<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:
        path = [[1,0], [-1, 0], [0, 1], [0, -1]]
        global record
        record = []
        for i in range(len(matrix)):
            record.append([-1]*len(matrix[0]))
        def dfs(matrix, x, y):
            step = 0
            for i in path:
                if len(matrix) > (x + i[0]) >=0 and  len(matrix[0]) > (y + i[1]) >=0 and \
                    matrix[x + i[0]][y + i[1]] > matrix[x][y]:
                    if record[x + i[0]][y + i[1]] == -1:
                        step = max(step, 1 + dfs(matrix, x + i[0], y + i[1]))
                    else:
                        step = max(step,1 + record[x + i[0]][y + i[1]])
            record[x][y] = step
            return record[x][y]
        for i in range(len(matrix)):
            for j in range(len(matrix[0])):
                if record[i][j] == -1:
                    dfs(matrix, i, j)
        output = 0
        for i in range(len(matrix)):
            for j in range(len(matrix[0])): 
                output = max(output, record[i][j]) 
        return output + 1

17555