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]

Math solution

This approach is based on the idea that adding 1 to all the elements except one is equivalent to decrementing 1 from a single element, since we are interested in the relative levels of the elements which need to be equalized. Thus, the problem is simplified to find the number of decrement operations required to equalize all the elements of the given array. For finding this, it is obvious that we’ll reduce all the elements of the array to the minimum element.

import sys
class Solution(object):
    def minMoves(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        minNum = sys.maxint
        moves = 0
        for num in nums:
            minNum = min(minNum, num)
        
        for num in nums:
            moves += num - minNum
            
        return moves

imgRuntime: 92ms