<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 dfs(vector<vector<int>>& matrix, vector<vector<int>> &visited, vector<vector<int>> &lp, int x1, int y1){
        visited[x1][y1]=1;
        lp[x1][y1]=1;
        for(int i=x1-1;i<=x1+1;i++){
            for(int j=y1-1; j<=y1+1; j++){
                if(i<0 || j<0 || i>=matrix.size() || j>=matrix[0].size() || (i!=x1 && j!=y1) || (i==x1 && j==y1)) continue;
                if(matrix[i][j]<=matrix[x1][y1]) continue;
                if(visited[i][j]==1) lp[x1][y1]=max(lp[x1][y1],1 + lp[i][j] );
                else {
                    int t1 = dfs(matrix, visited, lp, i, j);
                    lp[x1][y1]=max(lp[x1][y1],1 + t1 );
                }
            }
        }
        return lp[x1][y1];
    }
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        vector<vector<int>> visited(matrix.size(), vector<int> (matrix[0].size(), 0));
        vector<vector<int>> lp(matrix.size(), vector<int> (matrix[0].size(), 0));
        int ans1 = 1;
        for(int i=0;i<matrix.size();i++){
            for(int j=0;j<matrix[0].size();j++){
                if(visited[i][j]==0) ans1=max(ans1, dfs(matrix, visited, lp, i, j));
                else ans1 = max(ans1, lp[i][j]);
                // cout<<i<<" "<<j<<" "<<lp[i][j]<<endl;
            }
        }
        return ans1;

    
    }
};
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