Three pointers, one per array, pick the smallest head each step and advance that pointer.
Use a min-heap to efficiently merge the three sorted arrays by repeatedly extracting the smallest element. Initialize the heap with the first element of each array, then after extracting an element, insert the next element from the same array. This yields O(n_a + n_b + n_c) time because each element is inserted and extracted once.
Pro tip: Mention that for exactly three arrays, a simpler three-pointer approach without a heap also achieves O(n) time and O(1) extra space, but the heap solution generalizes to k arrays. Discussing trade-offs shows depth.
Restate the problem to ensure understanding: merge three sorted arrays into one sorted array in linear time. Ask about input sizes, memory constraints, and whether in-place is required.
Select a min-heap (priority queue) to efficiently track the smallest current element among the three arrays. Alternatively, for exactly three arrays, use three pointers.
Insert the first element of each array into the heap (or initialize pointers to 0). While the heap is not empty, extract the minimum, append it to the result, and if the extracted element's array has more elements, insert the next one.
Explain that each element is inserted and extracted once, so total operations are O(n_a + n_b + n_c). Heap operations are O(log 3) = O(1), so overall linear time.
Consider empty arrays, arrays of different lengths, and duplicate values. Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Knew immediately it was a min-heap situation.
Start by generalizing the two-array merge to k arrays using a min-heap of size k, then discuss the time and space complexity trade-offs. Also mention alternative approaches like divide-and-conquer or tournament tree, and when each is preferable.
Pro tip: Emphasize that the heap approach is optimal for streaming or when k is large, but for small k, pairwise merging might be simpler and more cache-friendly. Show awareness of real-world constraints like memory and input size.
Ask about the size of k, whether arrays are sorted, and if they fit in memory. This shows you consider practical limits before diving into solutions.
Explain how to use a min-heap to efficiently extract the smallest element among the k arrays, pushing the next element from the same array. This yields O(N log k) time where N is total elements.
Mention divide-and-conquer (merge pairs iteratively) with O(N log k) time but different constant factors, and tournament tree for O(N log k) with potentially better cache performance.
Compare time and space complexity, stability, and suitability for streaming vs. in-memory data. Highlight that heap uses O(k) extra space, while divide-and-conquer may use O(N) or O(k) depending on implementation.
Summarize which approach you'd choose based on typical constraints (e.g., heap for large k, divide-and-conquer for small k or when memory is tight) and mention potential optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.