## Description

https://leetcode.com/problems/diameter-of-binary-tree/

Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the **longest** path between any two nodes in a tree. This path may or may not pass through the root.

**Example:**

Given a binary tree

1 / \ 2 3 / \ 4 5

Return **3**, which is the length of the path [4,2,1,3] or [5,2,1,3].

**Note:** The length of path between two nodes is represented by the number of edges between them.

## Explanation

the pass of two nodes are the sum of maximum heights of left, right subtrees.

## Python Solution

```
# Definition for a binary tree node.
# class TreeNode:
# def __init__(self, x):
# self.val = x
# self.left = None
# self.right = None
class Solution:
def diameterOfBinaryTree(self, root: TreeNode) -> int:
if root == None:
return 0
left_max = self.max_height(root.left)
right_max = self.max_height(root.right)
return max(self.diameterOfBinaryTree(root.left), self.diameterOfBinaryTree(root.right), left_max + right_max)
def max_height(self, root):
if root == None:
return 0
left = self.max_height(root.left)
right = self.max_height(root.right)
return max(left, right) + 1
```

- Time complexity: O(N).
- Space complexity: O(N).

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