<p>Given an <code>m x n</code> integers <code>matrix</code>, return <em>the length of the longest increasing path in </em><code>matrix</code>.</p>

<p>From each cell, you can either move in four directions: left, right, up, or down. You <strong>may not</strong> move <strong>diagonally</strong> or move <strong>outside the boundary</strong> (i.e., wrap-around is not allowed).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/05/grid1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> matrix = [[9,9,4],[6,6,8],[2,1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest increasing path is <code>[1, 2, 6, 9]</code>.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/27/tmp-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> matrix = [[3,4,5],[3,2,6],[2,2,1]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>The longest increasing path is <code>[3, 4, 5, 6]</code>. Moving diagonally is not allowed.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[1]]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= matrix[i][j] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution {
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        // Do a topological sort
        // Go through that st that last incoming edge in toposort is the path considered and find length of max length
        int n=matrix.size(), m=matrix[0].size();
        vector<vector<int>> noincoming(n, vector<int>(m, 0));

        for(int i=0; i<n; i++)
            for(int j=0; j<m; j++){
                if(i>0)
                    if(matrix[i-1][j]<matrix[i][j])
                        noincoming[i][j]++;
                if(i<n-1)
                    if(matrix[i+1][j]<matrix[i][j])
                        noincoming[i][j]++;
                if(j>0)
                    if(matrix[i][j-1]<matrix[i][j])
                        noincoming[i][j]++;
                if(j<m-1)
                    if(matrix[i][j+1]<matrix[i][j])
                        noincoming[i][j]++;
            }

        // for(int i=0; i<n; i++){
        //     for(int j=0; j<m; j++)
        //         cout << noincoming[i][j] << " ";
        //     cout << endl;
        // }

        queue<vector<int>> q;
        for(int i=0; i<n; i++)
            for(int j=0; j<m; j++){
                if(noincoming[i][j]==0)
                    q.push({i, j});
            }
        
        int largestpath=0;
        vector<vector<int>> visited(n, vector<int>(m, 0));
        // cout << q.size() << " ";
        while(q.size()>0){
            queue<vector<int>> nq;
            while(q.size()>0){
                vector<int> ele = q.front();
                int i=ele[0], j=ele[1];
                visited[i][j]=1;

                q.pop();

                if(i>0)
                    if(matrix[i-1][j]>matrix[i][j])
                        noincoming[i-1][j]--;
                if(i<n-1)
                    if(matrix[i+1][j]>matrix[i][j])
                        noincoming[i+1][j]--;
                if(j>0)
                    if(matrix[i][j-1]>matrix[i][j])
                        noincoming[i][j-1]--;
                if(j<m-1)
                    if(matrix[i][j+1]>matrix[i][j])
                        noincoming[i][j+1]--;
                    
                if(i>0)
                    if(matrix[i-1][j]>matrix[i][j] && noincoming[i-1][j]==0 && !visited[i-1][j])
                        nq.push({i-1, j});
                if(i<n-1)
                    if(matrix[i+1][j]>matrix[i][j] && noincoming[i+1][j]==0 && !visited[i+1][j])
                        nq.push({i+1, j});
                if(j>0)
                    if(matrix[i][j-1]>matrix[i][j] && noincoming[i][j-1]==0 && !visited[i][j-1])
                        nq.push({i, j-1});
                if(j<m-1)
                    if(matrix[i][j+1]>matrix[i][j] && noincoming[i][j+1]==0 && !visited[i][j+1])
                        nq.push({i, j+1});
            }
            q=nq;
            // cout << q.size() << " ";
            largestpath++;
        }
        return largestpath;
    }
// private: 
    // int maxincpath(vector<vector<int>>& matrix, int i, int j, set<vector<int>> ignore){
    //     int ans=1;
    //     int n=matrix.size(), m=matrix[0].size();

    //     if(i>0){
    //         if(matrix[i-1][j] > matrix[i][j] && ignore.find({i-1, j})==ignore.end()){
    //             set<vector<int>> temp=ignore;
    //             temp.insert({i-1, j});
    //             ans = max(ans, 1+maxincpath(matrix, i-1, j, temp));
    //         }
    //     }
    //     if(i<n-1){
    //         if(matrix[i+1][j] > matrix[i][j] && ignore.find({i+1, j})==ignore.end())
    //         {
    //             set<vector<int>> temp = ignore;
    //             temp.insert({i+1, j});
    //             ans = max(ans, 1+maxincpath(matrix, i+1, j, temp));
    //         }
    //     }
    //     if(j>0){
    //         if(matrix[i][j-1] > matrix[i][j] && ignore.find({i, j-1})==ignore.end())
    //         {
    //             set<vector<int>> temp = ignore;
    //             temp.insert({i, j-1});
    //             ans = max(ans, 1+maxincpath(matrix, i, j-1, temp));
    //         }
    //     }
    //     if(j<m-1){
    //         if(matrix[i][j+1] > matrix[i][j] && ignore.find({i, j+1})==ignore.end()){
    //             set<vector<int>> temp = ignore;
    //             temp.insert({i, j+1});
    //             ans = max(ans, 1+maxincpath(matrix, i, j+1, temp));
    //         }
    //     }
    //     return ans;
    // }
};
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