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

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AC代码：

#include <iostream>#include <algorithm>#include <cstdio>#include <cstring>#include <vector>#define MAX 1007using 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 );    }}
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