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Minimum Moves to Equal Array Elements II

Difficulty: Medium

Problem Description

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 or decrement an element of the array by 1.

Key Insights

  • The optimal target value to minimize moves is the median of the array.
  • Moves needed for each element can be calculated by the absolute difference from the median.
  • Sorting the array helps in easily finding the median.

Space and Time Complexity

Time Complexity: O(n log n) due to sorting the array.
Space Complexity: O(1) if sorting is done in place; O(n) if a new sorted array is created.

Solution

To solve this problem, we will:

  1. Sort the array to find the median.
  2. Calculate the total number of moves required to convert all elements to the median value.
  3. Use the absolute difference between each element and the median to compute the total moves.

The primary data structure used is an array for storing the elements, and the algorithmic approach involves sorting to find the median.

Code Solutions

def minMoves2(nums):
    nums.sort()  # Sort the array to find the median
    median = nums[len(nums) // 2]  # Find the median
    return sum(abs(num - median) for num in nums)  # Calculate total moves needed
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