Minimum Operations to Make Median of Array Equal to K

Problem Description

You are given an integer array nums and a non-negative integer k. In one operation, you can increase or decrease any element by 1. Return the minimum number of operations needed to make the median of nums equal to k. The median of an array is defined as the middle element of the array when it is sorted in non-decreasing order. If there are two choices for a median, the larger of the two values is taken.

Key Insights

• The median is affected by the middle elements of the sorted array.
• The number of operations required depends on how far the middle element(s) are from k.
• The approach involves sorting the array to determine the median position and adjusting the necessary values.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array.
Space Complexity: O(1) - if we consider the space used for sorting in-place.

Solution

To solve the problem, we follow these steps:

1. Sort the array nums.
2. Determine the median based on the length of the array:
   • If the array length is odd, the median is the middle element.
   • If the array length is even, the median is the larger of the two middle elements.
3. Calculate the difference between the median and k.
4. The total number of operations required is the absolute difference calculated in the previous step.

Code Solutions