Build a Matrix With Conditions

arraygraph theorytopological sort

Problem Statement

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

a 2D integer array rowConditions of size n where rowConditions[i] = [above _i , below _i ] , and

a 2D integer array colConditions of size m where colConditions[i] = [left _i , right _i ] .

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

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

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

Examples

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]]
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: []
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.

Constraints

2 <= k <= 400

1 <= rowConditions.length, colConditions.length <= 10 ^4

rowConditions[i].length == colConditions[i].length == 2

1 <= above _i , below _i , left _i , right _i <= k

above _i != below _i

left _i != right _i

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGraph Theory