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Solution: Kth Smallest Element in a Sorted Matrix

Explore how to use the k-way merge pattern to find the kth smallest element in an n x n sorted matrix. Understand how to implement a min-heap solution that merges rows of the matrix treated as sorted lists. This lesson covers the algorithm approach, time and space complexity analysis, and practical steps to apply the pattern effectively.

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
...