<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 {
    int dfs(vector<vector<int>>& matrix, int row, int col, vector<vector<int>>& cache, vector<vector<int>>& directions)
    {
        if(cache[row][col] != -1) return cache[row][col];

        int path = 0;
        for(auto dir : directions)
        {
            int newRow = row + dir[0];
            int newCol = col + dir[1];

            if(newRow < 0 || newCol < 0 || newRow >= matrix.size() || newCol >= matrix[0].size()) continue;
            if(matrix[row][col] < matrix[newRow][newCol]) path = max(dfs(matrix, newRow, newCol, cache, directions), path);
        }

        return cache[row][col] = path + 1;
    }
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int rowCount = matrix.size();
        int colCount = matrix[0].size();
        vector<vector<int>> longestPaths(rowCount, vector<int>(colCount, -1));
        vector<vector<bool>> visited(rowCount, vector<bool>(colCount, false));
        vector<vector<int>> directions = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
        
        int longestPath = 0;
      
        for(int row = 0; row < rowCount; row++)
        {
            for(int col = 0; col < colCount; col++)
            {
                if(longestPaths[row][col] != -1) longestPath = max(longestPath, longestPaths[row][col]);
                else longestPath = max(longestPath, dfs(matrix, row, col, longestPaths, directions));
            }
        }
        
        return longestPath;
    }
};
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