<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:
    def longestIncreasingPath(self, matrix: List[List[int]]) -> int:
        """
        [
            [9,9,4],
            [6,6,8],
            [2,1,1]
        ]
        
        [
            [1,1,2],
            [2,2,1],
            [3,4,2]
        ]
        """
        n = len(matrix)
        m = len(matrix[0])
        visited = [[0] * m for _ in range(n)]
        
        def findInceasingPath(r, c, prev):
            nonlocal n
            nonlocal m
            
            if r < 0 or r == n or c < 0 or c == m:
                return 0
            
            if matrix[r][c] <= prev:
                return 0
            
            if visited[r][c] > 0:
                return visited[r][c]
            
            maxLen = 0
            maxLen = max(maxLen, findInceasingPath(r + 1, c, matrix[r][c]))
            maxLen = max(maxLen, findInceasingPath(r, c + 1, matrix[r][c]))
            maxLen = max(maxLen, findInceasingPath(r - 1, c, matrix[r][c]))
            maxLen = max(maxLen, findInceasingPath(r, c - 1, matrix[r][c]))
            
            visited[r][c] = maxLen + 1
            
            return visited[r][c]
            
            
        maxPathLen = 0
        for r in range(n):
            for c in range(m):
                pathLen = findInceasingPath(r, c, -1)
                maxPathLen = max(maxPathLen, pathLen)
                
        return maxPathLen
                
                
                
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