Diameter of Binary Tree

LeetCode 543 | Difficulty: Easy

Easy

Problem 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:

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, 10^4]`.

- `-100 <= Node.val <= 100`

Topics: Tree, Depth-First Search, Binary Tree

---

Approach

Tree DFS

Traverse the tree recursively (or with a stack). At each node, decide: what information do I need from the left/right subtrees? Process: go left → go right → combine results. Consider preorder, inorder, or postorder traversal based on when you need to process the node.

When to use

Path problems, subtree properties, tree structure manipulation.

---

Solutions

Solution 1: C# (Best: 120 ms)

Metric	Value
Runtime	120 ms
Memory	N/A
Date	2018-04-25

Solution

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left;
 *     public TreeNode right;
 *     public TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int DiameterOfBinaryTree(TreeNode root) {
        if(root==null) return 0;
            int left = DiameterOfBinaryTree(root.left);
            int right = DiameterOfBinaryTree(root.right);
            int cur = Depth(root.left) + Depth(root.right);
            return Math.Max(cur, Math.Max(left, right));

        }

        public int Depth(TreeNode root){
            if(root==null) return 0;
            else return 1 + Math.Max(Depth(root.left), Depth(root.right));
        }
}

---

Complexity Analysis

Approach	Time	Space
Tree Traversal	$O(n)$	$O(h)$

---

Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.
• Consider: "What information do I need from each subtree?" — this defines your recursive return value.