Minimum number of moves required to make all array elements equal

Time: O(N) on average; Space: O(1); medium

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 1:

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]

[1]:

import random

class Solution1(object):
    # Quick select solution
    def minMoves(self, nums) -> int:
        """
        :type nums: List[int]
        :rtype: int
        """
        def kthElement(nums, k):

            def PartitionAroundPivot(left, right, pivot_idx, nums):

                pivot_value = nums[pivot_idx]
                new_pivot_idx = left
                nums[pivot_idx], nums[right] = nums[right], nums[pivot_idx]

                for i in range(left, right):
                    if nums[i] > pivot_value:
                        nums[i], nums[new_pivot_idx] = nums[new_pivot_idx], nums[i]
                        new_pivot_idx += 1

                nums[right], nums[new_pivot_idx] = nums[new_pivot_idx], nums[right]
                return new_pivot_idx

            left, right = 0, len(nums) - 1
            while left <= right:

                pivot_idx = random.randint(left, right)
                new_pivot_idx = PartitionAroundPivot(left, right, pivot_idx, nums)

                if new_pivot_idx == k - 1:
                    return nums[new_pivot_idx]
                elif new_pivot_idx > k - 1:
                    right = new_pivot_idx - 1
                else:       # new_pivot_idx < k - 1
                    left = new_pivot_idx + 1

        median = kthElement(nums, len(nums)//2 + 1)
        return sum(abs(num - median) for num in nums)

[2]:

s = Solution1()
assert s.minMoves([1,2,3]) == 2

[3]:

class Solution2(object):
    def minMoves(self, nums) -> int:
        """
        :type nums: List[int]
        :rtype: int
        """
        median = sorted(nums)[len(nums)//2]
        return sum(abs(num - median) for num in nums)

[4]:

s = Solution2()
assert s.minMoves([1,2,3]) == 2