<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:
        m = len(matrix)
        n = len(matrix[0])
        size = m * n
        g = defaultdict(list)

        def add(a,b):
            g[a].append(b)
        
        def toSingle(i,j):
            return i * n + j
        
        for i in range(m):
            for j in range(n):
                if i - 1 >= 0 and matrix[i-1][j] > matrix[i][j]:
                    add(toSingle(i,j), toSingle(i-1,j))
                if i + 1 < m and matrix[i+1][j] > matrix[i][j]:
                    add(toSingle(i,j), toSingle(i+1,j))
                if j - 1 >= 0 and matrix[i][j-1] > matrix[i][j]:
                    add(toSingle(i,j), toSingle(i,j-1))
                if j+1 < n and matrix[i][j+1] > matrix[i][j]:
                    add(toSingle(i,j), toSingle(i,j+1))
        degree = [0]*size
        q = deque()
        for k,arr in g.items():
            # print(k,arr)
            for v in arr:
                degree[v] += 1
        dis = [1]*size
        for i, cnt in enumerate(degree):
            if cnt == 0:
                q.append((i, 1))
                dis[i] = 1
        
        while q:
            node, distance = q.popleft()
            for nei in g[node]:
                if distance + 1 > dis[nei]:
                    dis[nei] = distance + 1
                    q.append((nei, dis[nei]))
        # print(dis)
        return max(dis)

            

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