Educational DP Contest——J 期望dp

#include<bits/stdc++.h>
#define rep(i,x,y) for(int i=x; i<=y; ++i)
#define per(i,x,y) for(int i=x; i>=y; --i)
#define pushk push_back
#define popk pop_back
#define mem(a,b) memset(a,b,sizeof a)
#define ll long long
#define emk emplace_back
using namespace std;
const int  N = 300+9;
double dp[N][N][N];
int cnt[4];
int a[N];
int main() {
	
	int n;
	cin>>n;
	rep(i,1,n) cin>>a[i],cnt[a[i]]++;
	dp[0][0][0]=0;
	rep(k,0,n){
		rep(j,0,n){
			rep(i,0,n){
				int t = i+j+k; 
				if(i) dp[i][j][k]+=i*1.0/t*dp[i-1][j][k];
				//(i,j）用到了（i+1,j-1)，所以j要在i前面 
				if(j) dp[i][j][k]+=j*1.0/t*dp[i+1][j-1][k];
				// (j,k)用到了(j+1,k-1)，所以k要在j的外层 
				if(k) dp[i][j][k]+=k*1.0/t*dp[i][j+1][k-1]; 
				if(t) dp[i][j][k]+=n*1.0/t;
				//cout<<dp[i][j][k]<<endl;
			}
		} 
	}
	printf("%.10f\n",dp[cnt[1]][cnt[2]][cnt[3]]);
	return 0;
}