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Solution: Kth Smallest Number in M Sorted Lists

Understand how to efficiently find the kth smallest number among multiple sorted lists by using the k-way merge algorithm with a min-heap. Explore the optimized approach that improves performance over naive sorting by managing heap operations and maintaining time complexity within O((m+k) log m). Learn implementation steps and complexity analysis to apply this pattern confidently in coding interviews.

Statement

Given a list, lists, containing mm sorted lists of integers in ascending order, and an integer k, find the kthk^{th} smallest element among all the lists.

Even if some values appear multiple times across the lists, each occurrence is treated as a unique element when determining the kthk^{th} smallest number.

If k exceeds the total number of elements across all lists, return the largest element among them. If the lists are empty, return 0.

Constraints:

  • 1m501\leq m \leq50
  • 00\leq lists[i].length 50\leq 50
  • 109-10^9\leq lists[i][j] 109\leq 10^9
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