2016 Multi-University Training Contest 3 1002 Permutation Bo

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5753

题目：

Problem Description

There are two sequences h1∼hn and c1∼cn.h1∼hn is a permutation of 1∼n. particularly, h0=hn+1=0.

We define the expression [condition] is 1 when condition is True,is 0 when condition is False.

Define the function f(h)=∑ni=1ci[hi>hi−1  and  hi>hi+1]

Bo have gotten the value of c1∼cn, and he wants to know the expected value of f(h).

 

Input

This problem has multi test cases(no more than 12).

For each test case, the first line contains a non-negative integer n(1≤n≤1000), second line contains n non-negative integer ci(0≤ci≤1000).

 

Output

For each test cases print a decimal - the expectation off(h).

If the absolute error between your answer and the standard answer is no more than10−4, your solution will be accepted.

 

Sample Input

43 2 4 553 5 99 32 12

 

Sample Output

6.00000052.833333

对于i =1和 i = n，比相邻数大的概率为1/2，而对于中间的数，比相邻数大的概率为1/3。（可以考虑三个数，每个数为最大数的概率为1/3）

#include <iostream>#include<cstdio>#include<cstring>#include<cmath>using namespace std;double a[11000];int main(){    int n;    while(~scanf("%d",&n))    {        for(int i=1;i<=n;i++)   scanf("%lf",&a[i]);        double ans=0;        ans+=(a[1]+a[n])/2;        for(int i=2;i<n;i++)            ans+=a[i]/3;        printf("%.6f\n",ans);    }}