Is Minimum Operations to Make Median of Array Equal to K easy or hard?

This problem is typically classified as Medium difficulty. The challenge comes from recognizing that only elements affecting the median after sorting matter. Once that insight is clear, the greedy adjustment becomes straightforward.

Minimum Operations to Make Median of Array Equal to K Python/Java solution

Implementations in Python, Java, C++, or JavaScript follow the same steps: sort the array, compute the median index, and accumulate the difference between elements and k depending on whether the median must increase or decrease. The logic remains identical across languages with O(n log n) time complexity.

How to solve Minimum Operations to Make Median of Array Equal to K in O(n)?

A strict O(n) solution is difficult because determining the median typically requires sorting or selection. Most implementations sort the array in O(n log n) and then adjust elements around the median. If a linear-time median selection algorithm is used, the adjustment phase can run in O(n), but this is rarely required in interviews.

What is the best approach for Minimum Operations to Make Median of Array Equal to K?

The most common solution sorts the array and directly adjusts elements affecting the median. After sorting, check the middle index and either increase elements on the right or decrease elements on the left until the median becomes k. This greedy approach runs in O(n log n) time due to sorting and uses O(1) extra space.

Is Minimum Operations to Make Median of Array Equal to K asked at Google/Amazon/Meta?

Median manipulation and greedy adjustment problems appear frequently in interviews at companies like Amazon, Google, and Meta. Variations involving medians, cost minimization, and sorted arrays are common because they test understanding of ordering properties and greedy reasoning.

What data structure is used in Minimum Operations to Make Median of Array Equal to K?

The primary data structure is a simple array. The algorithm relies on sorting the array and then iterating from the median index. No additional structures like heaps or hash maps are required for the optimal approach.

What is the time complexity of Minimum Operations to Make Median of Array Equal to K?

The optimal solution runs in O(n log n) time because the array must be sorted first. After sorting, a single linear scan from the median outward computes the required operations, which takes O(n). Space complexity is O(1) if sorting is done in-place.

Description Hints 3 Solution Video 13:56

3107. Minimum Operations to Make Median of Array Equal to K

Medium47.7% acceptance1 company

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.

Example 1:

Input: nums = [2,5,6,8,5], k = 4

Output: 2

Explanation:

We can subtract one from nums[1] and nums[4] to obtain [2, 4, 6, 8, 4]. The median of the resulting array is equal to k.

Example 2:

Input: nums = [2,5,6,8,5], k = 7

Output: 3

Explanation:

We can add one to nums[1] twice and add one to nums[2] once to obtain [2, 7, 7, 8, 5].

Example 3:

Input: nums = [1,2,3,4,5,6], k = 4

Output: 0

Explanation:

The median of the array is already equal to k.

Constraints:

1 <= nums.length <= 2 * 10⁵
1 <= nums[i] <= 10⁹
1 <= k <= 10⁹

Asked at 1 company

IBM

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Hint 1

Sort nums in non-descending order.

Hint 2

For all the smaller values on the left side of the median, change them to k if they are larger than k.

Hint 3

For all the larger values on the right side of the median, change them to k if they are smaller than k.

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3107. Minimum Operations to Make Median of Array Equal to K

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