2392. Build a Matrix With Conditions
Hard
50 Points
Array
Graph
Topological Sort
Matrix
You are given a positive integer k. You are also given:
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:
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]]
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.
Constraints
2 <= k <= 4001 <= rowConditions.length, colConditions.length <= 104rowConditions[i].length == colConditions[i].length == 21 <= abovei, belowi, lefti, righti <= kabovei != belowilefti != righti
2392. Build a Matrix With Conditions
Hard
50 Points
Array
Graph
Topological Sort
Matrix
You are given a positive integer k. You are also given:
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:
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]]
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.
Constraints
2 <= k <= 4001 <= rowConditions.length, colConditions.length <= 104rowConditions[i].length == colConditions[i].length == 21 <= abovei, belowi, lefti, righti <= kabovei != belowilefti != righti