What is the optimal time complexity of solving Minimum sum absolute difference?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Minimum sum absolute difference?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Minimum sum absolute difference?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Minimum sum absolute difference?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Minimum sum absolute difference

Learn how to solve the 'Minimum sum absolute difference' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function min_sum_abs_diff(arr1, arr2) that takes two arrays of equal length and returns the minimum possible value of sum(|arr1[i] - arr2[i]|) after rearranging elements of both arrays in any order. To minimize this sum, sort both arrays and pair elements at the same index.

Constraints

•1 <= len(arr1) == len(arr2) <= 10^5
•-10^9 <= arr1[i], arr2[i] <= 10^9

Examples

Example 1

Input

arr1 = [4, 1, 8, 7], arr2 = [2, 3, 6, 5]

Output

Explanation

Sort arr1: [1,4,7,8]. Sort arr2: [2,3,5,6]. Sum: |1-2|+|4-3|+|7-5|+|8-6| = 1+1+2+2 = 6.

Example 2

Input

arr1 = [1, 2, 3], arr2 = [1, 2, 3]

Output

Explanation

Same arrays, so differences are all zero.

Example 3

Input

arr1 = [5, 5], arr2 = [5, 5]

Output

Explanation

All pairs match perfectly.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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