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Solution: Kth Smallest Element in a Sorted Matrix

Explore how to efficiently find the kth smallest element in an n-by-n matrix sorted by rows and columns. This lesson guides you through using the k-way merge pattern and a min-heap to systematically traverse matrix rows, pushing and popping elements until identifying the desired kth smallest value. You will understand the time and space complexity of this approach and learn to implement it effectively using priority queues in C++.

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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≤-10^3\leq
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