LeetCode 462. Minimum Moves to Equal Array Elements II

原题链接在这里：https://leetcode.com/problems/minimum-moves-to-equal-array-elements-ii/

题目：

Given a non-empty integer array, find the minimum number of moves required to make all array elements equal, where a move is incrementing a selected element by 1 or decrementing a selected element by 1.

You may assume the array's length is at most 10,000.

Example:

Input:
[1,2,3]
Output:
2
Explanation:
Only two moves are needed (remember each move increments or decrements one element):
[1,2,3]  =>  [2,2,3]  =>  [2,2,2]

题解：

The median minimizes the sum of absolute deviations. There is an article explaining this.

用quick sort找到median. 类似Kth Largest Element in an Array.

每一个元素对于median差值的绝对值的总和就是最小moves. 这里的median可以理解为第nums.length/2小的element.

Time Complexity: O(n), quick select O(n). n = nums.length. 

Space: O(1).

AC Java:

class Solution {
    public int minMoves2(int[] nums) {
        if(nums == null || nums.length < 2){
            return 0;
        }
        
        int n = nums.length;
        int median = findK(nums, (n - 1) / 2, 0, n - 1);
        int res = 0;
        for(int num : nums){
            res += Math.abs(num - median);
        }
        
        return res;
    }
    
    private int findK(int [] nums, int k, int l, int r){
        if(l >= r){
            return nums[l];
        }
        
        int m = partition(nums, l, r);
        if(m == k){
            return nums[k];
        }else if(m < k){
            return findK(nums, k, m + 1, r);
        }else{
            return findK(nums, k, l, m - 1);
        }
    }
    
    private int partition(int [] nums, int l, int r){
        int pivot = nums[l];
        while(l < r){
            while(l < r && nums[r] >= pivot){
                r--;
            }
            
            nums[l] = nums[r];
            
            while(l < r && nums[l] <= pivot){
                l++;
            }
            
            nums[r] = nums[l];
        }
        
        nums[l] = pivot;
        return l;
    }
}

类似Minimum Moves to Equal Array Elements, Best Meeting Point.