<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:
        
                
        adj_mat, dist, indeg = {}, {}, {}
        
        for i in range(len(matrix)):
            for j in range(len(matrix[0])):
                dist[(i, j)] = 1
                adj_mat[(i, j)] = set()
                indeg[(i, j)] = 0
        
        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
        
        from collections import deque
        q = deque([u for u in indeg if indeg[u]==0])
        while len(q) > 0:
            u = q.popleft()
            for v in adj_mat[u]:
                if 1+dist[u] > dist[v]:
                    dist[v] = 1+dist[u]
                    q.append(v)
        return max([v for v in dist.values()])
        

#         for u in indeg:
#             if indeg[u] == 0:
#                 dist[u] = 1
#         def recur(u):
#             for v in adj_mat[u]:
#                 if v not in dist:
#                     dist[v] = dist[u]+1
#                 else:
#                     dist[v] = max(dist[v], dist[u]+1)
                
            
#         for u in dist:
            
                
        
#         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 = set([u for u in indeg if indeg[u] == 0])
#         result = 1
#         while len(to_remove) != 0:
#             u = to_remove.pop()
#             del indeg[u]
#             for v in adj_mat[u]:
#                 indeg[v] -= 1
#                 if indeg[v] == 0:
#                     to_remove.add(v)
#                 dist[v] = max(dist[v], 1+dist[u])
#                 result = max(result, 1+dist[u])
#         return result
                
                
            
        
                        
                
        
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