<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>>& dp, int row, int col)
    {
        vector<int> dr{0, 0, -1, 1};
        vector<int> dc{1, -1, 0, 0};
        
        // visited[row][col] = true;   
        if(dp[row][col] != 0)
            return dp[row][col];

        for( int i = 0; i < dr.size(); i++)
        {
            int rr = row  + dr[i];
            int cc = col  + dc[i];

            if( rr < 0 || cc < 0 || rr >= matrix.size() || cc >= matrix[0].size() )
                continue;

            int len = 0;
            if(  matrix[rr][cc] > matrix[row][col] )
            {
                len = dfs(matrix, dp, rr, cc);
                dp[row][col] = max( dp[row][col], len);
            }
        }
        return ++dp[row][col];
    }
    
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        if( matrix.empty())
            return 0;
        int rows = matrix.size();
        int cols = matrix[0].size();
        
        vector<vector<int>>  dp(rows, vector<int>(cols, 0));
        // vector<vector<bool>> visited(rows, vector<bool>(cols, false));
        
        int path_len = 0;
        for( int r = 0; r < rows; r++)
        {
            for( int c = 0; c < cols; c++)
            {
                    int len = dfs( matrix, dp, r, c);
                    path_len = max( path_len, len);
            }
        }
        return path_len;
    }
};
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