BZOJ2302: [HAOI2011]Problem c

题目：http://www.lydsy.com/JudgeOnline/problem.php?id=2302

组合数学+dp（其实我完全不会。。。

首先题目转化成<=i的至少有i个，因为如果没有i个的话后面n-i个位置肯定是不够的。

然后dp，记录下必选点和可选点个数，然后做一个n^3的dp

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cmath>
#include<vector>
#include<cstring>
#define rep(i,l,r) for (int i=l;i<=r;i++)
#define down(i,l,r) for (int i=l;i>=r;i--)
#define clr(x,y) memset(x,y,sizeof(x))
#define maxn 305
#define ll long long
#define eps 1e-6
using namespace std;
int n,m,t;
ll c[maxn][maxn],f[maxn][maxn],M;
int cnt[maxn],sum[maxn];
int read(){
    int x=0,f=1; char ch=getchar();
    while (!isdigit(ch)) {if (ch==‘-‘) f=-1; ch=getchar();}
    while (isdigit(ch)) {x=x*10+ch-‘0‘; ch=getchar();}
    return x*f;
}
void init(){
    clr(cnt,0); clr(sum,0); clr(f,0); clr(c,0);
    c[0][0]=1;
    rep(i,1,n){
        c[i][0]=1;
        rep(j,1,i) c[i][j]=(c[i-1][j-1]+c[i-1][j])%M;
    }
}
int main(){
    t=read();
    while (t--){
        int x,y,gg;
        n=read(); m=read(); M=read();
        init();
        sum[0]=n-m;
        rep(i,1,m){
            x=read(); y=read(); cnt[y]++;
        }
        gg=0;
        rep(i,1,n) {
            sum[i]=sum[i-1]+cnt[i];
            if (sum[i]<i) {
                puts("NO"); gg=1;
                break;
            }
        }
        if (gg) continue;
        f[0][0]=1;
        rep(i,1,n)
            rep(j,i,sum[i])
                rep(k,cnt[i],j-i+1) {
                    f[i][j]=(f[i][j]+f[i-1][j-k]*c[sum[i]-j+k-cnt[i]][k-cnt[i]])%M;
                }
        printf("YES %lld\n",f[n][n]);
    }
    return 0;
}