Lightoj 1030 - Discovering Gold

/* ***********************************************
Author        :guanjun
Created Time  :2016/7/9 23:17:57
File Name     :1030.cpp
************************************************ */
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <stdio.h>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <iomanip>
#include <list>
#include <deque>
#include <stack>
#define ull unsigned long long
#define ll long long
#define mod 90001
#define INF 0x3f3f3f3f
#define maxn 10010
#define cle(a) memset(a,0,sizeof(a))
const ull inf = 1LL << 61;
const double eps=1e-5;
using namespace std;
priority_queue<int,vector<int>,greater<int> >pq;
struct Node{
    int x,y;
};
struct cmp{
    bool operator()(Node a,Node b){
        if(a.x==b.x) return a.y> b.y;
        return a.x>b.x;
    }
};

bool cmp(int a,int b){
    return a>b;
}
int n;
double a[maxn];
double dp[maxn];
int main()
{
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    #endif
    //freopen("out.txt","w",stdout);
    int T;
    cin>>T;
    for(int t=1;t<=T;t++){
        cin>>n;
        for(int i=1;i<=n;i++)scanf("%lf",&a[i]);
        cle(dp);
        double ans=0;
        dp[1]=1;
        for(int i=1;i<=n;i++){
            for(int j=max(1,i-6);j<i;j++){
                int k=min(n-j,6);
                dp[i]+=dp[j]/(k*1.0);
            }
            ans+=dp[i]*a[i];
        }
        printf("Case %d: %.10f\n",t,ans);
    }
    return 0;
}