4710: [Jsoi2011]分特产

4710: [Jsoi2011]分特产

链接

分析：

　　容斥原理+隔板法。

代码：

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#include<cmath>
#include<cctype>
#include<set>
#include<queue>
#include<vector>
#include<map>
using namespace std;
typedef long long LL;

inline int read() {
    int x=,f=;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-;
    for(;isdigit(ch);ch=getchar())x=x*+ch-'';return x*f;
}

const int N = , mod = 1e9 + ;
int C[N][N], a[N], n, m;

int Calc(int x) {
    int ans = ;
    for (int i = ; i <= m; ++i)
        ans = 1ll * ans * C[a[i] + x - ][x - ] % mod;
    ans = 1ll * ans * C[n][x] % mod;
    return ans;
}

int main() {
    n = read(), m = read();
    for (int i = ; i <= m; ++i) a[i] = read();
    C[][] = ;
    for (int i = ; i <= ; ++i) {
        C[i][] = ;
        for (int j = ; j <= i; ++j)
            C[i][j] = (C[i - ][j] + C[i - ][j - ]) % mod;
    }
    int ans = Calc(n);
    for (int i = ; i <= n; ++i) {
        if (i & ) ans = (ans - Calc(n - i) + mod) % mod;
        else ans = (ans + Calc(n - i)) % mod;
    }
    cout << (ans + mod) % mod;
    return ;
}