<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:
        indeg, adj_mat, dist = {}, {}, {}
        
        for i in range(len(matrix)):
            for j in range(len(matrix[0])):
                indeg[(i, j)] = 0
                adj_mat[(i, j)] = set() # u:v indicates path from u to v
                dist[(i, j)] = 1
        
        for i in range(len(matrix)):
            for j in range(len(matrix[0])):
                for di, dj in [(-1, 0), (1, 0), (0, -1), (0, 1)]:
                    ni, nj = i+di, j+dj
                    if 0<=ni<len(matrix) and 0<=nj<len(matrix[0]) and matrix[ni][nj] > matrix[i][j]:
                        adj_mat[(i, j)].add((ni, nj))
                        indeg[(ni, nj)] += 1
        
        to_remove = [u for u in indeg if indeg[u] == 0]
        result = 1
        while len(to_remove) != 0:
            new_to_remove = []
            for u in to_remove:
                del indeg[u]
                for v in adj_mat[u]:
                    indeg[v] -= 1
                    if indeg[v] == 0:
                        new_to_remove.append(v)
                    dist[v] = max(dist[v], 1+dist[u])
                    result = max(result, 1+dist[u])
            to_remove = new_to_remove
        return result
                
                
            
        
                        
                
        
25355