Probability dp exercises

Probability $dp$ exercises

Foreword: Too bad, I didn't learn this knowledge point, let's make up, hope not to coo.

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1.D. Bag of mice

Idea: Board question, find the probability of the princess winning, the state is set to $dp[i][j]$有$i$ white mouse,$With\; j$ black mouse, the princess will win the probability first.
First initialize:$dp[i][0]=1,dp[0][j]=0,i\in [1,w],j\in [0,b]$
Then state transition:
There are four situations:
1. The princess touches the white mouse,$dp[i][j]+=\frac{i}{i+j}$
2. The princess touches the black mouse, and the dragon touches the white mouse.
3. The princess touches the black mouse, the dragon touches the black mouse, and a black mouse runs out.
$dp\left[i\right]\left[j\right]+=\frac{j}{i+j}\times \frac{j-1}{i+j-1}\times \frac{j-2}{i+j-2}\times dp[i][j-3]$
4. The princess touched the black mouse, the dragon touched the black mouse, and ran out a white mouse.
$dp[i][j]+=\frac{j}{i+j}\times \frac{j-1}{i+j-1}\times \frac{i}{i+j-2}\times dp[i-1][j-2]$

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=1e3+5,M=2e4+5,inf=0x3f3f3f3f,mod=1e9+7;
#define mst(a,b) memset(a,b,sizeof a)
#define PII pair<int,int>
#define fi first
#define se second
#define pb push_back
int w,b;
double dp[N][N]; 
int main(){
    
    
	scanf("%d%d",&w,&b);
	for(int i=0;i<=w;i++) dp[i][0]=1;
	for(int i=0;i<=b;i++) dp[0][i]=0;
	for(int i=1;i<=w;i++)
		for(int j=1;j<=b;j++){
    
    
			dp[i][j]+=(double)i/(i+j);
			if(j>=3){
    
    
				dp[i][j]+=(double)j/(i+j)*(j-1)/(i+j-1)*(j-2)/(i+j-2)*dp[i][j-3];
			}
			if(j>=2){
    
    
				dp[i][j]+=(double)j/(i+j)*(j-1)/(i+j-1)*i/(i+j-2)*dp[i-1][j-2]; 
			}
		}
	printf("%.9f\n",dp[w][b]);
	return 0;
}