Build a Matrix with Conditions

Explore how to build a k by k matrix that satisfies given row and column conditions using topological sort. Understand how to manage dependencies between matrix elements and return a valid arrangement or detect if none exists.

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Statement

You are given a positive integer $k$ , and you’re also given two conditions:

A 2D integer array rowConditions of size $n$ , where rowConditions[i] = [above[i], below[i]]. This means that above[i] must appear in a row above below[i] in the final matrix.
A 2D integer array colConditions of size $m$ , where colConditions[i] = [left[i], right[i]]. This means that left[i] must appear in a column to the left of right[i] in the final matrix.

Both arrays contain integers from $1$ to $k$ .

Your task is to build a $k$ ...