# LeetCode 543. Diameter of Binary Tree

## 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).