LightOJ - 1259 - Goldbach`s Conjecture（整数分解定理）

链接:

https://vjudge.net/problem/LightOJ-1259

题意：

Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:

Every even integer, greater than 2, can be expressed as the sum of two primes [1].

Now your task is to check whether this conjecture holds for integers up to 107.

思路：

素数表，然后暴力。

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<math.h>
#include<vector>
#include<map>

using namespace std;
typedef long long LL;
const int INF = 1e9;

const int MAXN = 1e7+10;
const int MOD = 1e9+7;

bool IsPrime[MAXN];
int Prime[1000010];
int n, tot;

void Init()
{
    memset(IsPrime, 0, sizeof(IsPrime));
    IsPrime[1] = 1;
    tot = 0;
    for (int i = 2;i < MAXN;i++)
    {
        if (IsPrime[i] == 0)
            Prime[++tot] = i;
        for (int j = 1;j <= tot && i*Prime[j] < MAXN;j++)
        {
            IsPrime[i*Prime[j]] = 1;
            if (i%Prime[j] == 0)
                break;
        }
    }
}

int main()
{
    Init();
    int t, cnt = 0;
    scanf("%d", &t);
    while(t--)
    {
        printf("Case %d:", ++cnt);
        scanf("%d", &n);
        int sum = 0;
        for (int i = 1;i <= tot && Prime[i] <= n/2;i++)
        {
            if (IsPrime[n-Prime[i]] == 0)
                sum++;
        }
        printf(" %d\n", sum);
    }
    
    return 0;
}