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Grokking the Coding Interview Patterns

Solution: Kth Smallest Number in M Sorted Lists

Explore how to find the kth smallest number across multiple sorted integer lists by using a k-way merge technique with a min heap. Understand the algorithm steps, including initialization, heap operations, and how to maintain order to achieve an optimal time complexity. This lesson helps you implement a solution that handles duplicates uniquely and works efficiently even when k exceeds the total elements. Learn to analyze time complexity O((m+k) log m) and space complexity O(m) while applying these concepts to coding interviews.

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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:

  • 1≤m≤501\leq m \leq50
  • 0≤0\leq lists[i].length ≤50\leq 50
  • −109≤-10^9\leq lists[i][j] ≤109\leq 10^9
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