多校第七场 1010 hdu 5378 Leader in Tree Land(概率dp)

AC代码：

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <vector>
#define MAX 1007

using namespace std;
typedef long long LL;

const LL mod = 1e9+7;
int t,n,k,x,y;
LL dp[MAX][MAX];
LL fac[MAX];
LL rec[MAX];
int siz[MAX];
vector<int> e[MAX];

void add ( int u , int v )
{
    e[u].push_back ( v );
    e[v].push_back ( u );
}

void dfs ( int u , int p )
{
    siz[u] = 1;
    for ( int i = 0 ; i < e[u].size() ; i++ )
    {
        int v = e[u][i];
        if ( v == p ) continue;
        dfs ( v , u );
        siz[u] += siz[v];
    }
}

LL inv ( LL num , LL x )
{
    LL ret = 1LL;
    while ( x )
    {
        if ( x&1 )
        {
            ret *= num;
            ret %= mod;
        }
        num *= num;
        num %= mod;
        x >>= 1;
    }
    return ret;
}

void pre ()
{
    fac[0] = 1;
    for ( LL i = 1 ; i < MAX ; i++ )
    {
        fac[i] = fac[i-1]*i;
        fac[i] %= mod;
        rec[i] = inv ( i , mod-2 );
    }
}

void init ( )
{
    for ( int i = 0 ; i < MAX ; i++ )
        e[i].clear();
    memset ( dp , 0 , sizeof ( dp ));
}

int main ( )
{
    pre();
    scanf ( "%d" , &t );
    int cc = 1;
    while ( t-- )
    {
        init ();
        scanf ( "%d%d" , &n , &k );
        for ( int i = 1 ; i < n ; i++ )
        {
            scanf ( "%d%d" , &x , &y );
            add ( x , y );
        }
        dfs ( 1 , -1 );
        dp[0][0] = 1LL;
        for ( int i = 1 ; i <= n ; i++ )
            for ( int j = 0; j <= k ; j++ )
            {
                dp[i][j] = dp[i-1][j]*(siz[i]-1LL)%mod*rec[siz[i]]%mod;
                if ( j )
                {
                    dp[i][j] += dp[i-1][j-1]*rec[siz[i]]%mod;
                    dp[i][j] %= mod;
                }
            }
        printf ( "Case #%d: %I64d\n" , cc++ , fac[n]*dp[n][k]%mod );
    }
}