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Solution: Kth Smallest Number in M Sorted Lists

Explore how to solve the problem of finding the kth smallest element across multiple sorted lists. This lesson teaches you to use the K-way merge algorithm with a min heap to efficiently merge sorted lists and identify the kth smallest number. Understand both the naive sorting approach and the optimized heap method, analyze their time and space complexities, and implement the solution in C#.

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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