POJ 2262-Goldbach's Conjecture(素数筛)

浏览数：29 / 时间：2015年06月12日

Goldbach‘s Conjecture

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 39435		Accepted: 15119

Description

In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture:

Every even number greater than 4 can be
written as the sum of two odd prime numbers.

For example:

8 = 3 + 5. Both 3 and 5 are odd prime numbers.
20 = 3 + 17 = 7 + 13.
42 = 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23.

Today it is still unproven whether the conjecture is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.)
Anyway, your task is now to verify Goldbach‘s conjecture for all even numbers less than a million.

Input

The input will contain one or more test cases.
Each test case consists of one even integer n with 6 <= n < 1000000.
Input will be terminated by a value of 0 for n.

Output

For each test case, print one line of the form n = a + b, where a and b are odd primes. Numbers and operators should be separated by exactly one blank like in the sample output below. If there is more than one pair of odd primes adding up to n, choose the pair where the difference b - a is maximized. If there is no such pair, print a line saying "Goldbach‘s conjecture is wrong."

Sample Input

Sample Output

8 = 3 + 5
20 = 3 + 17
42 = 5 + 37

#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
#include <set>
#include <queue>
#include <stack>
#include <map>
using namespace std;
typedef long long LL;
int prime[1000010]={2,3,5};
int k=3;
int ip[1000010]={0};
void is_prime()
{
    int i,j;
    int flag=0;
    int gad=2;
    ip[2]=1;ip[3]=1;ip[5]=1;
    for(i=7;i<=1000010;i+=gad){
        flag=0;
        gad=6-gad;
        for(j=0;prime[j]*prime[j]<=i;j++){
            if(i%prime[j]==0){
                flag=1;
                break;
            }
        }
        if(!flag){
            prime[k++]=i;
            ip[i]=1;
        }
    }
}
int main()
{
    int n,i,j;
    is_prime();
    while(~scanf("%d",&n)){
        if(!n) break;
        int f=0;
        for(i=0;i<=k;i++){
            j=n-prime[i];
            if(ip[j]){
                f=1;
                break;
            }
        }
        if(!f)
            printf("Goldbach's conjecture is wrong.\n");
        else
            printf("%d = %d + %d\n",n,prime[i],j);

    }
    return 0;
}

郑重声明：本站内容如果来自互联网及其他传播媒体，其版权均属原媒体及文章作者所有。转载目的在于传递更多信息及用于网络分享，并不代表本站赞同其观点和对其真实性负责，也不构成任何其他建议。

POJ 2262-Goldbach's Conjecture(素数筛)