453. minimum moves to equal array elements

Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal.

In one move, you can increment n - 1 elements of the array by 1.

solution

Incrementing $n-1$ items is logically equivalent to decrementing a single item, which simplifies this problem greatly.

# O(n)
def minMoves(self, nums: List[int]) -> int:
	"""
	[2,3,3,3]
	=> [3,4,4,3] OR [2,3,3,2]
	=> [4,5,4,4] OR [2,3,2,2]
	=> [5,5,5,5] OR [2,2,2,2]
	  
	incrementing n-1 nums is logically equivalent to decrementing one num!
	"""
	minimum = min(nums)
	res = 0
	  
	for num in nums:
		res += num-minimum
	return res