<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:
        m = len(matrix)
        n = len(matrix[0])
        graph = defaultdict(list)
        deg = [[0 for j in range(n)] for i in range(m)]
        for i in range(m):
            for j in range(n):
                dirs = [(0, 1), (1, 0), (-1, 0), (0, -1)]
                for dx, dy in dirs:
                    new_i = i + dx
                    new_j = j + dy
                    if 0 <= new_i < m and 0 <= new_j < n and matrix[new_i][new_j] > matrix[i][j]:
                        graph[(i, j)].append((new_i, new_j))
                        deg[new_i][new_j] += 1
        
        dp = [[-1 for i in range(n)] for j in range(m)]
        def height(i, j):
            if dp[i][j] != -1:
                return dp[i][j]
            max_children_height = 0
            for new_i, new_j in graph[(i, j)]:
                max_children_height = max(max_children_height, height(new_i, new_j))
            dp[i][j] = max_children_height + 1
            return max_children_height + 1
        
        ret = float('-inf')

        for i in range(m):
            for j in range(n):
                if deg[i][j] == 0:
                    ret = max(ret, height(i, j))
        
        return ret
25875