HRY and codefire

传送门：

设 dp[i][j]为第一个号i等级，第二个号j等级的期望值

a[i]存每个等级上分的概率

dp[i][j]=a[i]*dp[i+1][j]+(1-a[i])*dp[j][i]+1

dp[j][i]=a[j]*dp[j+1][i]+(1-a[j])*dp[i][j]+1

这个鬼东西改变上面值会影响下面值，所以要化简

联立得:

dp[i][j]=(a[i]*dp[i+1][j]+1+(1-a[i])*(a[j]*dp[j+1][i]+1))/(1-(1-a[i])*(1-a[j]));

dp[j][i]=(a[j]*dp[j+1][i]+1+(1-a[j])*(a[i]*dp[i+1][j]+1))/(1-(1-a[i])*(1-a[j]));

#include <cstdio>
#include <cmath>
#include <cstring>
#include <string>
#include <sstream>
#include <iostream>
#include <cstdlib>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <vector>
#include <algorithm>
#include <functional>
using namespace std;
#define ll long long
#define re register
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define P pair<int,int>
void read(int &a)
{
    a=;
    int d=;
    char ch;
    while(ch=getchar(),!isdigit(ch))
        if(ch=='-')
            d=-;
    a=ch^;
    while(ch=getchar(),isdigit(ch))
        a=(a<<)+(a<<)+(ch^);
    a*=d;
}
void write(int x)
{
    if(x<)
        putchar(),x=-x;
    if(x>)
        write(x/);
    putchar(x%+'');
}
double dp[][],a[];
int main()
{
    int T;
    read(T);
    while(T--)
    {
        memset(dp,,sizeof(dp));
        memset(a,,sizeof(a));
        int n;
        read(n);
        for(re int i=;i<n;i++)
            scanf("%lf",&a[i]);
        for(re int i=n-;i>=;i--)
            for(re int j=n-;j>=;j--)
            {
                dp[i][j]=(a[i]*dp[i+][j]++(-a[i])*(a[j]*dp[j+][i]+))/(-(-a[i])*(-a[j]));
                dp[j][i]=(a[j]*dp[j+][i]++(-a[j])*(a[i]*dp[i+][j]+))/(-(-a[i])*(-a[j]));
            }
        printf("%.4lf\n",dp[][]);
    }
    return ;
}