<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_map = defaultdict(list)
        indegrees = defaultdict(int)
        
        for r in range(len(matrix)):
            for c in range(len(matrix[0])):
                indegrees[(r, c)] = 0

        for r in range(len(matrix)):
            for c in range(len(matrix[0])):
                for dir in [(1, 0), (-1, 0), (0, 1), (0, -1)]:
                    n = (r + dir[0], c + dir[1])
                    if 0 <= n[0] < len(matrix) and 0 <= n[1] < len(matrix[0]):
                        # if neighbor greater than curr, then edge from curr to neighbor
                        if matrix[n[0]][n[1]] > matrix[r][c]:
                            adj_map[(r, c)].append(n)
                            indegrees[n] += 1
        
        cells = []
        for k, v in indegrees.items():
            if v == 0:
                cells.append((k, 1)) # cells contains coord and length of path to that cell

        print(adj_map)
        print('\n' + str(indegrees))
        print(cells)
        max_path = 1
        while cells:
            cell, length = cells.pop(0)
            max_path = max(length, max_path)
            # visit neighbors of this cell with indegree 0 by decrementing neighbors indegrees
            for n in adj_map[cell]:
                indegrees[n] -= 1
                if indegrees[n] == 0:
                    cells.append((n, length + 1))
        
        return max_path
            




                
                

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