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Solution: Kth Smallest Element in a Sorted Matrix

Explore how to solve the problem of finding the kth smallest element in an n by n sorted matrix by applying the k-way merge pattern. Understand the algorithm that uses a min-heap to merge rows and efficiently track and extract elements until the kth smallest is found. Learn about the time and space complexity involved and how this approach leverages the sorted properties of the matrix for optimal performance.

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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
  • 1≤1\leq n ≤100\leq100
  • −103≤
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