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Solution: Kth Smallest Element in a Sorted Matrix

Explore how to identify the kth smallest element in an n by n sorted matrix by applying the k-way merge pattern with a min-heap. Learn to manage sorted rows as arrays and efficiently merge them to solve the problem with optimal 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
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