You are given a positive integer k. You are also given:
rowConditions of size n where rowConditions[i] = [abovei, belowi], andcolConditions 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:
\n\nabovei 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.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.
\n\n\n
Example 1:
\n![\"\"](\"https://assets.leetcode.com/uploads/2022/07/06/gridosdrawio.png\")
\n\nInput: k = 3, rowConditions = [[1,2],[3,2]], colConditions = [[2,1],[3,2]]\nOutput: [[3,0,0],[0,0,1],[0,2,0]]\nExplanation: The diagram above shows a valid example of a matrix that satisfies all the conditions.\nThe row conditions are the following:\n- Number 1 is in row 1, and number 2 is in row 2, so 1 is above 2 in the matrix.\n- Number 3 is in row 0, and number 2 is in row 2, so 3 is above 2 in the matrix.\nThe column conditions are the following:\n- Number 2 is in column 1, and number 1 is in column 2, so 2 is left of 1 in the matrix.\n- Number 3 is in column 0, and number 2 is in column 1, so 3 is left of 2 in the matrix.\nNote that there may be multiple correct answers.\n\n\n
Example 2:
\n\n\nInput: k = 3, rowConditions = [[1,2],[2,3],[3,1],[2,3]], colConditions = [[2,1]]\nOutput: []\nExplanation: From the first two conditions, 3 has to be below 1 but the third conditions needs 3 to be above 1 to be satisfied.\nNo matrix can satisfy all the conditions, so we return the empty matrix.\n\n\n
\n
Constraints:
\n\n2 <= k <= 4001 <= rowConditions.length, colConditions.length <= 104rowConditions[i].length == colConditions[i].length == 21 <= abovei, belowi, lefti, righti <= kabovei != belowilefti != rightiCompiled with clang 11 using the latest C++ 20 standard.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
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