<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 checkValid(self, i, j, n, m):
        if i>=0 and i<n and j>=0 and j<m:
            return True
        return False

    def dp(self, matrix, i, j): # longest incr path starting at (i, j)
        if self.mat[i][j] != -1:
            return self.mat[i][j]
        n = len(matrix)
        m = len(matrix[0])
        longestPath = 1
        for dir in self.dirs:
            x = i + dir[0]
            y = j + dir[1]
            if self.checkValid(x, y, n, m) and matrix[x][y] > matrix[i][j]:
                longestPath = max(longestPath, 1 + self.dp(matrix, x, y))
        self.mat[i][j] = longestPath
        return self.mat[i][j]

    def longestIncreasingPath(self, matrix: List[List[int]]) -> int:
        self.dirs = [[0, -1], [0, 1], [1, 0], [-1, 0]]
        self.mat = []
        n = len(matrix)
        m = len(matrix[0])
        for i in range(n):
            row = []
            for j in range(m):
                row.append(-1)
            self.mat.append(row)
        maxLen = 1
        for i in range(n):
            for j in range(m):
                maxLen = max(maxLen, self.dp(matrix, i, j))
        # print (self.mat)
        return maxLen
                




        
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