時間限制?1000 ms?內存限制?65536 KB

題目描述

? ?In a parallel universe, young Saber-chan does not have a humongous appetite, instead, she likes studying math in her spare time. This afternoon when Saber-chan is plunged in her study, she came across an interesting conjecture: for any even number n greater than or equal to 4, there exists at least one pair of prime numbers?p1?and?p2?such that?n=p1+p2.

? ? This conjecture is actually known as the Goldbach's conjecture. It is has not been proved nor refused yet. However in this universe, there are more programmers than mathematicians, people tend to prove math findings by programs. As the King of Knights and King of Britain, Saber-chan orders you to write a program that reports the number of all the pairs of prime numbers satisfying the condition in the conjecture for a given even number.

? ?A sequence of even numbers is given as input. Corresponding to each number, the program should output the number of pairs mentioned above. Notice that Saber-chan is interested in the number of essentially different pairs and therefore you should not count?(p1,p2)?and?(p2,p1)?separately as two different pairs.

輸入格式

? ?An integer is given in each input line. You may assume that each integer is even, and is greater than or equal to?4?and less than?215. The end of the input is indicated by a number?0.

輸出格式

? ? Each output line should contain an integer number. No other characters should appear in the output.

輸入樣例

6 10 12 0

輸出樣例

1 2 1 題意就是求出一個數可以被寫成多少種素數+素數的形式，比如

6=3+3

10=3+7，5+5

12=5+7

所以，篩出所有的素數的同時，將不是素數的數也標記好即可。

然后枚舉x=2+(x-2)=3+(x-3)=...

#include<bits/stdc++.h> #define N 100000 using namespace std; int notpri[N];int main(){int t,i,j,k;notpri[1]=1;int Lim=2<<15;for(i=2;i<Lim;i++){if(notpri[i]==0){for(j=2;j*i<Lim;j++){notpri[j*i]=1;}}}while(scanf("%d",&t)!=EOF){int res=0;if(t==0)break;for(i=2;i<=t/2;i++){if(notpri[i]==0&?pri[t-i]==0)res++;}printf("%d\n",res);}return 0; }

總結

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