<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:
        ln_i = len(matrix)
        ln_j = len(matrix[0])

        path_matrix = [[1 for _ in range(ln_j)] for _ in range(ln_i)]

        flag = True
        while flag:
            flag = False
            for ind_i in range(ln_i):
                for ind_j in range(ln_j):
                    i = matrix[ind_i][ind_j]
                    prev_path_ln_i = path_matrix[ind_i][ind_j]
                    path_ln_i = 1

                    if ind_i != 0 and matrix[ind_i-1][ind_j] > i:
                        path_ln_i = max(path_ln_i, path_matrix[ind_i-1][ind_j]+1)
                    if ind_j != ln_j-1 and matrix[ind_i][ind_j+1] > i:
                        path_ln_i = max(path_ln_i, path_matrix[ind_i][ind_j+1]+1)
                    if ind_i != ln_i-1 and matrix[ind_i+1][ind_j] > i:
                        path_ln_i = max(path_ln_i, path_matrix[ind_i+1][ind_j]+1)
                    if ind_j != 0 and matrix[ind_i][ind_j-1] > i:
                        path_ln_i = max(path_ln_i, path_matrix[ind_i][ind_j-1]+1)
                
                    path_matrix[ind_i][ind_j] = path_ln_i
                    if prev_path_ln_i != path_ln_i:
                        flag = True
        
        Max = 0
        for ind_i in range(ln_i):
            for ind_j in range(ln_j):
                Max = max(Max, path_matrix[ind_i][ind_j])
        return Max
17165