DSA Binary Trees
🌳 DSA Binary Trees – Complete Beginner Guide
(Concept • Types • Traversals • Implementation • Examples • Complexity)
A Binary Tree is one of the most important tree structures in DSA.
In a binary tree, each node can have at most two children.
1️⃣ What is a Binary Tree?
A Binary Tree is a tree where each node has:
Left child
Right child
Example
2️⃣ Binary Tree Terminology
| Term | Meaning |
|---|---|
| Root | Top node |
| Parent | Node with children |
| Child | Node below parent |
| Leaf | Node with no children |
| Edge | Connection |
| Level | Distance from root |
| Height | Longest path to leaf |
| Subtree | Part of tree |
3️⃣ Types of Binary Trees
1. Full Binary Tree
Each node has 0 or 2 children.
2. Complete Binary Tree
All levels filled except last, filled left to right.
3. Perfect Binary Tree
All internal nodes have 2 children and leaves at same level.
4. Balanced Binary Tree
Height difference ≤ 1 (example: AVL Tree).
5. Skewed Binary Tree
All nodes have only one child (left or right).
4️⃣ Binary Tree Traversals (Very Important)
Traversal = visiting nodes in a specific order.
1. Inorder Traversal
Left → Root → Right
2. Preorder Traversal
Root → Left → Right
3. Postorder Traversal
Left → Right → Root
Example Tree
| Traversal | Output |
|---|---|
| Inorder | 4 2 5 1 3 |
| Preorder | 1 2 4 5 3 |
| Postorder | 4 5 2 3 1 |
5️⃣ Binary Tree Node Structure (C++)
6️⃣ Binary Tree Example Program (C++)
Output
7️⃣ Binary Tree vs Binary Search Tree
| Feature | Binary Tree | BST |
|---|---|---|
| Ordering | ❌ No | ✅ Yes |
| Search | O(n) | O(log n) avg |
| Structure | Any | Ordered |
8️⃣ Time Complexity
| Operation | Time |
|---|---|
| Traversal | O(n) |
| Search | O(n) |
| Insert | O(n) |
📌 Binary Tree has no ordering, so operations are linear.
9️⃣ Real-Life Applications
✔ File systems
✔ Expression trees
✔ Syntax trees
✔ Decision trees
✔ Heaps
Interview Questions (Binary Tree)
Q1. What is a binary tree?
👉 Tree with at most 2 children per node
Q2. Difference between full and complete binary tree?
👉 Full = 0 or 2 children, Complete = left-filled
Q3. Traversal types?
👉 Inorder, Preorder, Postorder
Q4. Why binary tree traversal is important?
👉 Visiting nodes in structured order
Final Summary
✔ Binary tree = max 2 children per node
✔ Many types (full, complete, balanced)
✔ Traversals are key concept
✔ Important for DSA interviews
