哥德巴赫猜想

#include <iostream>
#include <cstring>
using namespace std;

const int maxn = 100000;
int prime[maxn] = { 0 }, visit[maxn] = { 0 }, cnt = 0, n;
void linearFilter() {
    memset(prime, 0, n * sizeof(int));
    memset(visit, 0, (n + 10) * sizeof(int));
    cnt = 0;
    for (int i = 2; i <= n; i++) {
        if (!visit[i])prime[cnt++] = i;
        for (int j = 0; j < cnt && i * prime[j] <= n; j++) {
            visit[i * prime[j]] = 1;
            if (i % prime[j] == 0)break;
        }
    }
}
bool exist(int k, int l, int r) {
    if (l >= r) {
        return k == prime[l];
    }
    int mid = (l + r) / 2;
    if (prime[mid] > k) {
        return exist(k, l, mid - 1);
    }
    else if (prime[mid] < k) {
        return exist(k, mid + 1, r);
    }
    else {
        return true;
    }
}
int main() {
    while (cin >> n) {
        linearFilter();
        int i, k;
        for (i = 2; i < n; i++) {
            if (exist(n - i, 0, cnt - 1)) {
                k = n - i;
                break;
            }
        }
        cout << i << "+" << k << endl;
    }
    return 0;
}