Crossing River

Crossing River

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 11814		Accepted: 4476

Description

A group of N people wishes to go across a river with only one boat, which can at most carry two persons. Therefore some sort of shuttle arrangement must be arranged in order to row the boat back and forth so that all people may cross. Each person has a different rowing speed; the speed of a couple is determined by the speed of the slower one. Your job is to determine a strategy that minimizes the time for these people to get across.

Input

The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. The first line of each case contains N, and the second line contains N integers giving the time for each people to cross the river. Each case is preceded by a blank line. There won't be more than 1000 people and nobody takes more than 100 seconds to cross.

Output

For each test case, print a line containing the total number of seconds required for all the N people to cross the river.

Sample Input

1
4
1 2 5 10

Sample Output

17


题目大意&解题思路：
一些人想要过河，例如4个人过河的所需时间分别为：1，2，5，10
那么过河有两种方法：
1. 1与2，1回来，1与5，1回来，1与10  结果耗时19
2. 1yu2，2回来，5与10，1回来，1与2  结果耗时15

总结两种方法：
设 x，y为最快和次快，a，b为次慢和最慢
那么第一种耗时t=y+x+a+x+b
第二种耗时t=y+y+b+x+y

重点就在于2*y和x+a谁大谁小

根据贪心的思想，每一次都比较一下呗
谁小选谁

代码：

#include"iostream"
#include"algorithm"
using namespace std;
int a[1010];
int main()
{
int T,n,sum;
cin>>T;
while(T--){
cin>>n;
for(int k=0;k<n;k++){
cin>>a[k];
}
sum=0;
sort(a,a+n);
if(n==1)
sum+=a[0];
while(n>1)
{
if(n==2)
sum+=a[1];
if(n==3)
sum+=(a[0]+a[1]+a[2]);
if(n>=4)
{
if(2*a[1]-a[n-2]-a[0]<0)
{
sum+=(a[0]+2*a[1]+a[n-1]);
}
else
{
sum+=(2*a[0]+a[n-2]+a[n-1]);
}
}
n-=2;
}
cout<<sum<<endl;
}

return 0;
};