leetcode 561. Array Partition I

Given an array of 2n integers, your task is to group these integers into n pairs of integer, say (a1, b1), (a2, b2), ..., (an, bn) which makes sum of min(ai, bi) for all i from 1 to n as large as possible.

Example 1:

Input: [1,4,3,2]

Output: 4
Explanation: n is 2, and the maximum sum of pairs is 4 = min(1, 2) + min(3, 4).

 

Note:

1. n is a positive integer, which is in the range of [1, 10000].
2. All the integers in the array will be in the range of [-10000, 10000].

 

题目大意：给定一个2n长度的整数数组，将其分n对整数， 即(a1, b1), (a2, b2), ..., (an, bn), 求

                                                                                                                                       

 

 

 

 

 

 

 

 

 而

                                                                    

 

 

 我们有

 

 

由于前面那项是常数，我们只要考虑让后面那项最小，即

 

显然，要让和最小，尽量让每一对数，尽可能接近。经过整理，得到最大值为数组排序后的奇数项之和。

class Solution {
public:
    int arrayPairSum(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int sum = 0;
        for (int i = 0; i < nums.size(); i += 2) {
            sum += nums[i];
        }
        return sum;
    }
};