Poj 2096 Collecting Bugs （概率與期望）

題目鏈接：poj 2096

dp[i][j]:descrip in this step we have found i kinds of bugs and these bugs belong to j kinds of system.
dp[i][j]=(i/j)*(n*s)*dp[i][j]+(i/j)*(1-j/s)*dp[i][j+1]+(1-i/n)*(j/s)*dp[i+1][j]+(1-i/n)*(1-j/s)*dp[i+1][j+1]

#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;

int N,S;

double dp[1005][1005];

int main(){
	cin>>N>>S;
	for(int i=N;i>=0;i--){
		for(int j=S;j>=0;j--){
			if(i==N && j==S)continue;//init dp[N][S]=0,it can't be calculated by follow way;
			double t1=((double)(S-j)*i)/N/S;
			double t2=((double)(N-i)*j)/N/S;
			double t3=((double)(N-i)*(S-j))/N/S;
			double t0=((double)(N*S-i*j))/N/S;
			dp[i][j]=t1*dp[i][j+1]+t2*dp[i+1][j]+t3*dp[i+1][j+1]+1;
			if(t0!=0)dp[i][j]=dp[i][j]/t0;
		}
	}
	printf("%.4lf",dp[0][0]);
	return 0;
}