hdu-1521 排列组合 指数型母函数

Posted 2020-10-09 Luke_Ye

高中知识，求全排列组合后，去重方法是除以相同物品的数量阶乘。那么如果我们再构造母函数的时候，就把阶乘作为每一项的分母，那求出来就可以直接乘上全排列系数了。

//
//  main.cpp
//  HDU4333
//
//  Created by teddywang on 16/3/9.
//  Copyright ? 2016年 teddywang. All rights reserved.
//

#include <iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define LL long long
using namespace std;
const LL N = 13;
int lim[N];
double dp[2][N];
LL fac[N];
double solve(int n,int m)
{
    fac[0] = 1;
    for (LL i = 1, f = 1; i < N; i++)
        f*=i,fac[i] = f;

    fill(dp[0], dp[0] + m + 1, 0);
    fill(dp[1], dp[1] + m + 1, 0);
    dp[0][0] = 1;
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j <= lim[i]; j++)
        {
            for (int k = 0; k + j <= m; k++)
            {
                dp[1][k + j] += dp[0][k]*1.0 / fac[j];
            }
        }
        for (int j = 0; j <= m; j++)
            dp[0][j] = dp[1][j], dp[1][j] = 0;
    }
    return dp[0][m]*fac[m];
}
int main()
{
    cin.sync_with_stdio(false);
    int n, m;
    while (scanf("%d%d",&n,&m)!=EOF)
    {
        for (int i = 0; i < n; i++)
            scanf("%d", &lim[i]);
        printf("%.0f\n", solve(n,m));
    }
}