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

Solution 1

/**
 * Equation: m = sum of (eachNum-minNum)
 * @param {number[]} nums
 * @return {number}
 */
var minMoves = function(nums) {
    "use strict";
    let min = Math.min(...nums);
    return nums.reduce((x, sum) => sum+(x-min), 0);
};

Solution 2

/**
 * Equation: m = sum - minNum*n
 * sum + m*(n-1) = x*n (x is the final equal element)
 * x = minNum + m
 * @param {number[]} nums
 * @return {number}
 */
var minMoves = function(nums) {
    "use strict";
    let sum = nums.reduce((x, sum) => sum+x, 0);
    return sum - Math.min(...nums)*nums.length;
};