uva 1434 - YAPTCHA(数论)

Posted 2020-06-11

题目链接：uva 1434 - YAPTCHA

题目大意：给定n和k，求题目中给定的式子S(n)。

解题思路：威尔逊定理，x为素数时有，((x?1)!+1)%x==0，所以对于本题。假设3*k+7为素数的话，[(3k+6)!+1(3k+7?[(3k+6)!3k+7]]=1

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;
const int maxn = 1e6;

int ans[maxn+5], vis[maxn*4+5];

void primeTable (int n) {
    memset(vis, 0, sizeof(vis));

    for (int i = 2; i <= n; i++) {
        if (vis[i])
            continue;

        for (int j = 2 * i; j <= n; j += i)
            vis[j] = 1;
    }
}

int main () {
    primeTable(maxn*4);
    ans[1] = 0;
    for (int i = 2; i <= maxn; i++)
        ans[i] = ans[i-1] + (vis[3*i+7] ? 0 : 1);
    int cas, n;
    scanf("%d", &cas);
    while (cas--) {
        scanf("%d", &n);
        printf("%d\n", ans[n]);
    }
    return 0;
}