#2392

Build a Matrix With Conditions

hard · verified · 79.3% accepted · 1,504 likes · top 90%

array · graph theory · topological sort · matrix

Description

You are given a positive integer k. You are also given:

- a 2D integer array rowConditions of size n where rowConditions[i] = [abovei, belowi], and

- a 2D integer array colConditions of size m where colConditions[i] = [lefti, righti].

The two arrays contain integers from 1 to k.

You have to build a k x k matrix that contains each of the numbers from 1 to k exactly once. The remaining cells should have the value 0.

The matrix should also satisfy the following conditions:

- The number abovei should appear in a row that is strictly above the row at which the number belowi appears for all i from 0 to n - 1.

- The number lefti should appear in a column that is strictly left of the column at which the number righti appears for all i from 0 to m - 1.

Return any matrix that satisfies the conditions. If no answer exists, return an empty matrix.

Example 1:

Input: k = 3, rowConditions = [[1,2],[3,2]], colConditions = [[2,1],[3,2]]

Output: [[3,0,0],[0,0,1],[0,2,0]]

Explanation: The diagram above shows a valid example of a matrix that satisfies all the conditions.

The row conditions are the following:

- Number 1 is in row 1, and number 2 is in row 2, so 1 is above 2 in the matrix.

- Number 3 is in row 0, and number 2 is in row 2, so 3 is above 2 in the matrix.

The column conditions are the following:

- Number 2 is in column 1, and number 1 is in column 2, so 2 is left of 1 in the matrix.

- Number 3 is in column 0, and number 2 is in column 1, so 3 is left of 2 in the matrix.

Note that there may be multiple correct answers.

Example 2:

Input: k = 3, rowConditions = [[1,2],[2,3],[3,1],[2,3]], colConditions = [[2,1]]

Output: []

Explanation: From the first two conditions, 3 has to be below 1 but the third conditions needs 3 to be above 1 to be satisfied.

No matrix can satisfy all the conditions, so we return the empty matrix.

Solution