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Solution: Kth Smallest Element in a Sorted Matrix

Understand how to use the k-way merge pattern to efficiently find the kth smallest element in a sorted matrix. This lesson teaches you to treat matrix rows as sorted lists and use a min-heap to merge and extract elements. You will learn the implementation details, time and space complexity, and how this pattern leverages sorting properties for optimal performance.

Statement

Find the kthk^{th} smallest element in an (n×n)(n \times n) matrix, where each row and column of the matrix is sorted in ascending order.

Although there can be repeating values in the matrix, each element is considered unique and, therefore, contributes to calculating the kthk^{th} smallest element.

Constraints:

  • n ==== matrix.length
  • n ==== matrix[i].length
  • 11\leq n 100\leq100
  • 103
...