POJ 1862

Stripies

Time Limit: 1000MS		Memory Limit: 30000K
Total Submissions: 20805		Accepted: 9248

Description

Our chemical biologists have invented a new very useful form of life called stripies (in fact, they were first called in Russian - polosatiki, but the scientists had to invent an English name to apply for an international patent). The stripies are transparent amorphous amebiform creatures that live in flat colonies in a jelly-like nutrient medium. Most of the time the stripies are moving. When two of them collide a new stripie appears instead of them. Long observations made by our scientists enabled them to establish that the weight of the new stripie isn't equal to the sum of weights of two disappeared stripies that collided; nevertheless, they soon learned that when two stripies of weights m1 and m2 collide the weight of resulting stripie equals to 2*sqrt(m1*m2). Our chemical biologists are very anxious to know to what limits can decrease the total weight of a given colony of stripies. 
You are to write a program that will help them to answer this question. You may assume that 3 or more stipies never collide together. 

Input

The first line of the input contains one integer N (1 <= N <= 100) - the number of stripies in a colony. Each of next N lines contains one integer ranging from 1 to 10000 - the weight of the corresponding stripie.

Output

The output must contain one line with the minimal possible total weight of colony with the accuracy of three decimal digits after the point.

Sample Input

3
72
30
50

Sample Output

120.000

Source

Northeastern Europe 2001, Northern Subregion

大致题意：

给你若干个数，每次可选两个数a,ba,b合并成2∗a∗b−−−−√2∗a∗b，直至最后剩下一个数，问你这个数最小是多少

解题思路：

由这个合并的式子可以看出最后的那个数是每个数进行了若干次取平方根再乘起来的结果，且取平方根的总次数是与合并顺序无关的，所以我们应该让尽量大的数进行尽量多次开根，所以应该从大到小依次合并最终得到结果

代码：

#include 
#include 
#include 
#include 
using namespace std;
int w[10001];
int main()
{
    int N;
    double ans;
    scanf("%d",&N);
    for(int i=0;i=0;i--)
        ans=2*sqrt(ans*w[i]);
    printf("%.3f",ans);
    return 0;
}