Learn how to use k-way merge for efficient data merging and finding k-th small elements.

Coding

The K-Way Merge pattern is an algorithmic strategy used to efficiently combine multiple sorted sequences into a single sorted result. By using a min-heap or priority queue to track the smallest elements among k sources, it ensures optimal merging performance across arrays, lists, or data streams.

K-way Merge

# Statement

Find the $k^{th}$ smallest element in an $(n \times n)$ 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 $k^{th}$ smallest element.

**Constraints:**

* `n` $==$ `matrix.length`
* `n` $==$ `matrix[i].length`
* $1\leq$ `n` $\leq100$
* $-10^3\leq$ `matrix[i][j]` $\leq10^3$
* $1\leq$ `k` $\leq n^2$

# Examples

Try to solve the Kth Smallest Element in a Sorted Matrix problem.

Kth Smallest Element in a Sorted Matrix

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Problem: Kth Smallest Element in a Sorted Matrix

Statement

Problem: Kth Smallest Element in a Sorted Matrix

Statement