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

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 pairs?

The space complexity is O(n) 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 pairs?

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 pairs?

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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Competitive ProgrammingEasy

Minimum sum absolute difference pairs

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

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Problem Statement

Easy

Write a function min_sum_abs_diff_pairs(arr1, arr2) that takes two arrays of the same length, sorts them, and pairs corresponding elements to minimize the sum of their absolute differences. Return this minimum sum.

Constraints

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

Examples

Example 1

Input

min_sum_abs_diff_pairs([3, 2, 1], [2, 1, 3])

Output

Explanation

Sort both arrays: [1, 2, 3] and [1, 2, 3]. Diffs: |1-1| + |2-2| + |3-3| = 0.

Example 2

Input

min_sum_abs_diff_pairs([4, 1, 8, 7], [2, 3, 6, 5])

Output

Explanation

Sorted arrays: [1, 4, 7, 8] and [2, 3, 5, 6]. Diffs: |1-2| + |4-3| + |7-5| + |8-6| = 1 + 1 + 2 + 2 = 6.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

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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