<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:

    void dfs(vector<bool>& visited, stack<int>&st, int num, unordered_map<int, vector<int>>&m){
        //cout<<"hello";
        for(int i =0; i<m[num].size();i++){
            if(visited[m[num][i]-1]==false){
                visited[m[num][i]-1] = true;
                dfs(visited, st, m[num][i], m);
            }
        }
        st.push(num);
    }

    vector<vector<int>> buildMatrix(int k, vector<vector<int>>& rowConditions, vector<vector<int>>& colConditions) {
        // try top sort with rows and columns
        // now if any position in visited array was empty in either, return empty matrix
        // make map and add row, column for each node
        // add that node in the matrix and rest 0
        // return matrix

        vector<vector<int>>ans;

        unordered_map<int,vector<int>>m;
        for(int i =0;i<rowConditions.size();i++){
            m[rowConditions[i][0]].push_back(rowConditions[i][1]);
        }

        for(auto i:m){
            for(auto p : i.second){
                cout<<p<<" ";
            }
            cout<<endl;
        }

        stack<int>st;
        vector<bool>visited(k, false);
        for(int i =1;i<=k;i++){
            if(visited[i-1]==false){
                visited[i-1]=true;
                dfs(visited, st, i, m);
            }
        }
        vector<int>rowPos(k, 0);
        int i =0;
        vector<int>rows;
        while(st.size()){
            rowPos[st.top()-1]=i;
            i++;
            rows.push_back(st.top());
            st.pop();
        }

        for(auto i : rowConditions){
            if(rowPos[i[0]-1] > rowPos[i[1]-1]){
                return ans;
            }
        }

        m.clear();

        for(int i =0;i<colConditions.size();i++){
            m[colConditions[i][0]].push_back(colConditions[i][1]);
        }

        visited.clear();

        visited.resize(k, false);

        for(int i =1;i<=k;i++){
            if(visited[i-1]==false){
                visited[i-1]=true;
                dfs(visited, st, i, m);
            }
        }

        vector<int>colPos(k, 0);
        int p =0;
        vector<int>cols;
        while(st.size()){
            colPos[st.top()-1]=p;
            p++;
            cols.push_back(st.top());
            st.pop();
        }

        for(auto i : colConditions){
            if(colPos[i[0]-1] > colPos[i[1]-1]){
                return ans;
            }
        }

        m.clear();

        for(int i =0;i<rows.size();i++){
            m[rows[i]].push_back(i);
        }

        for(int i =0;i<rows.size();i++){
            m[cols[i]].push_back(i);
        }

        vector<vector<int>>a(k, vector<int>(k, 0));
        for(auto i:m){
            a[i.second[0]][i.second[1]]=i.first;
        }
        return a;
    }
};
66717