# 543. Diameter of Binary Tree

#### Easy

***

Given the `root` of a binary tree, return *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`.

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

 

**Example 1:**

![](https://assets.leetcode.com/uploads/2021/03/06/diamtree.jpg)

```
Input: root = [1,2,3,4,5]
Output: 3
Explanation: 3 is the length of the path [4,2,1,3] or [5,2,1,3].
```

**Example 2:**

```
Input: root = [1,2]
Output: 1
```

 

**Constraints:**

* The number of nodes in the tree is in the range `[1, 104]`.
* `-100 <= Node.val <= 100`

```python
# 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:
        result = 0
        def recursion(root):
            nonlocal result
            if not root:
                return 0
            left = 0
            if root.left:
                left = recursion(root.left) + 1
            right = 0
            if root.right:
                right = recursion(root.right) + 1
            temp = max(left,right)
            if left+right > result:
                result = left+right
            return temp
        recursion(root)
        return result
```