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.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divi... | instruction | 0 | 50,718 | 22 | 101,436 |
No | output | 1 | 50,718 | 22 | 101,437 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Suppose you have a sequence of k integers A = [a_1, a_2, ... , a_k] where each a_i ≥ 2. A sequence of prime integers P = [p_1, p_2, ..., p_k] is called suitable for the sequence A if a_1 is divi... | instruction | 0 | 50,719 | 22 | 101,438 |
No | output | 1 | 50,719 | 22 | 101,439 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each wool sequence contains a subsequence of consecu... | instruction | 0 | 50,769 | 22 | 101,538 |
Tags: constructive algorithms, math
Correct Solution:
```
n,m=map(int,input().split());MOD=1000000009;o=1;m=pow(2,m,MOD)-1
for i in range(n):o=o*(m-i)%MOD
print(o)
# Made By Mostafa_Khaled
``` | output | 1 | 50,769 | 22 | 101,539 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each wool sequence contains a subsequence of consecu... | instruction | 0 | 50,770 | 22 | 101,540 |
Tags: constructive algorithms, math
Correct Solution:
```
n, m = map(int, input().split())
k = pow(2, m, 1000000009) - 1
ans = 1
for i in range(n):
ans = (ans * (k - i)) % 1000000009
print(ans)
``` | output | 1 | 50,770 | 22 | 101,541 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each wool sequence contains a subsequence of consecu... | instruction | 0 | 50,771 | 22 | 101,542 |
Tags: constructive algorithms, math
Correct Solution:
```
n, m = map(int, input().split())
MOD = 10 ** 9 + 9
ans = pow(2, m, MOD) - 1
step = pow(2, m, MOD) - 2
for i in range(n - 1):
ans = (ans * step) % MOD
step -= 1
while ans < 0:
ans += MOD
while ans >= MOD:
ans -= MOD
print(ans)
``` | output | 1 | 50,771 | 22 | 101,543 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each wool sequence contains a subsequence of consecu... | instruction | 0 | 50,772 | 22 | 101,544 |
Tags: constructive algorithms, math
Correct Solution:
```
n,m=map(int,input().split());MOD=1000000009;o=1;m=pow(2,m,MOD)-1
for i in range(n):o=o*(m-i)%MOD
print(o)
``` | output | 1 | 50,772 | 22 | 101,545 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each wool sequence contains a subsequence of consecu... | instruction | 0 | 50,773 | 22 | 101,546 |
Tags: constructive algorithms, math
Correct Solution:
```
n, m = map(int, input().split())
mod = 10 ** 9 + 9
s, ans = pow(2, m, mod) - 1, 1
for i in range(n):
ans = ans * (s - i) % mod;
print (ans)
``` | output | 1 | 50,773 | 22 | 101,547 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that <image>. In other words each wool sequence contains a subsequence of consecu... | instruction | 0 | 50,774 | 22 | 101,548 |
Tags: constructive algorithms, math
Correct Solution:
```
MOD = int(1e9+9)
def fast_power(b, e):
res = 1
while e:
if e % 2 == 1:
res = res * b % MOD
b = b * b % MOD
e >>= 1
return res
n, m = map(int, input().split())
a = fast_power(2, m) - 1
a = (a + MOD) % MOD
b = a -... | output | 1 | 50,774 | 22 | 101,549 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such s... | instruction | 0 | 51,000 | 22 | 102,000 |
Tags: dp, greedy, math, number theory
Correct Solution:
```
n = int(input())
i = 0
while i < n:
a = int(input())
if (a - 9)%4 == 0 and a >= 9:
print(1 + (a-9)//4)
elif (a - 6)%4 == 0 and a >= 6:
print(1 + (a-6)//4)
elif (a - 15)%4 == 0 and a >= 15:
print(2 + (a-15)//4)
elif ... | output | 1 | 51,000 | 22 | 102,001 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such s... | instruction | 0 | 51,001 | 22 | 102,002 |
Tags: dp, greedy, math, number theory
Correct Solution:
```
t = int(input())
for i in range(t):
n = int(input())
if n%4 == 3:
if n >= 15:
print((n-15)//4+2)
else:
print(-1)
elif n%4 == 1:
if n >= 9:
print((n-9)//4+1)
else:
print(-1)
elif n%4 == 0:
print(n//4)
elif n%4 == 2:
if n < 6:
pr... | output | 1 | 51,001 | 22 | 102,003 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such s... | instruction | 0 | 51,002 | 22 | 102,004 |
Tags: dp, greedy, math, number theory
Correct Solution:
```
for _ in range(int(input())):
ni = int(input())
if ni % 2 == 0:
print(-1) if ni == 2 else print(ni // 4)
else:
print(-1) if (ni < 9 or ni == 11) else print((ni - 9) // 4 + 1)
``` | output | 1 | 51,002 | 22 | 102,005 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such s... | instruction | 0 | 51,003 | 22 | 102,006 |
Tags: dp, greedy, math, number theory
Correct Solution:
```
def check(n):
c = 0
if (n == 1)or(n == 2)or(n == 3)or(n == 5)or(n == 7)or(n == 11):
c = -1
n = 0
elif (n < 11)and(n != 10)and(n != 8)and(n != 9):
c += 1
elif n == 9:
c += 1
n -= 9
else:
if (n ... | output | 1 | 51,003 | 22 | 102,007 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such s... | instruction | 0 | 51,004 | 22 | 102,008 |
Tags: dp, greedy, math, number theory
Correct Solution:
```
for _ in range(int(input())):
n=int(input())
if n==1 or n==2 or n==3 or n==5 or n==7 or n==11:
print(-1)
else:
if n%2==0:
print(n//4)
else:
print(n//4-1)
``` | output | 1 | 51,004 | 22 | 102,009 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such s... | instruction | 0 | 51,005 | 22 | 102,010 |
Tags: dp, greedy, math, number theory
Correct Solution:
```
def ans(n):
if(n%4 == 0):
return n//4
elif(n%4 == 1 and n>=9):
return (n-9)//4 + 1
elif(n%4 == 3 and n>=15):
return (n-15)//4 + 2
elif(n%4 == 2 and n>=6):
return (n-6)//4 + 1
else:
return -1
t = int... | output | 1 | 51,005 | 22 | 102,011 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such s... | instruction | 0 | 51,006 | 22 | 102,012 |
Tags: dp, greedy, math, number theory
Correct Solution:
```
from math import *
from sys import *
from collections import defaultdict
import os, sys
from io import IOBase, BytesIO
M=10**9+7
def pow(a,b):
res=1
while b>0:
if b&1:
res*=a
a*=a
b>>=1
return res
def powmod(a,b,... | output | 1 | 51,006 | 22 | 102,013 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maximum number, or print -1, if there are no such s... | instruction | 0 | 51,007 | 22 | 102,014 |
Tags: dp, greedy, math, number theory
Correct Solution:
```
n = int(input())
for i in range(n) :
a = int(input())
s = 0
if a >= 12 or a == 8 or a == 10:
if a % 2 == 1 :
a -= 9
s += 1
if a % 4 == 2 :
a -= 6
s += 1
s += a // 4
elif a ... | output | 1 | 51,007 | 22 | 102,015 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maxi... | instruction | 0 | 51,008 | 22 | 102,016 |
Yes | output | 1 | 51,008 | 22 | 102,017 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maxi... | instruction | 0 | 51,009 | 22 | 102,018 |
Yes | output | 1 | 51,009 | 22 | 102,019 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maxi... | instruction | 0 | 51,011 | 22 | 102,022 |
Yes | output | 1 | 51,011 | 22 | 102,023 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maxi... | instruction | 0 | 51,012 | 22 | 102,024 |
No | output | 1 | 51,012 | 22 | 102,025 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maxi... | instruction | 0 | 51,013 | 22 | 102,026 |
No | output | 1 | 51,013 | 22 | 102,027 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maxi... | instruction | 0 | 51,014 | 22 | 102,028 |
No | output | 1 | 51,014 | 22 | 102,029 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given several queries. In the i-th query you are given a single positive integer ni. You are to represent ni as a sum of maximum possible number of composite summands and print this maxi... | instruction | 0 | 51,015 | 22 | 102,030 |
No | output | 1 | 51,015 | 22 | 102,031 |
Provide a correct Python 3 solution for this coding contest problem.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
... | instruction | 0 | 51,144 | 22 | 102,288 |
"Correct Solution:
```
n=10**5
p=[0,0]+[1]*~-n
for i in range(2,int(n**0.5)+1):
if not p[i]:continue
for j in range(i*2,n+1,i):p[j]=0
c=[0]
for i in range(1,n+1):
c.append(c[-1]+(i%2and p[i]and p[-~i//2]))
for _ in range(int(input())):
l,r=map(int,input().split())
print(c[r]-c[l-1])
``` | output | 1 | 51,144 | 22 | 102,289 |
Provide a correct Python 3 solution for this coding contest problem.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
... | instruction | 0 | 51,145 | 22 | 102,290 |
"Correct Solution:
```
n=8**6;P=[0,0]+[1]*n;S=[0]*n
for i in range(2,n):
for j in range(2*i,n,i):P[j]=0
for i in range(1,n):S[i]+=(P[i]==P[(i+1)//2]==1)+S[i-1]
for _ in "_"*int(input()):l,r=map(int,input().split());print(S[r]-S[l-1])
``` | output | 1 | 51,145 | 22 | 102,291 |
Provide a correct Python 3 solution for this coding contest problem.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
... | instruction | 0 | 51,146 | 22 | 102,292 |
"Correct Solution:
```
INF=10**5+1
p=[1]*INF
for i in range(2,INF):
if p[i]:
for j in range(2*i,INF,i):p[j]=0
p[0],p[1]=0,0
q=[0]*INF
for i in range(INF):
if i%2==0:continue
if p[i]*p[(i+1)//2]:q[i]=1
for i in range(1,INF):
q[i]+=q[i-1]
n=int(input())
for _ in range(n):
l,r=map(int,input().split())
prin... | output | 1 | 51,146 | 22 | 102,293 |
Provide a correct Python 3 solution for this coding contest problem.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
... | instruction | 0 | 51,147 | 22 | 102,294 |
"Correct Solution:
```
p = [True] * 100010
p[0] = p[1] = False
for i in range(2, 100000):
if p[i]:
for j in range(2 * i, 100000, i):
p[j] = False
s = [0] * 100010
for i in range(100000):
if p[i] and p[(i + 1) // 2]:
s[i] = s[i - 1] + 1
else:
s[i] = s[i - 1]
q = int(inpu... | output | 1 | 51,147 | 22 | 102,295 |
Provide a correct Python 3 solution for this coding contest problem.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
... | instruction | 0 | 51,148 | 22 | 102,296 |
"Correct Solution:
```
n =10**5+1
p = [False] * 2 + [True] * (n-2)
for i in range(2,n):
if p[i]:
for j in range(i*2,n,i):
p[j] = False
a=[p[i]==True and p[(i+1)//2]==True for i in range(n)]
b=[0]*n
b[0]=a[0]
for i in range(1,n):
b[i]=b[i-1]+a[i]
q=int(input())
for i in range(q):
l,r=map(... | output | 1 | 51,148 | 22 | 102,297 |
Provide a correct Python 3 solution for this coding contest problem.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
... | instruction | 0 | 51,149 | 22 | 102,298 |
"Correct Solution:
```
tf = [True] * 100001
tf[0] = tf[1] = True
for i in range(2, 320):
if tf[i]:
for j in range(i ** 2, 100001, i):
tf[j] = False
tf2 = [False] * 100001
for i in range(3, 100001):
if tf[i] and tf[(i + 1) // 2]:
tf2[i] = True
count = []
acc = 0
for i in range(100001):
acc += tf2[i... | output | 1 | 51,149 | 22 | 102,299 |
Provide a correct Python 3 solution for this coding contest problem.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
... | instruction | 0 | 51,150 | 22 | 102,300 |
"Correct Solution:
```
N = 10**5
p = [0]*(N+1)
q = [0]*(N+1)
p[2] = 1
primes = [2]
for i in range(3,N+1):
f = 1
for t in primes:
if t*t > i:
break
if i%t == 0:
f = 0
break
if f == 1:
primes.append(i)
p[i] = 1
if p[(i+1)//2]:
q[i] = 1
m = 0
s = [0]*(N+1)
for i in range... | output | 1 | 51,150 | 22 | 102,301 |
Provide a correct Python 3 solution for this coding contest problem.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.
Constraints
... | instruction | 0 | 51,151 | 22 | 102,302 |
"Correct Solution:
```
l=[0]*(10**5)
for i in range(1,10**5+1):
for j in range(2,int(i**0.5)+1):
if i%j==0:
break
else:
l[i-1]=1
d=[0]*(10**5)
t=3
while t<=10**5:
if l[t-1]==1 and l[(t-1)//2]==1:
d[t-1]=1
t+=2
r=[0]*(10**5+1)
for i in range(10**5):
r[i+1]=r[i]+d[i]
q=int(input())
for... | output | 1 | 51,151 | 22 | 102,303 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x... | instruction | 0 | 51,154 | 22 | 102,308 |
Yes | output | 1 | 51,154 | 22 | 102,309 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x... | instruction | 0 | 51,157 | 22 | 102,314 |
No | output | 1 | 51,157 | 22 | 102,315 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x... | instruction | 0 | 51,158 | 22 | 102,316 |
No | output | 1 | 51,158 | 22 | 102,317 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.
You are given Q queries.
In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x... | instruction | 0 | 51,159 | 22 | 102,318 |
No | output | 1 | 51,159 | 22 | 102,319 |
Provide a correct Python 3 solution for this coding contest problem.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For exampl... | instruction | 0 | 51,208 | 22 | 102,416 |
"Correct Solution:
```
MAX = 50001
is_prime = [True for _ in range(MAX)]
is_prime[0] = is_prime[1] = False
for i in range(2, int(MAX ** (1 / 2)) + 1):
if is_prime[i]:
for j in range(i ** 2, MAX, i):
is_prime[j] = False
primes = [i for i in range(MAX) if is_prime[i]]
def main():
while True:
n = int(... | output | 1 | 51,208 | 22 | 102,417 |
Provide a correct Python 3 solution for this coding contest problem.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For exampl... | instruction | 0 | 51,209 | 22 | 102,418 |
"Correct Solution:
```
import bisect
primes = [0,0] + [1]*49999
for i in range(2, 224):
if primes[i]:
for j in range(i*i, 50001, i):
primes[j] = 0
values = [k for k, b in enumerate(primes) if b]
while True:
n = int(input())
if n == 0:
break
end = bisect.bisect_right(values, ... | output | 1 | 51,209 | 22 | 102,419 |
Provide a correct Python 3 solution for this coding contest problem.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For exampl... | instruction | 0 | 51,210 | 22 | 102,420 |
"Correct Solution:
```
MAX = 50001
is_prime = [True for _ in range(MAX)]
is_prime[0] = is_prime[1] = False
for i in range(2, int(MAX ** (1 / 2)) + 1):
if is_prime[i]:
for j in range(i ** 2, MAX, i):
is_prime[j] = False
primes = [i for i in range(MAX) if is_prime[i]]
while True:
n = int(input())
if no... | output | 1 | 51,210 | 22 | 102,421 |
Provide a correct Python 3 solution for this coding contest problem.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For exampl... | instruction | 0 | 51,211 | 22 | 102,422 |
"Correct Solution:
```
# -*- coding: utf-8 -*-
"""
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0056
"""
from math import sqrt, ceil, pow
import bisect
# https://github.com/mccricardo/sieve_of_atkin/blob/master/sieve_of_atkin.py
class SieveOfAtkin:
def __init__(self, limit):
self.limit = limit... | output | 1 | 51,211 | 22 | 102,423 |
Provide a correct Python 3 solution for this coding contest problem.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For exampl... | instruction | 0 | 51,212 | 22 | 102,424 |
"Correct Solution:
```
import bisect
primes = [0, 0] + [1] * 49999
for i in range(2, 224):
if primes[i]:
for j in range(i*i, 50001, i):
primes[j] = 0
values = [i for i, k in enumerate(primes) if k]
while True:
n = int(input())
if n == 0:
break
I = bisect.bisect(values, n//2)
... | output | 1 | 51,212 | 22 | 102,425 |
Provide a correct Python 3 solution for this coding contest problem.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For exampl... | instruction | 0 | 51,213 | 22 | 102,426 |
"Correct Solution:
```
def make_tbl(n):
tbl = [False, True, False, False, False, True] * (n // 6 + 1)
for i in range(1, 4):
tbl[i] = not tbl[i]
p, stp, sqrt = 5, 2, n ** 0.5
while p < sqrt:
for i in range(p ** 2, n, 2 * p):
tbl[i] = False
while True:
p += ... | output | 1 | 51,213 | 22 | 102,427 |
Provide a correct Python 3 solution for this coding contest problem.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For exampl... | instruction | 0 | 51,214 | 22 | 102,428 |
"Correct Solution:
```
import bisect
primes = [0, 0] + [1] * 49999
for i in range(2, 225):
if primes[i]:
for j in range(i*i, 50001, i):
primes[j] = 0
values = [i for i, k in enumerate(primes) if k]
while True:
n = int(input())
if n == 0:
break
I = bisect.bisect(values, n//2)
... | output | 1 | 51,214 | 22 | 102,429 |
Provide a correct Python 3 solution for this coding contest problem.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For exampl... | instruction | 0 | 51,215 | 22 | 102,430 |
"Correct Solution:
```
import bisect,sys
from itertools import *
n=range(50001);a=list(n);a[1]=0
for i in range(2,224):a[i*2::i]=[0]*len(a[i*2::i])
p=list(compress(n,a))
for x in sys.stdin:
x=int(x)
if x:print(sum(1 for d in p[:bisect.bisect(p,x//2)]if a[x-d]))
``` | output | 1 | 51,215 | 22 | 102,431 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed th... | instruction | 0 | 51,216 | 22 | 102,432 |
Yes | output | 1 | 51,216 | 22 | 102,433 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed th... | instruction | 0 | 51,217 | 22 | 102,434 |
Yes | output | 1 | 51,217 | 22 | 102,435 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed th... | instruction | 0 | 51,218 | 22 | 102,436 |
Yes | output | 1 | 51,218 | 22 | 102,437 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed th... | instruction | 0 | 51,219 | 22 | 102,438 |
Yes | output | 1 | 51,219 | 22 | 102,439 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed th... | instruction | 0 | 51,220 | 22 | 102,440 |
No | output | 1 | 51,220 | 22 | 102,441 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed th... | instruction | 0 | 51,221 | 22 | 102,442 |
No | output | 1 | 51,221 | 22 | 102,443 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed th... | instruction | 0 | 51,222 | 22 | 102,444 |
No | output | 1 | 51,222 | 22 | 102,445 |
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