What is the optimal time complexity of solving Closest Pair in Two Arrays?

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

What is the auxiliary space complexity for Closest Pair in Two Arrays?

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 Closest Pair in Two Arrays?

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 Closest Pair in Two Arrays?

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.

Back to Practice Dashboard

Competitive ProgrammingEasy

Closest Pair in Two Arrays

Learn how to solve the 'Closest Pair in Two Arrays' problem. This detailed resource details brute force and optimized approaches.

Mode Selected

Problem Statement

Easy

Write a function closest_pair_two_arrays(arr1, arr2, x) that takes two sorted arrays of integers arr1 and arr2, and a target integer x. It should find and return a tuple (a, b) where a is from arr1 and b is from arr2 such that the absolute difference between (a + b) and x is minimized. If there are multiple such pairs, return the one with the smallest element from arr1.

Constraints

•1 <= len(arr1), len(arr2) <= 10^5
•arr1 and arr2 are sorted in ascending order.
•-10^9 <= arr1[i], arr2[j], x <= 10^9

Examples

Example 1

Input

closest_pair_two_arrays([1, 4, 5, 7], [10, 20, 30, 40], 32)

Output

(1, 30)

Explanation

1 from arr1 and 30 from arr2 sum to 31, which is closest to 32 (absolute difference is 1).

Example 2

Input

closest_pair_two_arrays([1, 4, 5, 7], [10, 20, 30, 40], 50)

Output

(7, 40)

Explanation

7 from arr1 and 40 from arr2 sum to 47, which is closest to 50 (absolute difference is 3).

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

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor