Pattern this teaches:Tree DFS
Diameter of Binary Tree
An easy Binary Trees interview guide. Task statement, worked examples, intuition, and step-by-step solutions.
- Topic
- Binary Trees
- Sheets
- 3
- Core for
- 4 roles
The problem
Among every pair of nodes in a binary tree, find the pair that are farthest apart and return how many edges separate them. That longest path does not have to pass through the root.
Example 1
- Input
- [8,4,9,2,6,null,10,1,null,null,7]
- Output
- 5
- Why
- The longest path 1-2-4-8-9-10 crosses 5 edges.
Example 2
- Input
- [1,2]
- Output
- 1
- Why
- Only path 1-2 has 1 edge.
Example 3
- Input
- [1,null,2,3]
- Output
- 2
- Why
- The longest path is 3 -> 2 -> 1, with 2 edges.
Constraints
- The number of nodes is in the range [1, 104].
- -100 <= Node.val <= 100
How to think about it
Updated 2026-09-29Every path in a binary tree has a unique highest node where it turns around. The longest path curving through any specific node is the maximum depth of its left branch plus the maximum depth of its right branch. Track the global maximum of this sum while bubbling depth upwards.
Approaches, worst first
Separate height calls at every node
time O(n^2) · space O(h)
For each node in the tree, invoke a height function on left and right subtrees and compute `leftHeight + rightHeight`. Recurse into children. Repeatedly visits nodes across multiple height calculations.
Postorder bottom-up aggregationWrite this one
time O(n) · space O(h)
Bottom-up DFS returns the depth of the current subtree. Along the way, update a global diameter tracker with `leftDepth + rightDepth`. Returns tree depth to the parent in single-pass linear time.
Where people lose marks · 3
- Assuming the longest path must pass through the root node; a deep, lopsided subtree can contain the entire diameter.
- Counting nodes instead of edges; a path across 4 nodes contains 3 edges.
- Returning the diameter from the recursive helper instead of the subtree height, which corrupts parent depth calculations.
The theory behind it
Binary Trees — the ground this problem stands on. All Binary Trees problems
What Binary Trees is
A binary tree is a branching data structure that starts at a single top node called the root, like an upside-down family tree. Every node holds a piece of data and can branch out to at most two children below it, known as the left child and the right child. Because there is no ordering rule about which values go left or right, finding a specific item can require checking every single node in the entire tree.
When to reach for it
Reach for binary trees when problems present hierarchical data with left and right child pointers. Questions asking for tree height, maximum depth, path sums from root to leaf, diameter, lowest common ancestor, or checking whether two trees are mirror reflections of each other all signal binary tree traversals. Any problem asking to inspect or reconstruct a tree layer by layer or path by path belongs here.
How the pattern works
Think recursively by focusing on what a single node must do. If the current node is null, return the base answer immediately. Otherwise, ask the left child for its result, ask the right child for its result, and combine both answers with the current node value before returning up to the parent. For horizontal scans, use a queue to read nodes layer by layer, measuring the queue length at the start of each layer to group nodes by depth.
More Binary Trees problems
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