CF995F Cowmpany Cowmpensation 动态规划+容斥原理

Posted 2021-03-17 guangheli

数数题还是要多练啊  

code:

#include <cstdio>     
#include <cstring> 
#include <string>
#include <vector>   
#include <algorithm>    
#define N 3004  
#define ll long long 
#define mod 1000000007 
#define setIO(s) freopen(s".in","r",stdin) 
using namespace std;   
int n,D,g[N],f[N][N],s[N][N],fac[N],inv[N]; 
vector<int>G[N];     
int qpow(int x,int y)
{
    int tmp=1; 
    for(;y;y>>=1,x=(ll)x*x%mod) 
        if(y&1) tmp=(ll)tmp*x%mod;  
    return tmp; 
} 
int C(int x,int y) { return (ll)fac[x]*inv[y]%mod*inv[x-y]%mod; }  
void dfs(int x) 
{    
    for(int i=1;i<=n;++i) f[x][i]=1;   
    for(int i=0;i<G[x].size();++i) 
    {
        int y=G[x][i];  
        dfs(y);          
        for(int j=1;j<=n;++j) f[x][j]=1ll*f[x][j]*s[y][j]%mod;   
    }  
    for(int i=1;i<=n;++i) s[x][i]=(ll)(s[x][i-1]+f[x][i])%mod;  
}
int main() 
{ 
    // setIO("input");  
    int i,j; 
    scanf("%d%d",&n,&D);  
    for(i=2;i<=n;++i) 
    {
        int ff; 
        scanf("%d",&ff),G[ff].push_back(i);   
    }    
    dfs(1);              
    fac[0]=inv[0]=1;  
    for(i=1;i<=n;++i) fac[i]=(ll)i*fac[i-1]%mod, inv[i]=qpow(fac[i],mod-2); 
    for(i=1;i<=n;++i) 
    {
        g[i]=f[1][i];   
        for(j=1;j<i;++j)             
            g[i]=(ll)(g[i]-(ll)C(i-1,i-j)*g[j]%mod+mod)%mod; 
    }
    int ans=0;   
    int tmp=1;  
    for(i=1;i<=min(D,n);++i) 
    { 
        tmp=(ll)tmp*qpow(i,mod-2)%mod*(D-i+1)%mod;   
        ans=(ll)(ans+(ll)tmp*g[i]%mod)%mod;   
    }   
    printf("%d
",ans); 
    return 0;
}