<p>You are given a <strong>positive</strong> integer <code>k</code>. You are also given:</p>

<ul>
	<li>a 2D integer array <code>rowConditions</code> of size <code>n</code> where <code>rowConditions[i] = [above<sub>i</sub>, below<sub>i</sub>]</code>, and</li>
	<li>a 2D integer array <code>colConditions</code> of size <code>m</code> where <code>colConditions[i] = [left<sub>i</sub>, right<sub>i</sub>]</code>.</li>
</ul>

<p>The two arrays contain integers from <code>1</code> to <code>k</code>.</p>

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

<p>The matrix should also satisfy the following conditions:</p>

<ul>
	<li>The number <code>above<sub>i</sub></code> should appear in a <strong>row</strong> that is strictly <strong>above</strong> the row at which the number <code>below<sub>i</sub></code> appears for all <code>i</code> from <code>0</code> to <code>n - 1</code>.</li>
	<li>The number <code>left<sub>i</sub></code> should appear in a <strong>column</strong> that is strictly <strong>left</strong> of the column at which the number <code>right<sub>i</sub></code> appears for all <code>i</code> from <code>0</code> to <code>m - 1</code>.</li>
</ul>

<p>Return <em><strong>any</strong> matrix that satisfies the conditions</em>. If no answer exists, return an empty matrix.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/07/06/gridosdrawio.png" style="width: 211px; height: 211px;" />
<pre>
<strong>Input:</strong> k = 3, rowConditions = [[1,2],[3,2]], colConditions = [[2,1],[3,2]]
<strong>Output:</strong> [[3,0,0],[0,0,1],[0,2,0]]
<strong>Explanation:</strong> 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 <u>1</u>, and number 2 is in row <u>2</u>, so 1 is above 2 in the matrix.
- Number 3 is in row <u>0</u>, and number 2 is in row <u>2</u>, so 3 is above 2 in the matrix.
The column conditions are the following:
- Number 2 is in column <u>1</u>, and number 1 is in column <u>2</u>, so 2 is left of 1 in the matrix.
- Number 3 is in column <u>0</u>, and number 2 is in column <u>1</u>, so 3 is left of 2 in the matrix.
Note that there may be multiple correct answers.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> k = 3, rowConditions = [[1,2],[2,3],[3,1],[2,3]], colConditions = [[2,1]]
<strong>Output:</strong> []
<strong>Explanation:</strong> 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.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= k &lt;= 400</code></li>
	<li><code>1 &lt;= rowConditions.length, colConditions.length &lt;= 10<sup>4</sup></code></li>
	<li><code>rowConditions[i].length == colConditions[i].length == 2</code></li>
	<li><code>1 &lt;= above<sub>i</sub>, below<sub>i</sub>, left<sub>i</sub>, right<sub>i</sub> &lt;= k</code></li>
	<li><code>above<sub>i</sub> != below<sub>i</sub></code></li>
	<li><code>left<sub>i</sub> != right<sub>i</sub></code></li>
</ul>

class Solution {
public:
    struct node
    {
        int val;
        node* next;
        node(int v, node* n): val(v), next(n) {}
    };
    void topologicalDFS(int val, int& k, int& sorted_count, node**& adjList, int* conditionCount, int*& sorted_result)
    {
        node* current = adjList[val];
        while(current)
        {
            if(--conditionCount[current->val] == 0)
            {
                sorted_result[current->val] = sorted_count++;
                topologicalDFS(current->val, k, sorted_count, adjList, conditionCount, sorted_result);
            }
            current= current->next;
        }
    }
    bool topologicalSort(int k, vector<vector<int>>& rowConditions, vector<vector<int>>& colConditions, int*& sorted_row, int*& sorted_col)
    {
        node** rowAdjList = new node*[k+1]();
        node** colAdjList = new node*[k+1]();
        int* rowConditionCount = new int[k+1]();
        bool* rowHaveCondition = new bool[k+1]();
        bool* colHaveCondition = new bool[k+1]();
        int* colConditionCount = new int[k+1]();
        int n1 = rowConditions.size();
        int n2 = colConditions.size();
        int sorted_row_count = 0;
        int sorted_col_count = 0;
        for(int i = 0; i < n1; i++)
        {
            if(!rowAdjList[rowConditions[i][0]])
            {
                rowAdjList[rowConditions[i][0]] = new node(rowConditions[i][1], nullptr);
            }
            else
            {
                node* temp = new node(rowConditions[i][1], rowAdjList[rowConditions[i][0]]);
                rowAdjList[rowConditions[i][0]] = temp;
            }
            rowConditionCount[rowConditions[i][1]]++;
            rowHaveCondition[rowConditions[i][1]] = true;
        }
        for(int i = 0; i < n2; i++)
        {
             if(!colAdjList[colConditions[i][0]])
            {
                colAdjList[colConditions[i][0]] = new node(colConditions[i][1], nullptr);
            }
            else
            {
                node* temp = new node(colConditions[i][1], colAdjList[colConditions[i][0]]);
                colAdjList[colConditions[i][0]] = temp;
            }
            colConditionCount[colConditions[i][1]]++;
            colHaveCondition[colConditions[i][1]] = true;
        }

        //row
        for(int i = 1; i <= k; i++)
        {
            if(rowHaveCondition[i] == false)
            {
                sorted_row[i] = sorted_row_count++;
                topologicalDFS(i, k, sorted_row_count, rowAdjList, rowConditionCount, sorted_row);
            }
        }
        if(sorted_row_count != k)
        {
            return false;
        }

        //col
        for(int i = 1; i <= k; i++)
        {
            if(colHaveCondition[i] == false)
            {
                sorted_col[i] = sorted_col_count++;
                topologicalDFS(i, k, sorted_col_count, colAdjList, colConditionCount, sorted_col);
            }
        }

        if(sorted_col_count != k)
        {
            return false;
        }

        return true;

    }
    vector<vector<int>> buildMatrix(int k, vector<vector<int>>& rowConditions, vector<vector<int>>& colConditions)
    {
        vector<vector<int>> ans(k, vector<int>(k,0));
        int* sorted_row = new int[k+1];
        int* sorted_col = new int[k+1];

        if(topologicalSort( k, rowConditions, colConditions, sorted_row, sorted_col))
        {
            for(int i = 1; i <= k; i++)
            {
                ans[sorted_row[i]][sorted_col[i]] = i;
            }
        }
        else
        {
            return {};
        }

        return ans;
        
    }
};
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