<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:
        # build graph, if the number next to it is larger, create an edge
        edges = []
        nrow = len(matrix); ncol = len(matrix[0])
        for i in range(len(matrix)):
            for j in range(len(matrix[0])):
                cur = matrix[i][j]
                n1 = i * ncol + j
                if i > 0 and matrix[i-1][j] > cur:
                    n2 = (i - 1) * ncol + j
                    edges.append((n1, n2))
                if i < nrow - 1 and matrix[i+1][j] > cur:
                    n2 = (i + 1) * ncol + j
                    edges.append((n1, n2))
                if j > 0 and matrix[i][j-1] > cur:
                    n2 = i * ncol + j - 1
                    edges.append((n1, n2))
                if j < ncol - 1 and matrix[i][j+1] > cur:
                    n2 = i * ncol + j + 1
                    edges.append((n1, n2))

        childToParents = {}; parentToChildren = {}
        for edge in edges:
            child = edge[0]
            parent = edge[1]
            if child in childToParents:
                childToParents[child].append(parent)
            else:
                childToParents[child] = [parent]
            if parent in parentToChildren:
                parentToChildren[parent].append(child)
            else:
                parentToChildren[parent] = [child]

        lengths = [0] * ncol * nrow
        while len(childToParents) > 0:
            removeParents = []
            for parent in parentToChildren:
                if len(parentToChildren[parent]) == 0:
                    removeParents.append(parent)
            for parent in removeParents:
                del parentToChildren[parent]
            # find the leaves first, update the leaves iteratively
            notleaves = set(childToParents.keys()).intersection(set(parentToChildren.keys()))
            leaves = [node for node in childToParents.keys() if node not in notleaves]
            for leaf in leaves:
                parents = childToParents[leaf]
                for parent in parents:
                    lengths[parent] = max(1 + lengths[leaf], lengths[parent])
            # remove leaf from both childToParents and parentToChildren
                del childToParents[leaf]
                for parent in parents:
                    parentToChildren[parent].remove(leaf)
        return max(lengths) + 1
25095