杭电5753之Permutation Bo

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

分析：纯思维题！公式为result=(double)(a1+an)/2+(double)(a2+...+an-1)/3

AC代码如下：

#include  
#include 
#include 
#include 
#include 
#include 
using namespace std;

int a[1100];

int main() {
    int n;
    while (cin >> n) 
    {
        for (int i = 1; i<=n; i++)   cin >> a[i];
        double n1 = (double)(a[1] + a[n]) / 2;
        int sum = 0;
        for (int i = 2; i<=n-1; i++)     sum += a[i];
        double n2 = (double)sum/3;
        double n3 = n1+n2;
        printf("%.6lf\n",n3);
    }
    return 0;
}