Is Minimum Cost to Make Arrays Identical easy or hard?

Minimum Cost to Make Arrays Identical is typically classified as a Medium problem. The implementation is simple, but recognizing that sorting minimizes total absolute difference requires greedy insight and familiarity with array pairing strategies.

Minimum Cost to Make Arrays Identical Python/Java solution

Implement the greedy approach by first computing the direct difference cost, then sorting both arrays and recomputing the difference. Add the fixed rearrangement cost to the sorted version and return the minimum. This logic is straightforward to implement in Python, Java, C++, Go, or TypeScript.

How to solve Minimum Cost to Make Arrays Identical in O(n)?

An O(n) solution exists if you only compare arrays in their original order. Iterate through the arrays once and compute sum(abs(a[i] - b[i])). However, this ignores the possibility of rearranging elements, which may lead to a higher cost than the sorting-based O(n log n) optimal solution.

What is the best approach for Minimum Cost to Make Arrays Identical?

The optimal approach compares two strategies: keeping the arrays in their original order or sorting both arrays and aligning them greedily. Compute the direct cost using sum of absolute differences, then compute the sorted alignment cost and add the rearrangement fee. The minimum of the two gives the final answer. The sorting-based method runs in O(n log n) time.

Is Minimum Cost to Make Arrays Identical asked at Google/Amazon/Meta?

Problems involving minimizing absolute differences and greedy pairing after sorting are common in interviews at companies like Google, Amazon, and Meta. Variants often appear under array optimization or greedy matching patterns.

What data structure is used in Minimum Cost to Make Arrays Identical?

The solution mainly relies on arrays and sorting. After sorting both arrays, a simple linear scan computes the pairwise absolute difference. No complex data structures such as heaps or hash maps are required.

What is the time complexity of Minimum Cost to Make Arrays Identical?

The optimal solution runs in O(n log n) time due to sorting both arrays. After sorting, a single linear pass computes the total absolute difference in O(n). The space complexity is O(1) extra if sorting is done in place.

3424. Minimum Cost to Make Arrays Identical - Practice Online

You are given two integer arrays arr and brr of length n, and an integer k. You can perform the following operations on arr any number of times:

Split arr into any number of contiguous subarrays and rearrange these subarrays in any order. This operation has a fixed cost of k.
Choose any element in arr and add or subtract a positive integer x to it. The cost of this operation is x.

Return the minimum total cost to make arr equal to brr.

Example 1:

Input: arr = [-7,9,5], brr = [7,-2,-5], k = 2

Output: 13

Explanation:

Split arr into two contiguous subarrays: [-7] and [9, 5] and rearrange them as [9, 5, -7], with a cost of 2.
Subtract 2 from element arr[0]. The array becomes [7, 5, -7]. The cost of this operation is 2.
Subtract 7 from element arr[1]. The array becomes [7, -2, -7]. The cost of this operation is 7.
Add 2 to element arr[2]. The array becomes [7, -2, -5]. The cost of this operation is 2.

The total cost to make the arrays equal is 2 + 2 + 7 + 2 = 13.

Example 2:

Input: arr = [2,1], brr = [2,1], k = 0

Output: 0

Explanation:

Since the arrays are already equal, no operations are needed, and the total cost is 0.

Constraints:

1 <= arr.length == brr.length <= 10⁵
0 <= k <= 2 * 10¹⁰
-10⁵ <= arr[i] <= 10⁵
-10⁵ <= brr[i] <= 10⁵