What is the optimal time complexity of solving K Pairs with smallest sum?

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 K Pairs with smallest sum?

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 K Pairs with smallest sum?

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 K Pairs with smallest sum?

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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K Pairs with smallest sum

Learn how to solve the 'K Pairs with smallest sum' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function k_smallest_pairs(nums1, nums2, k) that takes two sorted integer arrays nums1 and nums2 and an integer k. Return the first k pairs [u, v] with the smallest sums, where u is from nums1 and v is from nums2, sorted by their sum in ascending order.

Constraints

•1 <= len(nums1), len(nums2) <= 10^4
•1 <= k <= 1000

Examples

Example 1

Input

nums1 = [1, 7, 11], nums2 = [2, 4, 6], k = 3

Output

[[1, 2], [1, 4], [1, 6]]

Explanation

The smallest sum pairs are (1,2) sum=3, (1,4) sum=5, (1,6) sum=7.

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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