Find K Pairs with Smallest Sums
Given two sorted integer arrays `nums1` and `nums2`, and an integer $k$, return the $k$ pairs $(u, v)$ with the smallest sums, where $u$ is from `nums1` and $v$ is from `nums2`. Use a Min-Heap.
Why Interviewers Ask This
Apple interviewers ask this to evaluate a candidate's ability to optimize brute-force solutions using advanced data structures. They specifically test if you can recognize that sorting all pairs is inefficient and instead leverage the sorted nature of input arrays with a Min-Heap for optimal performance. This assesses your grasp of time complexity trade-offs and priority queue manipulation in real-world constraint scenarios.
How to Answer This Question
1. Clarify constraints: Ask about array sizes and whether k exceeds the total possible pairs, as Apple values handling edge cases.
2. Identify the pattern: Explain that since inputs are sorted, the smallest sum must involve nums1[0] and nums2[0], establishing a baseline.
3. Propose the Min-Heap strategy: Describe initializing the heap with (nums1[i] + nums2[0], i, 0) for the first few elements or just the first pair, then iteratively extracting the minimum.
4. Detail the expansion logic: When popping (sum, i, j), push the next potential candidate (i, j+1) into the heap, ensuring you explore neighbors without redundant calculations.
5. Optimize space: Mention limiting the heap size to k or min(len(nums1), k) to save memory, demonstrating awareness of resource efficiency which aligns with Apple's focus on polished, performant code.
Key Points to Cover
- Recognizing that brute force generation of all pairs is too slow for large inputs
- Correctly initializing the Min-Heap with the smallest known candidates
- Understanding the specific expansion rule: moving from (i,j) to (i,j+1)
- Achieving O(K log K) time complexity rather than O(N*M)
- Handling boundary conditions where k is larger than the total number of pairs
Sample Answer
To solve finding the K pairs with the smallest sums efficiently, I would avoid generating all combinations, which would result in O(N*M log N*M) complexity. Instead, I'd leverage the fact that both arrays are already sor…
Common Mistakes to Avoid
- Generating all N*M pairs first and then sorting them, which fails on large datasets due to excessive memory usage
- Forgetting to check if the next index is within bounds before adding it to the heap, causing runtime errors
- Initializing the heap with only one element and failing to cover multiple starting rows when k is large
- Using a Max-Heap instead of a Min-Heap, which reverses the logic needed to find the smallest sums
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