<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:
        max_row=len(matrix)
        max_col=len(matrix[0])
        @cache
        def dfs(curr):
            out=[1]
            if curr[0]>0 and matrix[curr[0]][curr[1]]<matrix[curr[0]-1][curr[1]]:
                out.append(dfs((curr[0]-1,curr[1]))+1)
            if  curr[1]>0 and matrix[curr[0]][curr[1]]<matrix[curr[0]][curr[1]-1]:
                out.append(dfs((curr[0],curr[1]-1))+1)
            if curr[0]<max_row-1 and matrix[curr[0]][curr[1]]<matrix[curr[0]+1][curr[1]]:
                out.append(dfs((curr[0]+1,curr[1]))+1)
            if curr[1]<max_col-1 and matrix[curr[0]][curr[1]]<matrix[curr[0]][curr[1]+1]:
                out.append(dfs((curr[0],curr[1]+1))+1)
            return max(out)
        curr_max=1
        for i in range(max_row):
            for j in range(max_col):
                if (i==0 or matrix[i][j]<=matrix[i-1][j])and (j==0 or matrix[i][j]<=matrix[i][j-1]) and(i==max_row-1 or matrix[i][j]<=matrix[i+1][j])and (j==max_col-1 or matrix[i][j]<=matrix[i][j+1]):
                    curr_max=max(dfs((i,j)),curr_max)
        return curr_max
24055