{
    "id": 2472,
    "name": "build_a_matrix_with_conditions",
    "difficulty": "Hard",
    "link": "https://leetcode.com/problems/build-a-matrix-with-conditions/",
    "date": "1661040000000",
    "task_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. ``` **Constraints:** `2 <= k <= 400` `1 <= rowConditions.length, colConditions.length <= 104` `rowConditions[i].length == colConditions[i].length == 2` `1 <= abovei, belowi, lefti, righti <= k` `abovei != belowi` `lefti != righti`",
    "public_test_cases": [
        {
            "label": "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]] "
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        {
            "label": "Example 2",
            "input": "k = 3, rowConditions = [[1,2],[2,3],[3,1],[2,3]], colConditions = [[2,1]]",
            "output": "[] "
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    "haskell_template": "buildMatrix :: Int -> [[Int]] -> [[Int]] -> [[Int]]\nbuildMatrix k rowConditions colConditions ",
    "ocaml_template": "let buildMatrix (k: int) (rowConditions: int list list) (colConditions: int list list) : int list list =  ",
    "scala_template": "def buildMatrix(k: Int,rowConditions: List[List[Int]],colConditions: List[List[Int]]): List[List[Int]] = { \n    \n}",
    "java_template": "public static List<List<Integer>> buildMatrix(int k, List<List<Integer>> rowConditions, List<List<Integer>> colConditions) {\n\n}",
    "python_template": "class Solution(object):\n    def buildMatrix(self, k, rowConditions, colConditions):\n        \"\"\"\n        :type k: int\n        :type rowConditions: List[List[int]]\n        :type colConditions: List[List[int]]\n        :rtype: List[List[int]]\n        \"\"\"\n        "
}