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Solution: Kth Smallest Element in a Sorted Matrix

Explore how to apply the k-way merge pattern to find the kth smallest element in an n by n matrix sorted by rows and columns. Understand how a min-heap can merge sorted rows to efficiently retrieve the kth smallest value, and analyze the time and space complexities involved.

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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