<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:
        # # if len(matrix) == 1 and len(matrix[0]) ==1:
        # #     return 1
        # rows = len(matrix)
        # cols = len(matrix[0])
        # max_length = 0
        # directions = [(0,1),(0,-1),(1,0),(-1,0)] #right, left, down, up

        # def dfs( i, j, sequence, visited):
        #     nonlocal max_length
        #     if max_length <len(sequence):
        #         max_length = len(sequence)
        #     for w,z in directions:
        #         x, y = i+w, j+z
        #         if 0<= x< rows and 0 <= y < cols and matrix[i][j]<matrix[x][y] and (x,y) not in visited:
        #             sequence.append(matrix[x][y])
        #             visited.add((x,y))
        #             dfs(x, y, sequence, visited)
        #             sequence.pop()
        #             visited.remove((x,y))
        # visited = set()
        # for i in range(0, rows):
        #     for j in range(0,cols):
        #         visited.add((i,j))
        #         dfs(i, j, [matrix[i][j]], visited)
        #         visited.remove((i,j))
        # return max_length

        if not matrix or not matrix[0]:
            return 0
        
        rows, cols = len(matrix), len(matrix[0])
        directions = [(0,1),(0,-1),(1,0),(-1,0)]  # right, left, down, up
        
        @lru_cache(None)
        def dfs(i, j):
            max_length = 1
            for di, dj in directions:
                ni, nj = i + di, j + dj
                if 0 <= ni < rows and 0 <= nj < cols and matrix[ni][nj] > matrix[i][j]:
                    max_length = max(max_length, 1 + dfs(ni, nj))
            return max_length
        
        return max(dfs(i, j) for i in range(rows) for j in range(cols))



        
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