Use a min-heap to efficiently merge the M sorted sequences, similar to the k-way merge algorithm. Initialize the heap with the first element from each sequence, then repeatedly extract the minimum, add it to the result, and push the next element from the same sequence until K elements are collected.
Pro tip: Discuss the time and space complexity trade-offs: O(K log M) time and O(M) space for the heap, and mention that if M is very large, a tournament tree or divide-and-conquer merge could be considered. Also, clarify edge cases like empty sequences or K larger than total elements.
Confirm that sequences are sorted in ascending order, duplicates are kept, and K is a positive integer. Discuss handling of empty sequences and K exceeding total elements.
Select a min-heap (priority queue) to efficiently track the smallest current element from each sequence. Explain why a heap is better than merging all sequences first (O(N log N) vs O(K log M)).
Initialize the heap with the first element of each non-empty sequence along with its sequence index and element index. Then loop K times: pop the minimum, append to result, and if the same sequence has a next element, push it into the heap.
State time complexity O(K log M) and space O(M) for the heap. Mention that if M is large, we could use a more advanced approach like a tournament tree, but the heap solution is standard and efficient.
Walk through a small example (e.g., M=3, K=5) to verify correctness, including duplicates. Also test edge cases like empty sequences or K=0.
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