分析

多重集组合数。对于给定 $n$ 个物品，一共有 $k$ 个，$m$ 种，每种个数对应为 $n_1, n_2, n_3,…,n_m$ ，那么这些物品全排列数目为 $\frac{n!}{n_1!n_2!…n_m}$

C++ 代码

#include <iostream>
#include <cstdio>
#include <cmath>

using namespace std;
typedef long long ll;

const int N = 1024;
int n;
ll f[N];

int main()
{
    f[0] = 1;
    for (int i = 1; i <= 20; i++)
    {
        f[i] = f[i - 1] * i;
    }
    while (~scanf("%d", &n))
    {
        ll len = 0, sum = 1;
        for (int i = 2; i * i <= n; i++)
        {
            int cnt = 0;
            if (n % i == 0)
            {
                while (n % i == 0)
                {
                    n /= i;
                    cnt++;
                }
                len += cnt;
                sum *= f[cnt];
            }
        }
        if (n > 1) len++;
        cout << len << " " << f[len] / sum << endl;
    }
    return 0;
}