Find K Pairs with Smallest Sums

Find K Pairs with Smallest Sums is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Heap (Priority Queue) Patterns pattern, in the K-way Merge subpattern.

Problem statement

You are given two integer arrays nums1 and nums2 sorted in non-decreasing order and an integer k.

Define a pair (u, v) which consists of one element from the first array and one element from the second array.

Return the k pairs (u1, v1), (u2, v2), ..., (uk, vk) with the smallest sums.

Example 1:

Input: nums1 = [1,7,11], nums2 = [2,4,6], k = 3 Output: [[1,2],[1,4],[1,6]] Explanation: The first 3 pairs are returned from the sequence: [1,2],[1,4],[1,6],[7,2],[7,4],[11,2],[7,6],[11,4],[11,6]

Example 2:

Input: nums1 = [1,1,2], nums2 = [1,2,3], k = 2 Output: [[1,1],[1,1]] Explanation: The first 2 pairs are returned from the sequence: [1,1],[1,1],[1,2],[2,1],[1,2],[2,2],[1,3],[1,3],[2,3]

Constraints:

- 1 <= nums1.length, nums2.length <= 105

- -109 <= nums1[i], nums2[i] <= 109

- nums1 and nums2 both are sorted in non-decreasing order.

- 1 <= k <= 104

- k <= nums1.length nums2.length

Topics and companies

Topics: Array, Heap (Priority Queue).

Reported in interviews at Amazon, Walmart Labs.

How to practise Find K Pairs with Smallest Sums on Thita.ai

Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(k * log(min(n1, k))) where n1 = nums1.size(). Each heap operation is O(log(min(n1, k))) and we do up to k pops. time and O(min(n1, k)) for the heap, plus O(k) for the result vector. space.

Open Find K Pairs with Smallest Sums in the code editor, or read the Find K Pairs with Smallest Sums editorial for a worked solution with its approach and complexity analysis.

Where Find K Pairs with Smallest Sums sits in the DSA pattern sheet

• Heap (Priority Queue) Patterns pattern guide
• K-way Merge subpattern
• The full DSA patterns sheet
• All coding practice problems

Problems related to Find K Pairs with Smallest Sums

Other problems that use the same K-way Merge and Heap (Priority Queue) Patterns techniques:

• Kth Smallest Element in a Sorted Matrix — Medium, same subpattern
• Merge k Sorted Lists — Hard, same subpattern
• Smallest Range Covering Elements from K Lists — Hard, same subpattern
• Finding MK Average — Hard, same pattern
• Find Median from Data Stream — Hard, same pattern
• Furthest Building You Can Reach — Medium, same pattern