Is Minimum Array Changes to Make Differences Equal easy or hard?

Minimum Array Changes to Make Differences Equal is generally rated Medium difficulty. The challenge is recognizing that each pair contributes a cost of 0, 1, or 2 changes depending on the target difference and then aggregating these costs efficiently using prefix sums.

Minimum Array Changes to Make Differences Equal Python/Java solution

Typical implementations use arrays to store frequency counts and prefix sums. Python and Java solutions both iterate through symmetric pairs, compute the reachable difference range, update frequency arrays, and then scan all possible differences to compute the minimum cost in O(n + k) time.

How to solve Minimum Array Changes to Make Differences Equal in O(n)?

Process the array as n/2 symmetric pairs and compute their current difference and the maximum difference reachable with one change. Use frequency arrays to track exact matches and prefix sums to track one-change feasibility. This allows computing the total cost for each candidate difference in constant time, giving O(n + k) complexity.

What is the best approach for Minimum Array Changes to Make Differences Equal?

The most efficient approach uses frequency arrays combined with prefix sums. For each symmetric pair you compute the current difference and the maximum difference achievable with one modification. Aggregating these values allows you to evaluate the cost of every target difference in O(1) time, resulting in an overall O(n + k) algorithm.

Is Minimum Array Changes to Make Differences Equal asked at Google/Amazon/Meta?

Problems combining pair processing, difference constraints, and prefix-sum optimization appear frequently in interviews at large companies like Google, Amazon, and Meta. While this exact question is from LeetCode, the counting and cost-aggregation technique is commonly tested in system design and algorithm interviews.

What data structure is used in Minimum Array Changes to Make Differences Equal?

The core data structures are frequency arrays and prefix sums. These structures track how many pairs already match a difference and how many can reach a difference with one modification, enabling fast cost calculations for each candidate difference.

What is the time complexity of Minimum Array Changes to Make Differences Equal?

The optimized solution runs in O(n + k) time where n is the array length and k is the maximum allowed value. The array is scanned once to process symmetric pairs, and then the difference range 0..k is evaluated using prefix sums. Space complexity is O(k) for the frequency arrays.

Description Hints 2 Solution Video 37:15

3224. Minimum Array Changes to Make Differences Equal

Medium24.9% acceptance2 companies

You are given an integer array nums of size n where n is even, and an integer k.

You can perform some changes on the array, where in one change you can replace any element in the array with any integer in the range from 0 to k.

You need to perform some changes (possibly none) such that the final array satisfies the following condition:

There exists an integer X such that abs(a[i] - a[n - i - 1]) = X for all (0 <= i < n).

Return the minimum number of changes required to satisfy the above condition.

Example 1:

Input: nums = [1,0,1,2,4,3], k = 4

Output: 2

Explanation:
We can perform the following changes:

Replace nums[1] by 2. The resulting array is nums = [1,2,1,2,4,3].
Replace nums[3] by 3. The resulting array is nums = [1,2,1,3,4,3].

The integer X will be 2.

Example 2:

Input: nums = [0,1,2,3,3,6,5,4], k = 6

Output: 2

Explanation:
We can perform the following operations:

Replace nums[3] by 0. The resulting array is nums = [0,1,2,0,3,6,5,4].
Replace nums[4] by 4. The resulting array is nums = [0,1,2,0,4,6,5,4].

The integer X will be 4.

Constraints:

2 <= n == nums.length <= 10⁵
n is even.
0 <= nums[i] <= k <= 10⁵

Asked at 2 companies

Airbus

Google

Topics

Hints open one at a time

Hint 1

There are at most k + 1 possible values of the integer X.

Hint 2

How do we calculate the minimum number of changes efficiently if we fix the value of X before applying any changes?

37:15

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
2    def minChanges(self, nums: List[int], k: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[1,0,1,2,4,3]
4

Input

[0,1,2,3,3,6,5,4]
6

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