HDU 5680 zxa and set （数学 推导结论）

zxa and set

题目链接：

http://acm.hust.edu.cn/vjudge/contest/121332#problem/G

Description

zxa has a set , which has elements and obviously non-empty subsets.

For each subset of , which has elements, zxa defined its value as .

zxa is interested to know, assuming that represents the sum of the values of the non-empty sets, in which each set is a subset of and the number of elements in is odd, and represents the sum of the values of the non-empty sets, in which each set is a subset of and the number of elements in is even, then what is the value of , can you help him?

Input

The first line contains an positive integer , represents there are test cases.

For each test case:

The first line contains an positive integer , represents the number of the set is .

The second line contains distinct positive integers, repersent the elements .

There is a blank between each integer with no other extra space in one line.

Output

For each test case, output in one line a non-negative integer, repersent the value of .

Sample Input

3

1

10

3

1 2 3

4

1 2 3 4

Sample Output

10

3

4

Hint

题意：

给出集合A，B是A的任意子集；某个集合的权值定义为集合元素的最小值；

S-odd为元素个数为奇数的B的个数；

S-even为元素个数为偶数的B的个数；

求abs(S-odd - S-even)；

题解：

看上去好像很麻烦，要算很多次；

尝试把每个元素在结果中出现的次数写成组合数的形式；

再按题意加起来，运用组合数相关公式可以很容易得到：

结果即为A中的最大值；

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#define mid(a,b) ((a+b)>>1)
#define LL long long
#define maxn 600000
#define IN freopen("in.txt","r",stdin);
using namespace std;

int n;

int main(int argc, char const *argv[])
{
    //IN;

    int t;cin>>t;
    while(t--)
    {
        scanf("%d",&n);
        int ans = -1;
        while(n--){
            int x;
            cin >> x;
            ans = max(ans, x);
        }

        printf("%d\n", ans);
    }

    return 0;
}