uva 11105 - Semi-prime H-numbers(数论)

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https://blog.csdn.net/u011328934/article/details/36644069

题目大意：H-number为4∗k+1(k为非负数)，H-composites为因子中含有H-number(不包含自己本身)的数。反之久是H-prime，给定n。求有多少H-composites。

解题思路：首先用筛选法求出范围内的H-prime。然后枚举两个推断乘积是否在范围内。

#include <cstdio>

#include <cstring>

const int maxn = 1e6+5;

typedef long long ll;

int v[maxn], prime[maxn], cp;

void primeHtable(int n) {

    cp = 0;

    memset(v, 0, sizeof(v));

    for (int i = 5; i < n; i += 4) {

        if (v[i])

            continue;

        prime[cp++] = i;

        for (int j = i * 2; j < n; j += i)

            v[j] = 1;

    }

}

int solve (int n) {

    int ans = 0;

    memset(v, 0, sizeof(v));

    for (int i = 0; prime[i] < n && i < cp; i++) {

        if ((ll)prime[i] * prime[i] > n)

            break;

        for (int j = i; prime[j] < n && j < cp; j++) {

            ll u = (ll)prime[i] * prime[j];

            if (u > n)

                break;

            if (v[u])

                continue;

            ans++;

            v[u] = 1;

        }

    }

    return ans;

}

int main () {

    primeHtable(maxn);

    int n;

    while (scanf("%d", &n) == 1 && n) {

        printf("%d %d\n", n, solve(n));

    }

    return 0;

}