Solution: Build a Matrix with Conditions

Explore how to solve dependency constraints by performing topological sorts on row and column conditions. Understand how to detect cycles and map values to matrix positions, enabling you to build a matrix that satisfies strict ordering rules or determine when it's impossible.

We'll cover the following...

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 $k$ ...