Problem Description
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) with the smallest sums.
Key Insights
- The problem involves finding pairs of elements from two sorted arrays.
- Since both arrays are sorted, the smallest possible sums will involve the smallest elements from each array.
- A priority queue (min-heap) can be efficiently used to keep track of the smallest sums and their corresponding pairs.
- We can generate pairs in a controlled manner to avoid generating all possible pairs, which would be computationally expensive for large input sizes.
Space and Time Complexity
Time Complexity: O(k log k)
Space Complexity: O(k)
Solution
To solve the problem, we can use a min-heap (priority queue) to store pairs of elements along with their sums. Initially, we push the smallest pairs (the first element of nums1 paired with each element of nums2) into the heap. We will then repeatedly extract the smallest pair from the heap, and for each extracted pair, we will insert the next pair that can be formed with the next element in nums1. This process continues until we have extracted k pairs.