HDU5753 Permutation Bo

题目链接：HDU5753

Permutation Bo

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 451    Accepted Submission(s): 269
Special Judge

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 of  f(h).

If the absolute error between your answer and the standard answer is no more than  10−4, your solution will be accepted.

 

Sample Input

4 3 2 4 5 5 3 5 99 32 12

 

Sample Output

6.000000 52.833333

 

题意：2个序列h1~hn,c1~cn，第一个是1到n的一个排列，ans是c1到cn的连加，如果ci对应的hi比它周围2个数都大的话就去ci的值，否则不取。问结果的期望是多少。

题目分析：先求每个点取的概率，两边的点只与1个数比较，所以概率1／2，中间的点与2个数比较，概率1／3；之后求期望即可。注意对1的特判。

//
//  main.cpp
//  Permutation Bo
//
//  Created by teddywang on 2016/7/27.
//  Copyright © 2016年 teddywang. All rights reserved.
//

#include 
#include
#include
#include
#include
using namespace std;
int main()
{
    int n;
    double ans,buf;
    while(cin>>n)
    {
        ans=0;
        if(n==1)
        {
            cin>>buf;
            printf("%.6lf\n",buf);
        }
        else
        {
            for(int i=0;i>buf;
                if(i==0||i==n-1)
                {
                    ans+=buf/2;
                }
                else ans+=buf/3;
            }
            printf("%.6lf\n",ans);
        }
    }
}