > 0) from city X to city Y if (A_{X} \& A_{Y} \& L) = L, where \& represents the [bitwise AND] operator.
What is the minimum total length of roads he has to construct, in order to connect all the cities in Berland? Print -1 if it is impossible.
Note: City X and City Y are said to be connected if there exists a sequence of cities C_{1}, C_{2}, \ldots, C_{K} (K ≥ 1) such that C_{1} = X, C_{K} = Y, and there exists a road from C_{i} to C_{i+1}, (1 ≤ i < K). All the cities in Berland are said to be connected when every pair of cities in Berland are connected.
------ Input Format ------
- The first line of input will contain a single integer T, denoting the number of test cases.
- Each test case consists of two lines of input.
- The first line of each test case contains N — the number of cities.
- The second line contains N space-separated integers A_{1}, A_{2}, \ldots, A_{N} — the significance of each of the N cities.
------ Output Format ------
For each test case, output on a new line the minimum total length of roads to connect all the cities in Berland, or -1 if it is impossible.
------ Constraints ------
$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{5}$
$0 ≤ A_{i} ≤ 10^{9}$
- The sum of $N$ over all test cases won't exceed $3 \cdot 10^{5}$.
----- Sample Input 1 ------
2
4
4 4 4 4
3
2 4 6
----- Sample Output 1 ------
12
6
----- explanation 1 ------
Test case 1: The following roads with minimum total length can be constructed to connect Berland:
- A road with $L=4$ between city $1$ and city $2$, since ($A_{1} \& A_{2} \& 4) = 4$.
- A road with $L=4$ between city $2$ and city $3$, since ($A_{2} \& A_{3} \& 4) = 4$.
- A road with $L=4$ between city $3$ and city $4$, since ($A_{3} \& A_{4} \& 4) = 4$.
Test case 2: The following roads with minimum total length can be constructed to connect Berland:
- A road with $L=2$ between city $1$ and city $3$, since ($A_{1} \& A_{3} \& 2) = 2$.
- A road with $L=4$ between city $2$ and city $3$, since ($A_{2} \& A_{3} \& 4) = 4$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys, math, heapq, bisect, random, itertools
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 5)
ints = lambda : list(map(int, input().split()))
p = 10 ** 9 + 7
inf = 10 ** 20 + 7
alpha = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
p2 = [1]
for i in range(40):
p2.append(p2[-1] * 2)
for t in range(int(input())):
n = int(input())
a = ints()
if a.count(0):
if n == 1:
print(0)
else:
print(-1)
continue
store = [[] for i in range(32)]
for x in range(n):
for i in range(32):
if a[x] & p2[i]:
store[i].append(x)
done = set()
bitset = set()
ans = 0
for i in range(32):
if store[i]:
bitset.add(i)
queue = store[i]
done = set(store[i])
ans += p2[i] * (len(store[i]) - 1)
break
bits = set()
for i in queue:
for j in range(32):
if a[i] & p2[j]:
if j not in bitset:
bitset.add(j)
bits.add(j)
b = sorted(bits)
heapq.heapify(b)
while b:
x = heapq.heappop(b)
while store[x]:
i = store[x].pop()
if i not in done:
heapq.heappush(b, x)
done.add(i)
m = x
for j in range(32):
if p2[j] & a[i]:
if j in bitset:
m = min(m, j)
else:
bitset.add(j)
heapq.heappush(b, j)
ans += p2[m]
break
if len(done) == n:
print(ans)
else:
print(-1)
``` | vfc_138209 | {
"difficulty": "very_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/CNCTCT",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n4\n4 4 4 4\n3\n2 4 6",
"output": "12\n6\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/prime-factors-of-lcm-of-array-elements3940/1 | Solve the following coding problem using the programming language python:
Given an array of elements find all the prime factors of the LCM of the given numbers.
Example 1:
Input:
N = 8
Arr = {1 , 2, 3, 4, 5, 6, 7, 8}
Output: 2 3 5 7
Explaination: LCM of N elements is 840
and 840 = 2*2*2*3*5*7.so prime factors
would be 2, 3, 5, 7.
Example 2:
Input:
N = 4
Arr = {20, 10, 15, 60}
Output: 2 3 5
Explaination: LCM of N elements is 60
and 60 = 2*2*3*5.so prime factors
would be 2, 3, 5.
Your Task:
You don't need to read input or print anything. Your task is to complete the function primeFactorLcm() which takes the array Arr[] and its size N as input parameters and returns all the prime factors of the LCM of the given numbers.
Expected Time Complexity: O(Nsqrt(max(Arr_{i}))
Expected Auxiliary Space: O(N)
Constraints:
1 ≤ N ≤ 10^{4}
1 ≤ Arr_{i} ≤ 10^{4 }where 0≤i<N
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def primeFactorLcm(self, Arr, N):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def lcm(self, a, b):
from math import gcd
return a * b // gcd(a, b)
def primeFactorLcm(self, Arr, N):
lc = Arr[0]
lis = []
for i in Arr:
lc = self.lcm(lc, i)
d = 2
while lc >= d:
if lc % d == 0:
while lc % d == 0:
lc //= d
lis.append(d)
d += 1
return lis
``` | vfc_138213 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/prime-factors-of-lcm-of-array-elements3940/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "N = 8\r\nArr = {1 , 2, 3, 4, 5, 6, 7, 8}",
"output": "2 3 5 7",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "N = 4\r\nArr = {20, 10, 15, 60}",
"output": "2 3 5",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/rohans-love-for-matrix4723/1 | Solve the following coding problem using the programming language python:
Rohan has a special love for the matrices especially for the first element of the matrix. Being good at Mathematics, he also loves to solve the different problem on the matrices. So one day he started to multiply the matrix with the original matrix. The elements of the original matrix are given by a_{00}=1 , a_{01}=1, a_{10}=1, a_{11}=0.
Given the power of the matrix, n calculate the a^{n} and return the a_{10} element mod 1000000007.
Example 1:
Input: n = 3
Output: 2
Explanation: Take the cube of the original matrix
i.e a^{3} and the first element(a_{10}) is 2.
Example 2:
Input: n = 4
Output: 3
Explanation: Take the cube of the original matrix
i.e a^{4} and the first element(a_{10}) is 3.
Your Task:
You dont need to read input or print anything. Complete the function firstElement() which takes n as input parameter and returns the a_{10} element mod 1000000007.
Expected Time Complexity: O(n)
Expected Auxiliary Space: O(1)
Constraints:
1<= n <=10^{6}
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def firstElement (self, n):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def firstElement(self, n):
a = 0
b = 1
for i in range(2, n + 1):
c = (a + b) % 1000000007
a = b
b = c
return b
``` | vfc_138214 | {
"difficulty": "medium_hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/rohans-love-for-matrix4723/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "n = 3",
"output": "2",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "n = 4",
"output": "3",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
Problem Statement
We have planted $N$ flower seeds, all of which come into different flowers. We want to make all the flowers come out together.
Each plant has a value called vitality, which is initially zero. Watering and spreading fertilizers cause changes on it, and the $i$-th plant will come into flower if its vitality is equal to or greater than $\mathit{th}_i$. Note that $\mathit{th}_i$ may be negative because some flowers require no additional nutrition.
Watering effects on all the plants. Watering the plants with $W$ liters of water changes the vitality of the $i$-th plant by $W \times \mathit{vw}_i$ for all $i$ ($1 \le i \le n$), and costs $W \times \mathit{pw}$ yen, where $W$ need not be an integer. $\mathit{vw}_i$ may be negative because some flowers hate water.
We have $N$ kinds of fertilizers, and the $i$-th fertilizer effects only on the $i$-th plant. Spreading $F_i$ kilograms of the $i$-th fertilizer changes the vitality of the $i$-th plant by $F_i \times \mathit{vf}_i$, and costs $F_i \times \mathit{pf}_i$ yen, where $F_i$ need not be an integer as well. Each fertilizer is specially made for the corresponding plant, therefore $\mathit{vf}_i$ is guaranteed to be positive.
Of course, we also want to minimize the cost. Formally, our purpose is described as "to minimize $W \times \mathit{pw} + \sum_{i=1}^{N}(F_i \times \mathit{pf}_i)$ under $W \times \mathit{vw}_i + F_i \times \mathit{vf}_i \ge \mathit{th}_i$, $W \ge 0$, and $F_i \ge 0$ for all $i$ ($1 \le i \le N$)". Your task is to calculate the minimum cost.
Input
The input consists of multiple datasets. The number of datasets does not exceed $100$, and the data size of the input does not exceed $20\mathrm{MB}$. Each dataset is formatted as follows.
> $N$
> $\mathit{pw}$
> $\mathit{vw}_1$ $\mathit{pf}_1$ $\mathit{vf}_1$ $\mathit{th}_1$
> :
> :
> $\mathit{vw}_N$ $\mathit{pf}_N$ $\mathit{vf}_N$ $\mathit{th}_N$
The first line of a dataset contains a single integer $N$, number of flower seeds. The second line of a dataset contains a single integer $\mathit{pw}$, cost of watering one liter. Each of the following $N$ lines describes a flower. The $i$-th line contains four integers, $\mathit{vw}_i$, $\mathit{pf}_i$, $\mathit{vf}_i$, and $\mathit{th}_i$, separated by a space.
You can assume that $1 \le N \le 10^5$, $1 \le \mathit{pw} \le 100$, $-100 \le \mathit{vw}_i \le 100$, $1 \le \mathit{pf}_i \le 100$, $1 \le \mathit{vf}_i \le 100$, and $-100 \le \mathit{th}_i \le 100$.
The end of the input is indicated by a line containing a zero.
Output
For each dataset, output a line containing the minimum cost to make all the flowers come out. The output must have an absolute or relative error at most $10^{-4}$.
Sample Input
3
10
4 3 4 10
5 4 5 20
6 5 6 30
3
7
-4 3 4 -10
5 4 5 20
6 5 6 30
3
1
-4 3 4 -10
-5 4 5 -20
6 5 6 30
3
10
-4 3 4 -10
-5 4 5 -20
-6 5 6 -30
0
Output for the Sample Input
43.5
36
13.5
0
Example
Input
3
10
4 3 4 10
5 4 5 20
6 5 6 30
3
7
-4 3 4 -10
5 4 5 20
6 5 6 30
3
1
-4 3 4 -10
-5 4 5 -20
6 5 6 30
3
10
-4 3 4 -10
-5 4 5 -20
-6 5 6 -30
0
Output
43.5
36
13.5
0
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
def main():
readline = sys.stdin.readline
write = sys.stdout.write
def gcd(m, n):
while n:
(m, n) = (n, m % n)
return m
def init(p, q=1):
g = gcd(p, q)
return (p // g, q // g)
def add(A, B):
(pa, qa) = A
(pb, qb) = B
if pa == 0:
return B
if pb == 0:
return A
g = gcd(qa, qb)
ra = pa * qb // g + pb * qa // g
rb = qa * qb // g
g = gcd(ra, rb)
return (ra // g, rb // g)
INF = 10 ** 18
def cp(X):
(vw, pf, vf, th) = X
if vw == 0:
return INF
return th / vw
while 1:
N = int(readline())
if N == 0:
break
pw = int(readline())
P = [list(map(int, readline().split())) for i in range(N)]
P.append((1, 0, 1, 0))
P.sort(key=cp)
A = [init(0)] * (N + 1)
B = [init(0)] * (N + 1)
a = b = init(0)
a = init(pw)
for (i, (vw, pf, vf, th)) in enumerate(P):
if vw == 0:
if th > 0:
b = add(b, (th * pf, vf))
continue
if vw > 0:
if th ^ vw >= 0:
a = add(a, (-vw * pf, vf))
b = add(b, (th * pf, vf))
A[i] = init(vw * pf, vf)
B[i] = init(-th * pf, vf)
elif th ^ vw >= 0:
A[i] = init(-vw * pf, vf)
B[i] = init(th * pf, vf)
else:
a = add(a, (-vw * pf, vf))
b = add(b, (th * pf, vf))
ans = INF
for (i, (vw, pf, vf, th)) in enumerate(P):
if vw == 0:
continue
if th ^ vw < 0:
continue
a = add(a, A[i])
b = add(b, B[i])
(pa, qa) = a
(pb, qb) = b
v = (pa * th * qb + pb * vw * qa) / (vw * qa * qb)
if ans + 0.01 < v:
break
ans = min(ans, v)
write('%.016f\n' % ans)
main()
``` | vfc_138215 | {
"difficulty": "unknown_difficulty",
"memory_limit": "536.870912 megabytes",
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "8.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n10\n5 3 4 10\n5 4 5 20\n6 5 6 30\n3\n7\n-4 3 4 -10\n5 4 5 20\n6 5 6 30\n3\n1\n-4 3 4 -10\n-5 4 5 -20\n6 5 6 30\n3\n10\n-4 3 4 -10\n-5 4 5 -20\n-6 5 6 -30\n0",
"output": "43\n36\n13.5\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3\n10\n4 3 4 10\n5 4 5 20\n6 5 6 30\n3\n7\n-4 3 4 -10\n5 4 5 20\n6 5 6 30\n3\n1\n-4 3 4 -10\n-4 4 5 -20\n6 5 6 30\n3\n10\n-4 3 4 -10\n-5 4 5 -20\n-6 5 6 -30\n0",
"output": "43.5\n36\n12.5\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3\n10\n4 3 4 10\n5 4 5 18\n6 5 6 30\n3\n7\n-4 3 4 -10\n5 4 5 20\n6 5 6 30\n3\n1\n-4 3 4 -10\n-5 4 5 -20\n6 5 6 30\n3\n10\n-4 3 4 -10\n-5 4 5 -20\n-6 5 6 -30\n0",
"output": "41.9\n36\n13.5\n0\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3\n10\n4 3 4 10\n5 4 5 18\n8 5 6 30\n3\n7\n-4 3 4 -10\n5 4 5 20\n6 5 6 30\n3\n1\n-4 3 4 -10\n-5 4 5 -20\n6 5 6 30\n3\n10\n-4 3 4 -10\n-5 4 5 -20\n-6 5 6 -30\n0",
"output": "37\n36\n13.5\n0\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://www.codechef.com/problems/CHEFSHIP | Solve the following coding problem using the programming language python:
Read problems statements in [Hindi], [Mandarin Chinese], [Russian], [Vietnamese], and [Bengali] as well.
In Chefland, each person has their own non-empty personal string. When two people with personal strings $T_{1}$ and $T_{2}$ (possibly identical) become friends in Chefland, their strings are replaced by a new string $S = T_{1} + T_{1} + T_{2} + T_{2}$, where $+$ denotes string concatenation.
Chef recently became friends with Chefina. However, Chefina's personal string was her favourite and she got upset when it was replaced by $S$. She wanted her personal string back. Chef does not remember $T_{1}$ and $T_{2}$ now, he only knows $S$.
Find the number of ways in which Chef can retrieve valid strings $T_{1}$ and $T_{2}$ from the given string $S$. It is also possible that Chef does not remember $S$ correctly, in which case there is no way to retrieve $T_{1}$ and $T_{2}$.
------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first and only line of each test case contains a single string $S$.
------ Output ------
For each test case, print a single line containing one integer ― the number of ways to retrieve $T_{1}$ and $T_{2}$ from $S$.
------ Constraints ------
$1 ≤ T ≤ 10^{4}$
$4 ≤ |S| ≤ 10^{5}$
$|S|$ is divisible by $2$
$S$ contains only lowercase English letters
the sum of $|S|$ over all test cases does not exceed $2 \cdot 10^{6}$
----- Sample Input 1 ------
3
abcd
aaaa
ababcdccdc
----- Sample Output 1 ------
0
1
1
----- explanation 1 ------
Example case 1: There is no way to choose $T_{1}$ and $T_{2}$.
Example case 2: Both $T_{1}$ and $T_{2}$ must be "a".
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
for i in range(int(input())):
s = input()
c = 0
l = len(s)
for i in range(2, l, 2):
a = i
b = l - i
t11 = s[0:a // 2]
t12 = s[a // 2:a]
t21 = s[a:a + b // 2]
t22 = s[a + b // 2:]
if t11 == t12 and t21 == t22:
c = c + 1
print(c)
``` | vfc_138219 | {
"difficulty": "medium_hard",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/CHEFSHIP",
"time_limit": "1 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\nabcd\naaaa\nababcdccdc",
"output": "0\n1\n1",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/301/A | Solve the following coding problem using the programming language python:
Yaroslav has an array, consisting of (2·n - 1) integers. In a single operation Yaroslav can change the sign of exactly n elements in the array. In other words, in one operation Yaroslav can select exactly n array elements, and multiply each of them by -1.
Yaroslav is now wondering: what maximum sum of array elements can be obtained if it is allowed to perform any number of described operations?
Help Yaroslav.
-----Input-----
The first line contains an integer n (2 ≤ n ≤ 100). The second line contains (2·n - 1) integers — the array elements. The array elements do not exceed 1000 in their absolute value.
-----Output-----
In a single line print the answer to the problem — the maximum sum that Yaroslav can get.
-----Examples-----
Input
2
50 50 50
Output
150
Input
2
-1 -100 -1
Output
100
-----Note-----
In the first sample you do not need to change anything. The sum of elements equals 150.
In the second sample you need to change the sign of the first two elements. Then we get the sum of the elements equal to 100.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
n = int(input())
lst = [int(x) for x in input().split()]
x = len([elem for elem in lst if elem < 0])
values = sorted([abs(elem) for elem in lst])
result = sum(values)
if n % 2 == 0 and x % 2 == 1:
result -= 2 * values[0]
print(result)
``` | vfc_138224 | {
"difficulty": "medium_hard",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/301/A",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "2\n50 50 50\n",
"output": "150\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n-1 -100 -1\n",
"output": "100\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3\n-959 -542 -669 -513 160\n",
"output": "2843\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n717 473 344 -51 -548 703 -869\n",
"output": "3603\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "5\n270 -181 957 -509 -6 937 -175 434 -625\n",
"output": "4094\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "6\n-403 901 -847 -708 -624 413 -293 709 886 445 716\n",
"output": "6359\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1047/C | Solve the following coding problem using the programming language python:
Mr. F has n positive integers, a_1, a_2, …, a_n.
He thinks the greatest common divisor of these integers is too small. So he wants to enlarge it by removing some of the integers.
But this problem is too simple for him, so he does not want to do it by himself. If you help him, he will give you some scores in reward.
Your task is to calculate the minimum number of integers you need to remove so that the greatest common divisor of the remaining integers is bigger than that of all integers.
Input
The first line contains an integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of integers Mr. F has.
The second line contains n integers, a_1, a_2, …, a_n (1 ≤ a_i ≤ 1.5 ⋅ 10^7).
Output
Print an integer — the minimum number of integers you need to remove so that the greatest common divisor of the remaining integers is bigger than that of all integers.
You should not remove all of the integers.
If there is no solution, print «-1» (without quotes).
Examples
Input
3
1 2 4
Output
1
Input
4
6 9 15 30
Output
2
Input
3
1 1 1
Output
-1
Note
In the first example, the greatest common divisor is 1 in the beginning. You can remove 1 so that the greatest common divisor is enlarged to 2. The answer is 1.
In the second example, the greatest common divisor is 3 in the beginning. You can remove 6 and 9 so that the greatest common divisor is enlarged to 15. There is no solution which removes only one integer. So the answer is 2.
In the third example, there is no solution to enlarge the greatest common divisor. So the answer is -1.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from sys import stdin
from collections import deque
mod = 10 ** 9 + 7
from bisect import bisect_right
from bisect import bisect_left
from collections import defaultdict
from math import sqrt, factorial, gcd, log2, inf, ceil
n = int(input())
l = list(map(int, input().split()))
m = max(l) + 1
prime = [0] * m
cmd = [0] * m
def sieve():
for i in range(2, m):
if prime[i] == 0:
for j in range(2 * i, m, i):
prime[j] = i
for i in range(2, m):
if prime[i] == 0:
prime[i] = i
g = 0
for i in range(n):
g = gcd(l[i], g)
sieve()
ans = -1
for i in range(n):
ele = l[i] // g
while ele > 1:
div = prime[ele]
cmd[div] += 1
while ele % div == 0:
ele //= div
ans = max(ans, cmd[div])
if ans == -1:
print(-1)
exit()
print(n - ans)
``` | vfc_138228 | {
"difficulty": "medium_hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1047/C",
"time_limit": "1.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n1 100003 100003\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3\n24 24 12\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "2\n1 7\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n4 8 8 8\n",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n5 10 10 10\n",
"output": "1\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://www.codechef.com/problems/AORB | Solve the following coding problem using the programming language python:
There are two problems in a contest.
Problem A is worth 500 points at the start of the contest.
Problem B is worth 1000 points at the start of the contest.
Once the contest starts, after each minute:
Maximum points of Problem A reduce by 2 points .
Maximum points of Problem B reduce by 4 points.
It is known that Chef requires X minutes to solve Problem A correctly and Y minutes to solve Problem B correctly.
Find the maximum number of points Chef can score if he optimally decides the order of attempting both the problems.
------ Input Format ------
- First line will contain T, number of test cases. Then the test cases follow.
- Each test case contains of a single line of input, two integers X and Y - the time required to solve problems A and B in minutes respectively.
------ Output Format ------
For each test case, output in a single line, the maximum number of points Chef can score if he optimally decides the order of attempting both the problems.
------ Constraints ------
$1 ≤ T ≤ 1000$
$1 ≤ X, Y ≤ 100$
----- Sample Input 1 ------
4
10 20
8 40
15 15
20 10
----- Sample Output 1 ------
1360
1292
1380
1400
----- explanation 1 ------
Test Case $1$: If Chef attempts in the order $A \rightarrow B$ then he submits Problem A after $10$ minutes and Problem B after $30$ minutes.
Thus, he gets $500 - 10 \cdot 2 = 480$ points for problem A and $1000 - 30 \cdot 4 = 880$ points for problem B. Thus, total $480+880=1360$ points for both the problems.
If Chef attempts in the order $B \rightarrow A$ then he submits Problem B after $20$ minutes and Problem A after $30$ minutes.
Thus, he gets $1000 - 20 \cdot 4 = 920$ points for Problem B and $500 - 30 \cdot 2 = 440$ points for Problem A. Thus total $920+440=1360$ points for both the problems.
So, in both cases Chef gets $1360$ points in total.
Test Case $2$: If Chef attempts in the order $A \rightarrow B$ then he submits Problem A after $8$ minutes and Problem B after $48$ minutes.
Thus, he gets $500 - 8 \cdot 2 = 484$ points for problem A and $1000 - 48 \cdot 4 = 808$ points for problem B. Thus, total $484+808=1292$ points for both the problems.
If Chef attempts in the order $B \rightarrow A$ then he submits Problem B after $40$ minutes and Problem A after $48$ minutes.
Thus, he gets $1000 - 40 \cdot 4 = 840$ points for Problem B and $500 - 48 \cdot 2 = 404$ points for Problem A. Thus total $840+404=1244$ points for both the problems.
So, Chef will attempt in the order $A \rightarrow B$ and thus obtain $1292$ points.
Test Case $3$: If Chef attempts in the order $A \rightarrow B$ then he submits Problem A after $15$ minutes and Problem B after $30$ minutes.
Thus, he gets $500 - 15 \cdot 2 = 470$ points for problem A and $1000 - 30 \cdot 4 = 880$ points for problem B. Thus, total $470+880=1350$ points for both the problems.
If Chef attempts in the order $B \rightarrow A$ then he submits Problem B after $15$ minutes and Problem A after $30$ minutes.
Thus, he gets $1000 - 15 \cdot 4 = 940$ points for Problem B and $500 - 30 \cdot 2 = 440$ points for Problem A. Thus total $940+440=1380$ points for both the problems.
So, Chef will attempt in the order $B \rightarrow A$ and thus obtain $1380$ points.
Test Case $4$: If Chef attempts in the order $A \rightarrow B$ then he submits Problem A after $20$ minutes and Problem B after $30$ minutes.
Thus, he gets $500 - 20 \cdot 2 = 460$ points for problem A and $1000 - 30 \cdot 4 = 880$ points for problem B. Thus, total $460+880=1340$ points for both the problems.
If Chef attempts in the order $B \rightarrow A$ then he submits Problem B after $10$ minutes and Problem A after $30$ minutes.
Thus, he gets $1000 - 10 \cdot 4 = 960$ points for Problem B and $500 - 30 \cdot 2 = 440$ points for Problem A. Thus total $960+440=1400$ points for both the problems.
So, Chef will attempt in the order $B \rightarrow A$ and thus obtain $1400$ points.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
t = int(input())
for i in range(t):
(X, Y) = map(int, input().split())
FirstA = 500 - 2 * X + (1000 - 4 * (X + Y))
FirstB = 1000 - 4 * Y + (500 - 2 * (X + Y))
if FirstB > FirstA:
print(FirstB)
else:
print(FirstA)
``` | vfc_138233 | {
"difficulty": "easy",
"memory_limit": "50000 bytes",
"memory_limit_bytes": null,
"problem_url": "https://www.codechef.com/problems/AORB",
"time_limit": "0.5 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "4\n10 20\n8 40\n15 15\n20 10\n",
"output": "1360\n1292\n1380\n1400\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
A bipartite graph G = (V, E) is a graph in which the vertex set V can be divided into two disjoint subsets X and Y such that every edge e ∈ E has one end point in X and the other end point in Y.
A matching M is a subset of edges such that each node in V appears in at most one edge in M.
Given a bipartite graph, find the size of the matching which has the largest size.
Constraints
* 1 ≤ |X|, |Y| ≤ 100
* 0 ≤ |E| ≤ 10,000
Input
|X| |Y| |E|
x0 y0
x1 y1
:
x|E|-1 y|E|-1
|X| and |Y| are the number of vertices in X and Y respectively, and |E| is the number of edges in the graph G. The vertices in X are named with the numbers 0, 1,..., |X|-1, and vertices in Y are named with the numbers 0, 1,..., |Y|-1, respectively.
xi and yi are the node numbers from X and Y respectevely which represent the end-points of the i-th edge.
Output
Print the largest size of the matching.
Example
Input
3 4 6
0 0
0 2
0 3
1 1
2 1
2 3
Output
3
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
def generate_adj_table(_edges):
for edge in _edges:
(vx, vy) = map(int, edge)
init_adj_table[vx].add(vy)
return init_adj_table
def graph_dfs(current, matching, visited):
for adj in range(y_num):
if not visited[adj] and adj in adj_table[current]:
visited[adj] = True
if matching[adj] == -1 or graph_dfs(matching[adj], matching, visited):
matching[adj] = current
return True
return False
def mbm():
matching = [-1] * y_num
res = 0
for v in range(x_num):
visited = [False] * y_num
if graph_dfs(v, matching, visited):
res += 1
return res
_input = sys.stdin.readlines()
(x_num, y_num, e_num) = map(int, _input[0].split())
edges = map(lambda x: x.split(), _input[1:])
init_adj_table = [set() for _ in range(x_num)]
adj_table = generate_adj_table(edges)
print(mbm())
``` | vfc_138242 | {
"difficulty": "unknown_difficulty",
"memory_limit": "134.217728 megabytes",
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "1.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3 4 6\n0 0\n0 0\n0 3\n1 1\n2 1\n2 3",
"output": "3\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3 7 2\n1 0\n0 0\n0 3\n0 1\n1 1\n2 3",
"output": "1\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3 4 5\n0 0\n0 2\n0 3\n1 1\n2 1\n2 0",
"output": "2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "6 7 10\n2 2\n0 0\n0 1\n1 0\n1 0\n3 5",
"output": "4\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3 6 0\n2 0\n1 0\n0 3\n0 1\n0 1\n6 1",
"output": "0\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/jays-apples2724/1 | Solve the following coding problem using the programming language python:
One day Jay, on getting his first salary, decides to distribute apples among the poverty-stricken persons. He gave each person 1kg of apples. People are coming in a queue and he makes sure that he gives every person 1 kg of apples only once. Every person is identified by a specific integer.
Given the length of the queue N followed by an array of N integers, denoting the persons in that queue, find the minimum kilograms of apples Jay will have to distribute.
Example 1:
ââ¬â¹Input : arr[ ] = {1, 1, 1, 1, 1}
Output : 1
Explanation:
For test case 1, the same person (identified
by the integer '1' comes again and again in
the queue, but Jay will not give him apples
again and again. He gave him apples only
once so minimum kg's of apples here
required-1kg).
ââ¬â¹Example 2:
Input : arr[ ] = {1, 2, 3, 1, 2}
Output : 3
Your Task:
This is a function problem. The input is already taken care of by the driver code. You only need to complete the function minimum_apple() that takes an array (arr), sizeOfArray (n) and return the minimum kilograms of apples Jay will have to distribute. The driver code takes care of the printing.
Expected Time Complexity: O(N).
Expected Auxiliary Space: O(N).
Constraints:
1 ≤ N ≤ 10^{5}
1 ≤ A_{i} ≤ 10^{5}
Write your solution by modifying this code:
```python
#User function Template for python3
def minimum_apple (arr, n) :
#Complete the function
```
Your solution should implemented in the function "minimum_apple". The inputs will be passed to it and it should return the correct solution.
Now solve the problem and return the code. | ```python
def minimum_apple(arr, n):
arr = list(set(arr))
return len(arr)
``` | vfc_138246 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/jays-apples2724/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": "minimum_apple",
"input": "arr[ ] = {1, 1, 1, 1, 1}",
"output": "1",
"type": "function_call"
},
{
"fn_name": "minimum_apple",
"input": "arr[ ] = {1, 2, 3, 1, 2}",
"output": "3",
"type": "function_call"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/26/C | Solve the following coding problem using the programming language python:
Once Bob decided to lay a parquet floor in his living room. The living room is of size n × m metres. Bob had planks of three types: a planks 1 × 2 meters, b planks 2 × 1 meters, and c planks 2 × 2 meters. Help Bob find out, if it is possible to parquet the living room with such a set of planks, and if it is possible, find one of the possible ways to do so. Bob doesn't have to use all the planks.
Input
The first input line contains 5 space-separated integer numbers n, m, a, b, c (1 ≤ n, m ≤ 100, 0 ≤ a, b, c ≤ 104), n and m — the living room dimensions, a, b and c — amount of planks 1 × 2, 2 × 1 и 2 × 2 respectively. It's not allowed to turn the planks.
Output
If it is not possible to parquet the room with such a set of planks, output IMPOSSIBLE. Otherwise output one of the possible ways to parquet the room — output n lines with m lower-case Latin letters each. Two squares with common sides should contain the same letters, if they belong to one and the same plank, and different letters otherwise. Different planks can be marked with one and the same letter (see examples). If the answer is not unique, output any.
Examples
Input
2 6 2 2 1
Output
aabcca
aabdda
Input
1 1 100 100 100
Output
IMPOSSIBLE
Input
4 4 10 10 10
Output
aabb
aabb
bbaa
bbaa
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
(n, m, a, b, c) = map(int, input().split())
mat = [0] * n
for i in range(n):
mat[i] = [0] * m
n1 = [min(n * m // 4, c), min(m // 2 * n, a), min(n // 2 * m, b)]
p = ['c', 'a', 'b']
z = ['d', 'e', 'f', 'g']
z1 = ['m', 'n', 'u', 'o']
z2 = ['p', 'q', 'r', 'w']
def fill(h, w):
if h <= 0 or w <= 0:
return True
i = 0
j = 0
for k in range(3):
while n1[k] > 0:
if k == 0:
if i % 4 and j % 4:
o = 3
elif i % 4 and (not j % 4):
o = 2
elif not i % 4 and j % 4:
o = 1
else:
o = 0
mat[i][j] = mat[i + 1][j] = mat[i][j + 1] = mat[i + 1][j + 1] = z[o]
if p[k] == 'a':
if j % 4:
o = 2
else:
o = 0
mat[i][j] = mat[i][j + 1] = z1[o]
mat[i + 1][j] = mat[i + 1][j + 1] = z1[o + 1]
elif p[k] == 'b':
if i % 4:
o = 0
else:
o = 2
mat[i][j] = mat[i + 1][j] = z2[o]
mat[i][j + 1] = mat[i + 1][j + 1] = z2[o + 1]
if k == 0:
n1[k] -= 1
else:
n1[k] -= 2
j += 2
if j >= w:
i += 2
j = 0
if i >= h:
return True
return False
def pmat():
for i in range(n):
for j in range(m):
print(mat[i][j], end='')
print('\n', end='')
def even(h, w):
k1 = 0
k2 = 0
if n1[1] % 2 == 1:
n1[1] -= 1
k1 = 1
if n1[2] % 2 == 1:
n1[2] -= 1
k2 = 1
if fill(h, w):
n1[1] += k1
n1[2] += k2
return True
else:
n1[1] += k1
n1[2] += k2
return False
if n * m % 2 == 0:
if n % 2 == 0 and m % 2 == 0:
if even(n, m):
pmat()
else:
print('IMPOSSIBLE')
elif n % 2 == 0 and m % 2 != 0:
n1 = [min(n * m // 4, c), min(m // 2 * n, a), min(n // 2 * m, b)]
p = ['c', 'a', 'b']
f = 'b'
if even(n, m - 1):
for i in range(0, n, 2):
mat[i][m - 1] = f
mat[i + 1][m - 1] = f
if f == 'a':
f = 'b'
else:
f = 'a'
n1[2] -= 1
else:
if n1[2] >= 0:
pmat()
else:
print('IMPOSSIBLE')
else:
print('IMPOSSIBLE')
else:
n1 = [min(n * m // 4, c), min(n // 2 * m, b), min(m // 2 * n, a)]
p = ['c', 'b', 'a']
f = 'a'
if even(n - 1, m):
for i in range(0, m, 2):
mat[n - 1][i] = f
mat[n - 1][i + 1] = f
if f == 'a':
f = 'b'
else:
f = 'a'
n1[2] -= 1
else:
if n1[2] >= 0:
pmat()
else:
print('IMPOSSIBLE')
else:
print('IMPOSSIBLE')
elif n * m % 2 != 0:
print('IMPOSSIBLE')
``` | vfc_138247 | {
"difficulty": "hard",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/26/C",
"time_limit": "2.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "100 100 10000 10000 10000\n",
"output": 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abbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaa\nbbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaabbaa\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "100 100 0 0 0\n",
"output": "IMPOSSIBLE\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "100 100 2498 2498 1\n",
"output": "IMPOSSIBLE\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "1 2 0 1 0\n",
"output": "IMPOSSIBLE\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | Solve the following coding problem using the programming language python:
A dial lock is a kind of lock which has some dials with printed numbers. It has a special sequence of numbers, namely an unlocking sequence, to be opened.
You are working at a manufacturer of dial locks. Your job is to verify that every manufactured lock is unlocked by its unlocking sequence. In other words, you have to rotate many dials of many many locks.
It’s a very hard and boring task. You want to reduce time to open the locks. It’s a good idea to rotate multiple dials at one time. It is, however, a difficult problem to find steps to open a given lock with the fewest rotations. So you decided to write a program to find such steps for given initial and unlocking sequences.
Your company’s dial locks are composed of vertically stacked k (1 ≤ k ≤ 10) cylindrical dials. Every dial has 10 numbers, from 0 to 9, along the side of the cylindrical shape from the left to the right in sequence. The neighbor on the right of 9 is 0.
A dial points one number at a certain position. If you rotate a dial to the left by i digits, the dial newly points the i-th right number. In contrast, if you rotate a dial to the right by i digits, it points the i-th left number. For example, if you rotate a dial pointing 8 to the left by 3 digits, the dial newly points 1.
You can rotate more than one adjacent dial at one time. For example, consider a lock with 5 dials. You can rotate just the 2nd dial. You can rotate the 3rd, 4th and 5th dials at the same time. But you cannot rotate the 1st and 3rd dials at one time without rotating the 2nd dial. When you rotate multiple dials, you have to rotate them to the same direction by the same digits.
Your program is to calculate the fewest number of rotations to unlock, for given initial and unlocking sequences. Rotating one or more adjacent dials to the same direction by the same digits is counted as one rotation.
Input
The input consists of multiple datasets. Each datset consists of two lines. The first line contains an integer k. The second lines contain two strings, separated by a space, which indicate the initial and unlocking sequences.
The last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.
Output
For each dataset, print the minimum number of rotations in one line.
Example
Input
4
1357 4680
6
777777 003330
0
Output
1
2
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import math, string, itertools, fractions, heapq, collections, re, array, bisect, sys, random, time, copy, functools
sys.setrecursionlimit(10 ** 7)
inf = 10 ** 20
eps = 1.0 / 10 ** 13
mod = 10 ** 9 + 7
dd = [(-1, 0), (0, 1), (1, 0), (0, -1)]
ddn = [(-1, 0), (-1, 1), (0, 1), (1, 1), (1, 0), (1, -1), (0, -1), (-1, -1)]
def LI():
return [int(x) for x in sys.stdin.readline().split()]
def LI_():
return [int(x) - 1 for x in sys.stdin.readline().split()]
def LF():
return [float(x) for x in sys.stdin.readline().split()]
def LS():
return sys.stdin.readline().split()
def I():
return int(sys.stdin.readline())
def F():
return float(sys.stdin.readline())
def S():
return input()
def pf(s):
return print(s, flush=True)
def main():
rr = []
def f(n):
(a, b) = LS()
if a == b:
return 0
a = [int(c) for c in a]
b = [int(c) for c in b]
aa = [a]
ad = set()
ad.add(tuple(a))
r = 0
while True:
r += 1
na = []
for a in aa:
ti = 0
for i in range(r - 1, n):
if a[i] != b[i]:
ti = i
break
sa = b[ti] - a[ti]
for j in range(ti + 1, n + 1):
t = [(a[i] + sa) % 10 if ti <= i < j else a[i] for i in range(n)]
k = tuple(t)
if k in ad:
continue
if t == b:
return r
ad.add(k)
na.append(t)
aa = na
while True:
n = I()
if n == 0:
break
rr.append(f(n))
return '\n'.join(map(str, rr))
print(main())
``` | vfc_138251 | {
"difficulty": "unknown_difficulty",
"memory_limit": "134.217728 megabytes",
"memory_limit_bytes": null,
"problem_url": null,
"time_limit": "8.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "4\n1433 4680\n6\n777777 003330\n0",
"output": "4\n2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n1357 4680\n6\n509138 003330\n0",
"output": "1\n4\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n1357 4680\n6\n297443 003330\n0",
"output": "1\n5\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n1357 5363\n6\n777777 003330\n0",
"output": "3\n2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "4\n1357 1908\n6\n509138 003330\n0",
"output": "3\n4\n",
"type": "stdin_stdout"
}
]
} |
|
taco | verifiable_code | https://codeforces.com/problemset/problem/175/B | Solve the following coding problem using the programming language python:
Vasya has been playing Plane of Tanks with his friends the whole year. Now it is time to divide the participants into several categories depending on their results.
A player is given a non-negative integer number of points in each round of the Plane of Tanks. Vasya wrote results for each round of the last year. He has n records in total.
In order to determine a player's category consider the best result obtained by the player and the best results of other players. The player belongs to category:
* "noob" — if more than 50% of players have better results;
* "random" — if his result is not worse than the result that 50% of players have, but more than 20% of players have better results;
* "average" — if his result is not worse than the result that 80% of players have, but more than 10% of players have better results;
* "hardcore" — if his result is not worse than the result that 90% of players have, but more than 1% of players have better results;
* "pro" — if his result is not worse than the result that 99% of players have.
When the percentage is calculated the player himself is taken into account. That means that if two players played the game and the first one gained 100 points and the second one 1000 points, then the first player's result is not worse than the result that 50% of players have, and the second one is not worse than the result that 100% of players have.
Vasya gave you the last year Plane of Tanks results. Help Vasya determine each player's category.
Input
The first line contains the only integer number n (1 ≤ n ≤ 1000) — a number of records with the players' results.
Each of the next n lines contains a player's name and the amount of points, obtained by the player for the round, separated with a space. The name contains not less than 1 and no more than 10 characters. The name consists of lowercase Latin letters only. It is guaranteed that any two different players have different names. The amount of points, obtained by the player for the round, is a non-negative integer number and does not exceed 1000.
Output
Print on the first line the number m — the number of players, who participated in one round at least.
Each one of the next m lines should contain a player name and a category he belongs to, separated with space. Category can be one of the following: "noob", "random", "average", "hardcore" or "pro" (without quotes). The name of each player should be printed only once. Player names with respective categories can be printed in an arbitrary order.
Examples
Input
5
vasya 100
vasya 200
artem 100
kolya 200
igor 250
Output
4
artem noob
igor pro
kolya random
vasya random
Input
3
vasya 200
kolya 1000
vasya 1000
Output
2
kolya pro
vasya pro
Note
In the first example the best result, obtained by artem is not worse than the result that 25% of players have (his own result), so he belongs to category "noob". vasya and kolya have best results not worse than the results that 75% players have (both of them and artem), so they belong to category "random". igor has best result not worse than the result that 100% of players have (all other players and himself), so he belongs to category "pro".
In the second example both players have the same amount of points, so they have results not worse than 100% players have, so they belong to category "pro".
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
from collections import defaultdict
from bisect import bisect_left
(p, n) = (defaultdict(int), int(input()))
for i in range(n):
(a, b) = input().split()
p[a] = max(p[a], int(b))
(p, n) = (sorted(((b, a) for (a, b) in p.items())), len(p))
t = [0] + [bisect_left(p, (p[n - 1 - n // k][0], '')) for k in [2, 5, 10, 100]] + [n]
s = ['noob', 'random', 'average', 'hardcore', 'pro']
for i in range(1, len(t)):
d = s[i - 1]
for j in range(t[i - 1], t[i]):
p[j] = p[j][1] + ' ' + d
print(n)
print('\n'.join(p))
``` | vfc_138255 | {
"difficulty": "medium",
"memory_limit": "256.0 megabytes",
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/175/B",
"time_limit": "2.0 seconds"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "10\nj 10\ni 9\nh 8\ng 7\nf 6\ne 5\nd 4\nc 3\nb 2\na 1\n",
"output": "10\na noob\nb noob\nc noob\nd noob\ne random\nf random\ng random\nh average\ni hardcore\nj pro\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://codeforces.com/problemset/problem/1335/F | Solve the following coding problem using the programming language python:
There is a rectangular grid of size $n \times m$. Each cell of the grid is colored black ('0') or white ('1'). The color of the cell $(i, j)$ is $c_{i, j}$. You are also given a map of directions: for each cell, there is a direction $s_{i, j}$ which is one of the four characters 'U', 'R', 'D' and 'L'.
If $s_{i, j}$ is 'U' then there is a transition from the cell $(i, j)$ to the cell $(i - 1, j)$; if $s_{i, j}$ is 'R' then there is a transition from the cell $(i, j)$ to the cell $(i, j + 1)$; if $s_{i, j}$ is 'D' then there is a transition from the cell $(i, j)$ to the cell $(i + 1, j)$; if $s_{i, j}$ is 'L' then there is a transition from the cell $(i, j)$ to the cell $(i, j - 1)$.
It is guaranteed that the top row doesn't contain characters 'U', the bottom row doesn't contain characters 'D', the leftmost column doesn't contain characters 'L' and the rightmost column doesn't contain characters 'R'.
You want to place some robots in this field (at most one robot in a cell). The following conditions should be satisfied.
Firstly, each robot should move every time (i.e. it cannot skip the move). During one move each robot goes to the adjacent cell depending on the current direction. Secondly, you have to place robots in such a way that there is no move before which two different robots occupy the same cell (it also means that you cannot place two robots in the same cell). I.e. if the grid is "RL" (one row, two columns, colors does not matter there) then you can place two robots in cells $(1, 1)$ and $(1, 2)$, but if the grid is "RLL" then you cannot place robots in cells $(1, 1)$ and $(1, 3)$ because during the first second both robots will occupy the cell $(1, 2)$.
The robots make an infinite number of moves.
Your task is to place the maximum number of robots to satisfy all the conditions described above and among all such ways, you have to choose one where the number of black cells occupied by robots before all movements is the maximum possible. Note that you can place robots only before all movements.
You have to answer $t$ independent test cases.
-----Input-----
The first line of the input contains one integer $t$ ($1 \le t \le 5 \cdot 10^4$) — the number of test cases. Then $t$ test cases follow.
The first line of the test case contains two integers $n$ and $m$ ($1 < nm \le 10^6$) — the number of rows and the number of columns correspondingly.
The next $n$ lines contain $m$ characters each, where the $j$-th character of the $i$-th line is $c_{i, j}$ ($c_{i, j}$ is either '0' if the cell $(i, j)$ is black or '1' if the cell $(i, j)$ is white).
The next $n$ lines also contain $m$ characters each, where the $j$-th character of the $i$-th line is $s_{i, j}$ ($s_{i, j}$ is 'U', 'R', 'D' or 'L' and describes the direction of the cell $(i, j)$).
It is guaranteed that the sum of the sizes of fields does not exceed $10^6$ ($\sum nm \le 10^6$).
-----Output-----
For each test case, print two integers — the maximum number of robots you can place to satisfy all the conditions described in the problem statement and the maximum number of black cells occupied by robots before all movements if the number of robots placed is maximized. Note that you can place robots only before all movements.
-----Example-----
Input
3
1 2
01
RL
3 3
001
101
110
RLL
DLD
ULL
3 3
000
000
000
RRD
RLD
ULL
Output
2 1
4 3
2 2
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
import sys
from collections import deque
input = sys.stdin.readline
t = int(input())
for _ in range(t):
(n, m) = map(int, input().split())
s = [input() for i in range(n)]
grid = [input() for i in range(n)]
robot_cnt = 0
black_cnt = 0
graph = [-1] * (n * m)
rev_graph = [[] for i in range(n * m)]
for i in range(n):
for j in range(m):
if grid[i][j] == 'U':
graph[i * m + j] = (i - 1) * m + j
rev_graph[(i - 1) * m + j].append(i * m + j)
elif grid[i][j] == 'R':
graph[i * m + j] = i * m + (j + 1)
rev_graph[i * m + (j + 1)].append(i * m + j)
elif grid[i][j] == 'D':
graph[i * m + j] = (i + 1) * m + j
rev_graph[(i + 1) * m + j].append(i * m + j)
elif grid[i][j] == 'L':
graph[i * m + j] = i * m + (j - 1)
rev_graph[i * m + (j - 1)].append(i * m + j)
is_start = [True] * (n * m)
for i in graph:
is_start[i] = False
is_cycle = [False] * (n * m)
period = [0] * (n * m)
for i in range(n * m):
if not is_start[i]:
continue
st = i
period[i] = 1
while True:
nxt_i = graph[i]
if period[nxt_i] < 0:
tmp = period[nxt_i]
break
if period[nxt_i] > 0:
tmp = -(period[i] - period[nxt_i] + 1)
is_cycle[nxt_i] = True
break
period[graph[i]] = period[i] + 1
i = graph[i]
i = st
period[i] = tmp
while True:
nxt_i = graph[i]
if period[nxt_i] < 0:
break
period[graph[i]] = tmp
i = graph[i]
for i in range(n * m):
if period[i] == 0:
robot_cnt += 1
if s[i // m][i % m] == '0':
black_cnt += 1
for i in range(n * m):
if not is_cycle[i]:
continue
MOD = -period[i]
period[i] = 0
is_black = [False] * MOD
if s[i // m][i % m] == '0':
is_black[0] = True
q = deque([i])
while q:
v = q.pop()
for nxt_v in rev_graph[v]:
if period[nxt_v] >= 0:
continue
period[nxt_v] = (period[v] + 1) % MOD
if s[nxt_v // m][nxt_v % m] == '0':
is_black[period[nxt_v]] = True
q.append(nxt_v)
robot_cnt += MOD
black_cnt += sum(is_black)
print(robot_cnt, black_cnt)
``` | vfc_138259 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://codeforces.com/problemset/problem/1335/F",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "3\n1 2\n01\nRL\n3 3\n001\n101\n110\nRLL\nDLD\nULL\n3 3\n000\n000\n000\nRRD\nRLD\nULL\n",
"output": "2 1\n4 3\n2 2\n",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "3\n1 2\n01\nRL\n3 3\n000\n101\n110\nRLL\nDLD\nULL\n3 3\n000\n000\n000\nRRD\nRLD\nULL\n",
"output": "2 1\n4 3\n2 2\n",
"type": "stdin_stdout"
}
]
} |
taco | verifiable_code | https://practice.geeksforgeeks.org/problems/faulty-keyboard2842/1 | Solve the following coding problem using the programming language python:
Geek has a unique keyboard containing only the numpad keys. ie - 1,2,3,4,5,6,7,8,9,0. But the keyboard is damaged and can only process M keys. Geek is supposed to use the keyboard to type as many natural numbers as possible starting from 1. What will be the greatest natural number he will type?
Example 1:
Input:
M = 5
Output: 5
Explaination:
Geek can only press 5 keys. He will type
1,2,3,4,5. The greatest number is 5.
Example 2:
Input:
M = 15
Output: 12
Explaination:
1 key each from 1 to 9.
2 keys each from 10 to 12.
Total keys pressed = 15.
Your Task:
You do not need to read input or print anything. Your task is to complete the function maxNatural() which takes M as input parameter and returns the maximum natural number possible to get after pressing M keys.
Expected Time Complexity: O(logN)
Expected Auxiliary Space: O(1)
Constraints:
1 ≤ M ≤ 38890
Write your solution by modifying this code:
```python
#User function Template for python3
class Solution:
def maxNatural(self, M):
# code here
```
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code. | ```python
class Solution:
def maxNatural(self, M):
if M <= 9:
return M
M -= 9
if M <= 180:
M = M // 2
return 9 + M
M -= 180
if M <= 2700:
M = M // 3
return 99 + M
M -= 2700
if M <= 36000:
M = M // 4
return 999 + M
M -= 36000
if M <= 38890:
M = M // 5
return 9999 + M
return 0
``` | vfc_138263 | {
"difficulty": "easy",
"memory_limit": null,
"memory_limit_bytes": null,
"problem_url": "https://practice.geeksforgeeks.org/problems/faulty-keyboard2842/1",
"time_limit": "None"
} | {
"language": "python",
"test_cases": [
{
"fn_name": null,
"input": "M = 5",
"output": "5",
"type": "stdin_stdout"
},
{
"fn_name": null,
"input": "M = 15",
"output": "12",
"type": "stdin_stdout"
}
]
} |
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