<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) {
        vector<vector<int>> dirs={{-1,0},{0,-1},{1,0},{0,1}};
        
        int n=matrix.size();
        int m=matrix[0].size();
        vector<vector<int>> indegree(n,vector<int>(m));
        for(int i=0;i<n;i++) {
            for(int j=0;j<m;j++){
                for(auto x:dirs){
                    if(i+x[0]>=0 && i+x[0]<n && j+x[1]>=0 && j+x[1]<m && matrix[i+x[0]][j+x[1]]>matrix[i][j]){
                        indegree[i+x[0]][j+x[1]]++;
                    }
                }       
            }
        } 
        queue<pair<int,int>> q;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(indegree[i][j]==0) q.push({i,j});

            }
        }
        int count =0;
        while(!q.empty()){
            for(int size=q.size();size>0;size--){
                int i=q.front().first;
                int j= q.front().second;
                q.pop();
                for(auto x:dirs){
                    if(i+x[0]>=0 && i+x[0]<n && j+x[1]>=0 && j+x[1]<m && matrix[i+x[0]][j+x[1]]>matrix[i][j]){
                        if(--indegree[i+x[0]][j+x[1]]==0) q.push({i+x[0],j+x[1]});
                    }
                }
            }
 
            count++;
        }
        return count;  
    }
};
71828