Solution: Build a Matrix with Conditions

Explore how to construct a k × k matrix from integer conditions on rows and columns by applying topological sort. Understand how to detect cycles in constraints, map values to positions, and handle cases where a valid matrix cannot be formed.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given a positive integer $k$ and two conditions:

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

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

You need to construct a $k \times k$ matrix that includes all the integers from $1$ to $k$ ...