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Solution: Kth Smallest Element in a Sorted Matrix

Explore how to apply the k-way merge pattern with a min-heap to find the kth smallest element in an n by n sorted matrix. Understand how merging rows treated as sorted arrays works and analyze the time and space complexities of this method.

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
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