message stringlengths 2 57.2k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 61 108k | cluster float64 22 22 | __index_level_0__ int64 122 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The f... | instruction | 0 | 102,170 | 22 | 204,340 |
No | output | 1 | 102,170 | 22 | 204,341 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The f... | instruction | 0 | 102,171 | 22 | 204,342 |
No | output | 1 | 102,171 | 22 | 204,343 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The f... | instruction | 0 | 102,172 | 22 | 204,344 |
No | output | 1 | 102,172 | 22 | 204,345 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of t... | instruction | 0 | 102,269 | 22 | 204,538 |
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import io,os, math
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# python3 15.py<in>op
t = int(input())
for _ in range(t):
n = int(input())
ans = 0
i = 3
while((((i*i) + 1)//2) <=n):
ans+=1
i+=2
... | output | 1 | 102,269 | 22 | 204,539 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of t... | instruction | 0 | 102,270 | 22 | 204,540 |
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import math
t=int(input())
for _ in range (t):
n=int(input())
count=-1
k=1
i=1
z=int(math.sqrt(((n-1)/2)+0.25)-0.5)
print(z)
``` | output | 1 | 102,270 | 22 | 204,541 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of t... | instruction | 0 | 102,271 | 22 | 204,542 |
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import bisect
from itertools import accumulate
import os
import sys
import math
from decimal import *
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file... | output | 1 | 102,271 | 22 | 204,543 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of t... | instruction | 0 | 102,272 | 22 | 204,544 |
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import math
for i in range(int(input())):
n=int(input())
print(math.floor(((math.sqrt(2*n-1)+1)//2)-1))
``` | output | 1 | 102,272 | 22 | 204,545 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of t... | instruction | 0 | 102,273 | 22 | 204,546 |
Tags: binary search, brute force, math, number theory
Correct Solution:
```
t=int(input())
for i in range(t):
n=int(input())
m=int(pow(2*n-1,0.5))
ans=(m+1)//2
print(ans-1)
``` | output | 1 | 102,273 | 22 | 204,547 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of t... | instruction | 0 | 102,274 | 22 | 204,548 |
Tags: binary search, brute force, math, number theory
Correct Solution:
```
t=int(input())
for i in range(t):
n=int(input())
m=int((2*n-1)**(1/2))
k=int((m-1)/2)
print(k)
``` | output | 1 | 102,274 | 22 | 204,549 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of t... | instruction | 0 | 102,275 | 22 | 204,550 |
Tags: binary search, brute force, math, number theory
Correct Solution:
```
import sys
input = sys.stdin.readline
t=int(input())
for _ in range(t):
n=int(input())
i=3
ans=0
#print(i*i-1)
while i<=n and ((i*i-1)//2)<=n:
#print('ads',_)
if (i*i-1)%2==0 and (i*i-1)//2>=i and i*i-(i... | output | 1 | 102,275 | 22 | 204,551 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A Pythagorean triple is a triple of integer numbers (a, b, c) such that it is possible to form a right triangle with the lengths of the first cathetus, the second cathetus and the hypotenuse equal to a, b and c, respectively. An example of t... | instruction | 0 | 102,276 | 22 | 204,552 |
Tags: binary search, brute force, math, number theory
Correct Solution:
```
def answer(n):
l=int(((2*n)-1)**0.5)
c=0
for i in range(3,l+1,2):
c+=1
print(c)
t=int(input())
for i in range(t):
n=int(input())
answer(n)
``` | output | 1 | 102,276 | 22 | 204,553 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image... | instruction | 0 | 102,351 | 22 | 204,702 |
Tags: brute force, implementation, two pointers
Correct Solution:
```
"""
Author - Satwik Tiwari .
19th Jan , 2021 - Tuesday
"""
#===============================================================================================
#importing some useful libraries.
from __future__ import division, print_function
#... | output | 1 | 102,351 | 22 | 204,703 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image... | instruction | 0 | 102,352 | 22 | 204,704 |
Tags: brute force, implementation, two pointers
Correct Solution:
```
from fractions import Fraction
x,y,n=map(int,input().split())
ans=Fraction(x,y).limit_denominator(n)
num=ans.numerator
denom=ans.denominator
print (str(num) + '/' + str(denom))
``` | output | 1 | 102,352 | 22 | 204,705 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image... | instruction | 0 | 102,353 | 22 | 204,706 |
Tags: brute force, implementation, two pointers
Correct Solution:
```
from fractions import Fraction
x, y, n = input().split()
x = int(x)
y = int(y)
n = int(n)
if Fraction(x / y).limit_denominator(n) == 0:
print('0/1')
elif Fraction(x / y).limit_denominator(n) == int(Fraction(x, y).limit_denominator(n)):
print... | output | 1 | 102,353 | 22 | 204,707 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image... | instruction | 0 | 102,354 | 22 | 204,708 |
Tags: brute force, implementation, two pointers
Correct Solution:
```
class Fraction:
def __init__(self, x, y):
self.x = x
self.y = y
def __sub__(self, a):
return Fraction(self.x * a.y - a.x * self.y, self.y * a.y)
def __lt__(self, a):
return self.x * a.y < self.y * a.x
def __abs__(s... | output | 1 | 102,354 | 22 | 204,709 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image... | instruction | 0 | 102,355 | 22 | 204,710 |
Tags: brute force, implementation, two pointers
Correct Solution:
```
from fractions import Fraction as frac
a, b, n = map(int, input().split())
f = frac(a, b).limit_denominator(n)
print(str(f.numerator)+'/'+str(f.denominator))
``` | output | 1 | 102,355 | 22 | 204,711 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image... | instruction | 0 | 102,356 | 22 | 204,712 |
Tags: brute force, implementation, two pointers
Correct Solution:
```
"""
Author : co_devil Chirag Garg
Institute : JIIT
"""
from __future__ import division, print_function
from sys import stdin,stdout
import itertools, os, sys, threading
from collections import deque, Counter, OrderedDict, defaultdict
import heapq
... | output | 1 | 102,356 | 22 | 204,713 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image... | instruction | 0 | 102,357 | 22 | 204,714 |
Tags: brute force, implementation, two pointers
Correct Solution:
```
import sys
s = input()
all = s.split()
ans = "lol"
n = int(all[2])
x = float(all[0])
y = float(all[1])
a = 0
b = 1
dif = x / y
for i in range(1, n + 1):
#print(str(a) + " : " + str(b) + " : " + str(dif))
na = int((x * i) / y)
if (dif >... | output | 1 | 102,357 | 22 | 204,715 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value <image... | instruction | 0 | 102,358 | 22 | 204,716 |
Tags: brute force, implementation, two pointers
Correct Solution:
```
def gcd(a, b):
return gcd(b % a, a) if a else b
x, y, n = map(int, input().split())
d = gcd(x, y)
x, y = x // d, y // d
if n < y:
d = [min(i, y - i) for i in ((x * i) % y for i in range(0, n + 1))]
for i in range(n - 1, 0, -1):
if... | output | 1 | 102,358 | 22 | 204,717 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integer... | instruction | 0 | 102,361 | 22 | 204,722 |
Yes | output | 1 | 102,361 | 22 | 204,723 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integer... | instruction | 0 | 102,365 | 22 | 204,730 |
No | output | 1 | 102,365 | 22 | 204,731 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction <image> whose denominator is no more than n.
Formally, you should find such pair of integer... | instruction | 0 | 102,366 | 22 | 204,732 |
No | output | 1 | 102,366 | 22 | 204,733 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maxim... | instruction | 0 | 103,085 | 22 | 206,170 |
Tags: dp
Correct Solution:
```
n, m, k = map(int, input().split())
# a = []
# for _ in range(n):
# a.append(list(map(int, input().split())))
dp = [float("-inf") for i in range(k)]
dp[0] = 0
sz = m // 2
for _ in range(n):
a = list(map(int, input().split()))
pre = dp
dp = [[float("-inf") for _ in range(k)] for _ i... | output | 1 | 103,085 | 22 | 206,171 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maxim... | instruction | 0 | 103,086 | 22 | 206,172 |
Tags: dp
Correct Solution:
```
import sys,math,itertools
from collections import Counter,deque,defaultdict
from bisect import bisect_left,bisect_right
mod = 10**9+7
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def IND(i,j):
return... | output | 1 | 103,086 | 22 | 206,173 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maxim... | instruction | 0 | 103,087 | 22 | 206,174 |
Tags: dp
Correct Solution:
```
from math import inf as _inf
import sys as _sys
_NEGATIVE_INF = -_inf
def main():
n, m, k = _read_ints()
a = tuple(tuple(_read_ints()) for i_row in range(n))
result = find_max_sum(a, k)
print(result)
def _read_line():
result = _sys.stdin.readline()
assert resu... | output | 1 | 103,087 | 22 | 206,175 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maxim... | instruction | 0 | 103,088 | 22 | 206,176 |
Tags: dp
Correct Solution:
```
n, m, k = map(int, input().split())
l = m // 2
p = [-1] * k
p[0] = 0
for _ in range(n):
t = [[-1] * (l + 1) for i in range(k)]
t[0][0] = 0
for q in map(int, input().split()):
for j in range(l - 1, -1, -1):
for i in range(k):
if t[i][j] != -1... | output | 1 | 103,088 | 22 | 206,177 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maxim... | instruction | 0 | 103,089 | 22 | 206,178 |
Tags: dp
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
def main():
n, m, k = getints()
m //= 2
dp = [int(-1e9)] * k
dp[0] = 0
for _ in range(n):
tmp = [[int(-1e9)] * (m + 1) for _ in range(k)]
tmp[0][0] = 0
for a in getints():
for x i... | output | 1 | 103,089 | 22 | 206,179 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maxim... | instruction | 0 | 103,090 | 22 | 206,180 |
Tags: dp
Correct Solution:
```
import sys
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for k in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for k in range(c)] for k in range(b)] for i in r... | output | 1 | 103,090 | 22 | 206,181 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maxim... | instruction | 0 | 103,091 | 22 | 206,182 |
Tags: dp
Correct Solution:
```
n, m, k = map(int, input().split())
dp = [-10000000000 for i in range(k)]
dp[0] = 0
sz = m//2
mat = []
for i in range(n):
mat.append(list(map(int,input().split())))
for a in mat:
pre = dp
dp = [[-10000000000 for i in range(k)] for j in range(sz+1)]
dp[0] = pre
for x in a:
for i in... | output | 1 | 103,091 | 22 | 206,183 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maxim... | instruction | 0 | 103,092 | 22 | 206,184 |
Tags: dp
Correct Solution:
```
# by the authority of GOD author: manhar singh sachdev #
import os,sys
from io import BytesIO, IOBase
def main():
n,m,k = map(int,input().split())
arr = [list(map(int,input().split())) for _ in range(n)]
dp = [[[0]*k for _ in range(m//2+1)]for _ in range(n)]
for i in... | output | 1 | 103,092 | 22 | 206,185 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their ... | instruction | 0 | 103,093 | 22 | 206,186 |
Yes | output | 1 | 103,093 | 22 | 206,187 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their ... | instruction | 0 | 103,094 | 22 | 206,188 |
Yes | output | 1 | 103,094 | 22 | 206,189 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their ... | instruction | 0 | 103,095 | 22 | 206,190 |
Yes | output | 1 | 103,095 | 22 | 206,191 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their ... | instruction | 0 | 103,096 | 22 | 206,192 |
Yes | output | 1 | 103,096 | 22 | 206,193 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their ... | instruction | 0 | 103,097 | 22 | 206,194 |
No | output | 1 | 103,097 | 22 | 206,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their ... | instruction | 0 | 103,098 | 22 | 206,196 |
No | output | 1 | 103,098 | 22 | 206,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their ... | instruction | 0 | 103,099 | 22 | 206,198 |
No | output | 1 | 103,099 | 22 | 206,199 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given a matrix a of size n × m consisting of integers.
You can choose no more than \left⌊m/2\right⌋ elements in each row. Your task is to choose these elements in such a way that their ... | instruction | 0 | 103,100 | 22 | 206,200 |
No | output | 1 | 103,100 | 22 | 206,201 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Everybody seems to think that the Martians are green, but it turns out they are metallic pink and fat. Ajs has two bags of distinct nonnegative integers. The bags are disjoint, and the union of the sets of numbers in the bags is \{0,1,…,M-1\... | instruction | 0 | 103,697 | 22 | 207,394 |
Tags: hashing, number theory
Correct Solution:
```
import sys
input = sys.stdin.readline
def main():
n, m = map(int, input().split())
a = list(map(int, input().split())) + [0]*500000
ans_S = 0
a[n] = a[0] + m
s = [0]*600600
for i in range(n):
s[i] = a[i + 1] - a[i]
s[n] = -1
for... | output | 1 | 103,697 | 22 | 207,395 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Everybody seems to think that the Martians are green, but it turns out they are metallic pink and fat. Ajs has two bags of distinct nonnegative integers. The bags are disjoint, and the union of ... | instruction | 0 | 103,698 | 22 | 207,396 |
No | output | 1 | 103,698 | 22 | 207,397 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and b) or say that there is no such pair.
Input
T... | instruction | 0 | 103,849 | 22 | 207,698 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import math
import sys
from collections import deque
from fractions import Fraction
# ------------------------------warmup----------------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
... | output | 1 | 103,849 | 22 | 207,699 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and b) or say that there is no such pair.
Input
T... | instruction | 0 | 103,850 | 22 | 207,700 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import math as mt
def sieve(MAXN):
spf = [0 for i in range(MAXN)]
spf[1] = 1
for i in range(2, MAXN):
# marking smallest prime factor
# for every number to be itself.
spf[i] = i
# separ... | output | 1 | 103,850 | 22 | 207,701 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and b) or say that there is no such pair.
Input
T... | instruction | 0 | 103,851 | 22 | 207,702 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
from sys import stdout, stdin
import os,io
# input = stdin.readline
# input_all = stdin.read
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# input_all = io.BytesIO(os.read(0,os.fstat(0).st_size)).read
def read_int():
return map(int,... | output | 1 | 103,851 | 22 | 207,703 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and b) or say that there is no such pair.
Input
T... | instruction | 0 | 103,852 | 22 | 207,704 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import io
import math
import os
from collections import Counter
"""
def primeFactors(n):
assert n >= 1
factors = Counter()
while n % 2 == 0:
factors[2] += 1
n //= 2
x = 3
while x * x <= n:
while n % x =... | output | 1 | 103,852 | 22 | 207,705 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and b) or say that there is no such pair.
Input
T... | instruction | 0 | 103,853 | 22 | 207,706 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import sys, os, io
def rs(): return sys.stdin.readline().rstrip()
def ri(): return int(sys.stdin.readline())
def ria(): return list(map(int, sys.stdin.readline().split()))
def ws(s): sys.stdout.write(s + '\n')
def wi(n): sys.stdout.write(str(n) + ... | output | 1 | 103,853 | 22 | 207,707 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and b) or say that there is no such pair.
Input
T... | instruction | 0 | 103,854 | 22 | 207,708 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
n=int(input())
al=list(map(int,input().split()))
MX=max(al)+5
seive=MX*[-1]
for i in range(2,MX):
if (seive[i]==-1):
seive[i]=i
j=i*i
while (j<MX):
if (seive[j]==-1):
seive[j]=i
j+=i
#print("seive = ",seive)
ans_d1=[]
ans_d2... | output | 1 | 103,854 | 22 | 207,709 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and b) or say that there is no such pair.
Input
T... | instruction | 0 | 103,855 | 22 | 207,710 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode o... | output | 1 | 103,855 | 22 | 207,711 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and b) or say that there is no such pair.
Input
T... | instruction | 0 | 103,856 | 22 | 207,712 |
Tags: constructive algorithms, math, number theory
Correct Solution:
```
import sys
from collections import deque, Counter
from itertools import product
from functools import reduce
input = sys.stdin.buffer.readline
n = int(input())
ls = list(map(int, input().split()))
mx = max(ls)
pr = [i for i in range(mx+1)]
for u... | output | 1 | 103,856 | 22 | 207,713 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and ... | instruction | 0 | 103,857 | 22 | 207,714 |
Yes | output | 1 | 103,857 | 22 | 207,715 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given n integers a_1, a_2, ..., a_n.
For each a_i find its two divisors d_1 > 1 and d_2 > 1 such that \gcd(d_1 + d_2, a_i) = 1 (where \gcd(a, b) is the greatest common divisor of a and ... | instruction | 0 | 103,858 | 22 | 207,716 |
Yes | output | 1 | 103,858 | 22 | 207,717 |
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