# 0543. Diameter of Binary Tree

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

## Description

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`

## ac

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    private int diameter = 0;

    public int diameterOfBinaryTree(TreeNode root) {
        max(root);
        return diameter;
    }

    private int max(TreeNode root) {
        // exit
        if (root == null) return 0;

        // divide and conquer
        int lmax = max(root.left);
        int rmax = max(root.right);

        diameter = Math.max(diameter, lmax + rmax);

        return Math.max(lmax+1, rmax+1);
    }
}
```
