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Solution: Kth Smallest Element in a Sorted Matrix

Understand how to apply the k-way merge pattern to find the kth smallest element in a sorted matrix. This lesson teaches you to use a min-heap to merge sorted rows, iteratively extracting the smallest element until the kth element is found. You will learn to implement this efficiently while analyzing 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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