453. Minimum Moves to Equal Array Elements

Description

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

Example:

Input:
[1,2,3]

Output:
3

Explanation:
Only three moves are needed (remember each move increments two elements):

[1,2,3] => [2,3,3] => [3,4,3] => [4,4,4]

Solution

Math, time O(n), space O(1)

这道题乍一看会没什么头绪，竟然还想到用递归去做。但后来发现还是有规律可循。
首先，将n - 1个元素都+1，等同于将数组中的某1个元素-1。
然后，本题最优的解法就是，将所有元素都变成数组的min元素。
所以moves = sum - n * min。

class Solution {
    public int minMoves(int[] nums) {
        if (nums == null || nums.length < 2) {
            return 0;
        }
        
        int sum = 0;
        int min = Integer.MAX_VALUE;
        
        for (int n : nums) {
            sum += n;
            min = Math.min(n, min);
        }
        
        return sum - nums.length * min;
    }
}