UVA 294 294 - Divisors (数论)

Posted 2020-09-23 liguangsunls

UVA 294 - Divisors

题目链接

题意：求一个区间内，因子最多的数字。

思路：因为区间保证最多1W个数字，因子能够遍历区间。然后利用事先筛出的素数求出质因子，之后因子个数为全部(质因子的个数+1)的积

代码：

#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;

const int N = 35005;
int prime[N], pn = 0, vis[N];
int t, a, b;

int cal(int num) {
    int ans = 1;
    for (int i = 0; i < pn && prime[i] <= num; i++) {
    if (num % prime[i]) continue;
    int count = 1;
    while (num % prime[i] == 0) {
        count++;
        num /= prime[i];
    }
    ans *= count;
    }
    return ans;
}

void solve() {
    int ans, Max = 0;
    for (int i = a; i <= b; i++) {
    if (Max < cal(i)) {
        ans = i;
        Max = cal(i);
    }
    }
    printf("Between %d and %d, %d has a maximum of %d divisors.\n", a, b, ans, Max);
}

int main() {
    for (int i = 2; i < N; i++) {
    if (vis[i]) continue;
    prime[pn++] = i;
    for (int j = i; j < N; j += i)
        vis[j] = 1;
    }
    scanf("%d", &t);
    while (t--) {
    scanf("%d%d", &a, &b);
    solve();
    }
    return 0;
}