<p>Given the <code>root</code> of a binary tree, return <em>the length of the <strong>diameter</strong> of the tree</em>.</p>

<p>The <strong>diameter</strong> of a binary tree is the <strong>length</strong> of the longest path between any two nodes in a tree. This path may or may not pass through the <code>root</code>.</p>

<p>The <strong>length</strong> of a path between two nodes is represented by the number of edges between them.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/06/diamtree.jpg" style="width: 292px; height: 302px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,5]
<strong>Output:</strong> 3
<strong>Explanation:</strong> 3 is the length of the path [4,2,1,3] or [5,2,1,3].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> root = [1,2]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>4</sup>]</code>.</li>
	<li><code>-100 &lt;= Node.val &lt;= 100</code></li>
</ul>

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def diameterOfBinaryTree(self, root: Optional[TreeNode]) -> int:
        stack = [(root, None, 0)]
        max_depth, max_depth_node, graph = 0, root, {}
        while stack:
            node, parent, depth = stack.pop()
            if depth > max_depth:
                max_depth = depth
                max_depth_node = node
            graph[node] = parent
            if node.left:
                stack.append((node.left, node, depth + 1))
            if node.right: 
                stack.append((node.right, node, depth + 1))
        
        stack = [(max_depth_node, 0)]
        max_length, visited = 0, set()
        while stack:
            node, length = stack.pop()
            visited.add(node)
            max_length = max(max_length, length)
            if graph[node] is not None and graph[node] not in visited:
                stack.append((graph[node], length + 1))
            if node.left and node.left not in visited:
                stack.append((node.left, length + 1))
            if node.right and node.right not in visited:
                stack.append((node.right, length + 1))

        return max_length
18800