<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, city: List[List[int]]) -> int:
        g = collections.defaultdict(list)
        direction =[[0,1], [0,-1], [-1,0],[1,0]]
        indegree = collections.defaultdict(int)
        
        m = len(city)
        n = len(city[0])
        
        # build a graph
        for i in range(m):
            for j in range(n):
                start_x, start_y = i, j
                for dx, dy in direction:
                    new_x, new_y = start_x+dx, start_y+dy
                    if new_x>=0 and new_x<m and new_y>=0 and new_y<n and city[new_x][new_y]>city[start_x][start_y]:
                        g[str([start_x, start_y])].append(str([new_x, new_y]))
                        v = indegree[str([new_x, new_y])]
                        v+=1
                        indegree[str([new_x, new_y])]=v
        
        
        all_keys = {str([i, j]) for i in range(m) for j in range(n)}
        queue = []
        for key in all_keys:
            if indegree[key]==0:
                queue.append([key, 1])
        
        res = float('-inf')
        out = []
        while queue:
            cur, cur_cnt = queue.pop(0)
            for adj in g[cur]:
                indegree[adj]-=1
                if indegree[adj]==0:
                    queue.append([adj, cur_cnt+1])   
                
            res = max(res, cur_cnt)
        return res
            # if cur_cnt>res:
            #     out.append(cur)
            #     res = cur_cnt
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