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Solution: Kth Smallest Element in a Sorted Matrix

Explore how to efficiently find the kth smallest element in a sorted matrix by applying the k-way merge pattern. This lesson teaches you to use a min-heap with multiple sorted rows to merge elements and extract the kth smallest, optimizing performance in time and space complexity.

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
...