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Solution: Build a Matrix with Conditions

Explore how to build a k by k matrix by applying topological sorting to row and column constraints. Learn to detect conflicting dependencies and position elements correctly to meet given conditions, enabling you to solve matrix construction problems with ordering rules effectively.

Statement

You are given a positive integer kk and two conditions:

  • A 2D integer array row_conditions of size nn, where row_conditions[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 col_conditions of size mm, where col_conditions[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 11 to kk.

You need to construct a k×kk \times k matrix that includes all the integers from 11 to kk ...