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 |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,029 | 22 | 80,058 |
Tags: brute force, math, number theory
Correct Solution:
```
def check(n):
d = 2
while d*d <= n:
if n % d == 0: return False
d += 1
return True
n = int(input())
flag = False
if check(n) and n > 10: print(1,'\n',n)
elif n >= 9:
Ans = [3]
n -= 3
for i in range(2,n):
if chec... | output | 1 | 40,029 | 22 | 80,059 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,030 | 22 | 80,060 |
Tags: brute force, math, number theory
Correct Solution:
```
def isPrime(x) :
if x == 1: return False
if x == 2: return True
if x%2 == 0: return False
i = 3
while i*i <= x :
if x % i == 0 :
return False
i += 2
return True
n = int(input())
if isPrime(n) :
ans... | output | 1 | 40,030 | 22 | 80,061 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,031 | 22 | 80,062 |
Tags: brute force, math, number theory
Correct Solution:
```
import math
def is_prime(a):
for i in range(2, int(math.sqrt(a) + 1)):
if a % i == 0:
return False
return True
def solve():
n, = map(int, input().split())
if is_prime(n):
print(1)
print(n)
retur... | output | 1 | 40,031 | 22 | 80,063 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,032 | 22 | 80,064 |
Tags: brute force, math, number theory
Correct Solution:
```
def isPrime(n) :
if (n==3 or n==2) :
return True
if (n % 2 == 0 or n % 3 == 0) :
return False
i = 5
while(i * i <= n) :
if (n % i == 0 or n % (i + 2) == 0) :
return False
i = i + 6
return Tru... | output | 1 | 40,032 | 22 | 80,065 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,033 | 22 | 80,066 |
Tags: brute force, math, number theory
Correct Solution:
```
l=list()
def prime(N):
count=0
i=1
while(i*i<=N):
if i*i==N:
count=count+1
elif N%i==0:
count=count+2
if count>2:
return 0
i=i+1
if count==2:
return 1
else:
return 0
n=int(input())
if n%2==0:
for j in range(2,n):
s=prime(j)
t=pr... | output | 1 | 40,033 | 22 | 80,067 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,034 | 22 | 80,068 |
Tags: brute force, math, number theory
Correct Solution:
```
import math as m
n=int(input())
def prime(n):
if n==1:
return False
for j in range(2,int(m.sqrt(n))+1):
if n%j==0:
return False
return True
if prime(n):
print(1)
print(n)
else :
ans=[]
ans.append(3)
... | output | 1 | 40,034 | 22 | 80,069 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,035 | 22 | 80,070 |
Tags: brute force, math, number theory
Correct Solution:
```
######### ## ## ## #### ##### ## # ## # ##
# # # # # # # # # # # # # # # # # # #
# # # # ### # # # # # # # # # # # #
# ##### # # # # ### # # # # # # # # #####
# # ... | output | 1 | 40,035 | 22 | 80,071 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,036 | 22 | 80,072 |
Tags: brute force, math, number theory
Correct Solution:
```
import math
n = int(input())
p = [0 for _ in range(1001)]
x = 2
p[0] = 1
p[1] = 1
while x * x <= 1001:
for i in range(2 * x, 1001, x):
p[i] = 1
x += 1
pr = 0
def isprime(num):
for i in range(2, int(math.sqrt(n)) + 1):
if num % i... | output | 1 | 40,036 | 22 | 80,073 |
Provide tags and a correct Python 2 solution for this coding contest problem.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.
More formally, you are given an odd... | instruction | 0 | 40,037 | 22 | 80,074 |
Tags: brute force, math, number theory
Correct Solution:
```
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
raw_input = stdin.readline
pr = stdout.write
mod=10**9+7
def ni():
return int(raw_input())
def li():
return map(int,raw_inpu... | output | 1 | 40,037 | 22 | 80,075 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr... | instruction | 0 | 40,038 | 22 | 80,076 |
Yes | output | 1 | 40,038 | 22 | 80,077 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr... | instruction | 0 | 40,039 | 22 | 80,078 |
Yes | output | 1 | 40,039 | 22 | 80,079 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr... | instruction | 0 | 40,040 | 22 | 80,080 |
Yes | output | 1 | 40,040 | 22 | 80,081 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr... | instruction | 0 | 40,041 | 22 | 80,082 |
Yes | output | 1 | 40,041 | 22 | 80,083 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr... | instruction | 0 | 40,042 | 22 | 80,084 |
No | output | 1 | 40,042 | 22 | 80,085 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr... | instruction | 0 | 40,043 | 22 | 80,086 |
No | output | 1 | 40,043 | 22 | 80,087 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr... | instruction | 0 | 40,044 | 22 | 80,088 |
No | output | 1 | 40,044 | 22 | 80,089 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than thr... | instruction | 0 | 40,045 | 22 | 80,090 |
No | output | 1 | 40,045 | 22 | 80,091 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an image, that can be represented with a 2-d n by m grid of pixels. Each pixel of the image is either on or off, denoted by the characters "0" or "1", respectively. You would like to compress this image. You want to choose an i... | instruction | 0 | 40,113 | 22 | 80,226 |
Tags: brute force
Correct Solution:
```
def debug(*a):
return
print('[DEBUG]', *a)
is_prime = [False, False] + [True] * (2600-2)
for i in range(2, 2600):
if is_prime[i]:
for j in range(i+i, 2600, i):
is_prime[j] = False
n, m = map(int, input().split())
a = [None] * n
for i in range(n):... | output | 1 | 40,113 | 22 | 80,227 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an image, that can be represented with a 2-d n by m grid of pixels. Each pixel of the image is either on or off, denoted by the characters "0" or "1", respectively. You would like to compress this image. You want to choose an i... | instruction | 0 | 40,114 | 22 | 80,228 |
Tags: brute force
Correct Solution:
```
def debug(*a):
return
print('[DEBUG]', *a)
is_prime = [False, False] + [True] * (2600-2)
for i in range(2, 2600):
if is_prime[i]:
for j in range(i+i, 2600, i):
is_prime[j] = False
n, m = map(int, input().split())
a = [None] * n
for i in range(n):... | output | 1 | 40,114 | 22 | 80,229 |
Provide a correct Python 3 solution for this coding contest problem.
Let M be a positive integer.
You are given 2 N integers a_1, a_2, \ldots, a_{2 N}, where 0 \leq a_i < M for each i.
Consider dividing the 2 N integers into N pairs. Here, each integer must belong to exactly one pair.
We define the ugliness of a pa... | instruction | 0 | 40,240 | 22 | 80,480 |
"Correct Solution:
```
def modulo_pairing(N: int, M: int, A: list)->int:
A.sort()
def check(n: int)->bool:
'''2*n の位置を区切りとして、右側が全て赤のペアになることを確認する。
'''
for i in range(2*n, N+n):
if A[i] + A[2*N+2*n-i-1] < M:
return False
return True
l, r = -1, N+1
... | output | 1 | 40,240 | 22 | 80,481 |
Provide a correct Python 3 solution for this coding contest problem.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are given Q queries. The i-th query is represented as a pair ... | instruction | 0 | 40,294 | 22 | 80,588 |
"Correct Solution:
```
m=10**9+7;f=max;r=range
for _ in r(int(input())):
x,y=sorted(map(int,input().split()));s=-1;i=j=1
while j<=x and i+j<=y:i,j,s=j,i+j,s+1
if x<2 or y<3:print(1,x*y%m);continue
a=f(0,(y-j)//i+1)+f(0,(x-j)//i+1);i=j=1
for c in r(s):
k,l=j,i+j*2
for _ in r(s-c):k,l=l,k+l
a+=(y>=k)*f(0,(x-l)... | output | 1 | 40,294 | 22 | 80,589 |
Provide a correct Python 3 solution for this coding contest problem.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are given Q queries. The i-th query is represented as a pair ... | instruction | 0 | 40,295 | 22 | 80,590 |
"Correct Solution:
```
from math import gcd
import random,time
def gcdcount(n,m):
x,y=min(n,m),max(n,m)
if x==0:
return 0
else:
return 1+gcdcount(x,y%x)
fibo=[0,1,2]
for i in range(100):
fibo.append(fibo[-1]+fibo[-2])
gcdfibo=[[],[(1,2)],[(2,3)],[(3,5),(4,7)]]
for i in range(4,101):
... | output | 1 | 40,295 | 22 | 80,591 |
Provide a correct Python 3 solution for this coding contest problem.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are given Q queries. The i-th query is represented as a pair ... | instruction | 0 | 40,296 | 22 | 80,592 |
"Correct Solution:
```
m=10**9+7;f=lambda a:max(0,(a-l)//k+1);r=range
for _ in r(int(input())):
x,y=sorted(map(int,input().split()));s=-1;i=j=k=l=1
while l<=x and k+l<=y:k,l,s=l,k+l,s+1;a=f(y)+f(x)
for c in r(s):
k,l=j,i+j*2
for _ in r(s-c):k,l=l,k+l
a,i,j=a+(y>=k)*f(x)+(x>=k)*f(y),j,i+j
if x<2 or y<3:print(1... | output | 1 | 40,296 | 22 | 80,593 |
Provide a correct Python 3 solution for this coding contest problem.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are given Q queries. The i-th query is represented as a pair ... | instruction | 0 | 40,297 | 22 | 80,594 |
"Correct Solution:
```
m=10**9+7
f=lambda x:max(x,0)
r=range
for _ in r(int(input())):
x,y=sorted(map(int,input().split()))
s=-1
i=j=1
while j<=x and i+j<=y:i,j,s=j,i+j,s+1
if x==1 or y<3:print(1,x*y%m)
else:
a=f((y-j)//i+1)+f((x-j)//i+1)
i=j=1
for c in r(s):
k,l=j,i+j*2
for _ in r(s-c):k,l=l,k+l
i... | output | 1 | 40,297 | 22 | 80,595 |
Provide a correct Python 3 solution for this coding contest problem.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are given Q queries. The i-th query is represented as a pair ... | instruction | 0 | 40,298 | 22 | 80,596 |
"Correct Solution:
```
m=10**9+7
f=max
r=range
for _ in r(int(input())):
x,y=sorted(map(int,input().split()))
s=-1
i=j=1
while j<=x and i+j<=y:i,j,s=j,i+j,s+1
if x<2 or y<3:print(1,x*y%m);continue
else:
a=f(0,(y-j)//i+1)+f(0,(x-j)//i+1)
i=j=1
for c in r(s):
k,l=j,i+j*2
for _ in r(s-c):k,l=l,k+l
if ... | output | 1 | 40,298 | 22 | 80,597 |
Provide a correct Python 3 solution for this coding contest problem.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are given Q queries. The i-th query is represented as a pair ... | instruction | 0 | 40,299 | 22 | 80,598 |
"Correct Solution:
```
m=10**9+7
f=max
r=range
for _ in r(int(input())):
x,y=sorted(map(int,input().split()))
s=-1
i=j=1
while j<=x and i+j<=y:i,j,s=j,i+j,s+1
if x==1 or y<3:print(1,x*y%m)
else:
a=f(0,(y-j)//i+1)+f(0,(x-j)//i+1)
i=j=1
for c in r(s):
k,l=j,i+j*2
for _ in r(s-c):k,l=l,k+l
if x>=k:a+=... | output | 1 | 40,299 | 22 | 80,599 |
Provide a correct Python 3 solution for this coding contest problem.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are given Q queries. The i-th query is represented as a pair ... | instruction | 0 | 40,300 | 22 | 80,600 |
"Correct Solution:
```
q=int(input())
m=10**9+7
for _ in range(q):
x,y=sorted(map(int,input().split()))
s=-1
i=j=1
while j<=x and i+j<=y:
i,j=j,i+j
s+=1
if x==1 or y<3:print(1,x*y%m)
else:
a=max(0,(y-j)//i+1)+max(0,(x-j)//i+1)
i=j=1
for c in range(s):
k,l=j,i+j*2
for _ in range(s-c):k,l=l,k+l
i... | output | 1 | 40,300 | 22 | 80,601 |
Provide a correct Python 3 solution for this coding contest problem.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are given Q queries. The i-th query is represented as a pair ... | instruction | 0 | 40,301 | 22 | 80,602 |
"Correct Solution:
```
from math import gcd
import random,time
def gcdcount(n,m):
x,y=min(n,m),max(n,m)
if x==0:
return 0
else:
return 1+gcdcount(x,y%x)
fibo=[0,1,2]
for i in range(100):
fibo.append(fibo[-1]+fibo[-2])
gcdfibo=[[],[(1,2),(1,3)]]
for i in range(2,101):
temp=[]
... | output | 1 | 40,301 | 22 | 80,603 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are g... | instruction | 0 | 40,302 | 22 | 80,604 |
Yes | output | 1 | 40,302 | 22 | 80,605 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are g... | instruction | 0 | 40,303 | 22 | 80,606 |
Yes | output | 1 | 40,303 | 22 | 80,607 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are g... | instruction | 0 | 40,304 | 22 | 80,608 |
Yes | output | 1 | 40,304 | 22 | 80,609 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are g... | instruction | 0 | 40,305 | 22 | 80,610 |
Yes | output | 1 | 40,305 | 22 | 80,611 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are g... | instruction | 0 | 40,306 | 22 | 80,612 |
No | output | 1 | 40,306 | 22 | 80,613 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are g... | instruction | 0 | 40,307 | 22 | 80,614 |
No | output | 1 | 40,307 | 22 | 80,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are g... | instruction | 0 | 40,308 | 22 | 80,616 |
No | output | 1 | 40,308 | 22 | 80,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kenus, the organizer of International Euclidean Olympiad, is seeking a pair of two integers that requires many steps to find its greatest common divisor using the Euclidean algorithm.
You are g... | instruction | 0 | 40,309 | 22 | 80,618 |
No | output | 1 | 40,309 | 22 | 80,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n positive integers.
Initially, you have an integer x = 0. During one move, you can do one of the following two operations:
1. Choose exactly one i fro... | instruction | 0 | 40,599 | 22 | 81,198 |
Yes | output | 1 | 40,599 | 22 | 81,199 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n positive integers.
Initially, you have an integer x = 0. During one move, you can do one of the following two operations:
1. Choose exactly one i fro... | instruction | 0 | 40,600 | 22 | 81,200 |
Yes | output | 1 | 40,600 | 22 | 81,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n positive integers.
Initially, you have an integer x = 0. During one move, you can do one of the following two operations:
1. Choose exactly one i fro... | instruction | 0 | 40,601 | 22 | 81,202 |
Yes | output | 1 | 40,601 | 22 | 81,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n positive integers.
Initially, you have an integer x = 0. During one move, you can do one of the following two operations:
1. Choose exactly one i fro... | instruction | 0 | 40,602 | 22 | 81,204 |
Yes | output | 1 | 40,602 | 22 | 81,205 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n positive integers.
Initially, you have an integer x = 0. During one move, you can do one of the following two operations:
1. Choose exactly one i fro... | instruction | 0 | 40,603 | 22 | 81,206 |
No | output | 1 | 40,603 | 22 | 81,207 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n positive integers.
Initially, you have an integer x = 0. During one move, you can do one of the following two operations:
1. Choose exactly one i fro... | instruction | 0 | 40,604 | 22 | 81,208 |
No | output | 1 | 40,604 | 22 | 81,209 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n positive integers.
Initially, you have an integer x = 0. During one move, you can do one of the following two operations:
1. Choose exactly one i fro... | instruction | 0 | 40,605 | 22 | 81,210 |
No | output | 1 | 40,605 | 22 | 81,211 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n positive integers.
Initially, you have an integer x = 0. During one move, you can do one of the following two operations:
1. Choose exactly one i fro... | instruction | 0 | 40,606 | 22 | 81,212 |
No | output | 1 | 40,606 | 22 | 81,213 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is.
Unfortunately, comp... | instruction | 0 | 40,724 | 22 | 81,448 |
Tags: implementation, math, number theory
Correct Solution:
```
def prim_roots(number):
if number == 2:
return 1
elif number == 4:
return 2
z, h = 1, 2
p = list()
while h < number:
k = pow(h, z, number)
while k > 1:
z += 1
k = (k * h) % number
... | output | 1 | 40,724 | 22 | 81,449 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is.
Unfortunately, comp... | instruction | 0 | 40,725 | 22 | 81,450 |
Tags: implementation, math, number theory
Correct Solution:
```
def isPrimitiveRoot(x,p):
i = 2
m = phi = p - 1
while i*i <= m:
if m%i == 0:
if pow(x,phi//i,p) == 1:
return 0
while m%i == 0: m //= i
i += 1
if m > 1: return pow(x,phi//m,p) != 1
return pow(x,phi,p)... | output | 1 | 40,725 | 22 | 81,451 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is.
Unfortunately, comp... | instruction | 0 | 40,726 | 22 | 81,452 |
Tags: implementation, math, number theory
Correct Solution:
```
p = int(input())
ans = 0
for i in range(1, p):
result = True
temp = i
for j in range(1, p):
if j == p-1:
if (temp-1) % p != 0:
result = False
else:
if (temp-1) % p == 0:
re... | output | 1 | 40,726 | 22 | 81,453 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is.
Unfortunately, comp... | instruction | 0 | 40,727 | 22 | 81,454 |
Tags: implementation, math, number theory
Correct Solution:
```
# python 3
"""
Modular arithmetic:
This has something to do with Extended Euclidean Algorithm
"""
def cows_and_primitive_roots(p_int):
if p_int == 2:
return 1
count = 0
for x in range(2, p_int):
x_to_i_mod_p = x
divisi... | output | 1 | 40,727 | 22 | 81,455 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is.
Unfortunately, comp... | instruction | 0 | 40,728 | 22 | 81,456 |
Tags: implementation, math, number theory
Correct Solution:
```
p=int(input())
count=0
for i in range(1,p):
z,x=1,1
for j in range(1,p-1):
x*=i
x%=p
if x==1:
z=0
break
if z==1:
x*=i
x%=p
if x==1:
count+=1
print(count)
``` | output | 1 | 40,728 | 22 | 81,457 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The cows have just learned what a primitive root is! Given a prime p, a primitive root <image> is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is.
Unfortunately, comp... | instruction | 0 | 40,729 | 22 | 81,458 |
Tags: implementation, math, number theory
Correct Solution:
```
p = int(input()) - 1
def hcf(a, b):
if a is 0:
return b
else:
return hcf(b % a, a)
cnt = 0
for i in range(1, p + 1):
if hcf(i, p) is 1:
cnt += 1
print(cnt)
``` | output | 1 | 40,729 | 22 | 81,459 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.