DSA Trees
DSA Trees – Complete Beginner Guide
(Concept • Terminology • Types • Traversals • Examples • Complexity)
A Tree is a non-linear data structure used to represent hierarchical relationships.
It is one of the most important DSA topics for exams, interviews, and real-world systems.
1️⃣ What is a Tree?
A Tree consists of nodes connected by edges.
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One special node → Root
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Each node can have children
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No cycles (unlike graphs)
Example
2️⃣ Basic Tree Terminology
| Term | Meaning |
|---|---|
| Root | Topmost node |
| Parent | Node that has children |
| Child | Node below a parent |
| Leaf | Node with no children |
| Edge | Connection between nodes |
| Height | Longest path from node to leaf |
| Depth | Distance from root |
| Subtree | Tree formed from a node |
3️⃣ Why Trees Are Important
✔ Represent hierarchy (folders, org charts)
✔ Fast searching & sorting
✔ Foundation of advanced structures (BST, Heap, Trie)
✔ Used in databases & compilers
4️⃣ Types of Trees
1. General Tree
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Any number of children per node
2. Binary Tree
Each node has at most two children:
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Left child
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Right child
3. Binary Search Tree (BST)
A binary tree with ordering property:
✔ Faster search
✔ Ordered data
4. Full Binary Tree
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Every node has 0 or 2 children
5. Complete Binary Tree
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All levels filled except possibly last
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Last level filled left to right
6. Perfect Binary Tree
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All internal nodes have 2 children
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All leaves at same level
7. Balanced Tree
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Height difference ≤ 1
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Example: AVL Tree
5️⃣ Tree Traversals (Very Important)
Traversal = visiting all nodes.
1. Inorder (Left → Root → Right)
Used in BST to get sorted order
2. Preorder (Root → Left → Right)
Used to copy tree
3. Postorder (Left → Right → Root)
Used to delete tree
Example
| Traversal | Output |
|---|---|
| Inorder | 2 1 3 |
| Preorder | 1 2 3 |
| Postorder | 2 3 1 |
6️⃣ Tree Node Structure (C++)
7️⃣ Binary Tree Example (C++)
8️⃣ Binary Search Tree (BST) – Insert Example
9️⃣ Time Complexity
| Operation | BST (Avg) | BST (Worst) |
|---|---|---|
| Search | O(log n) | O(n) |
| Insert | O(log n) | O(n) |
| Delete | O(log n) | O(n) |
📌 Worst case happens when tree becomes skewed.
🔟 Tree vs Linked List
| Feature | Tree | Linked List |
|---|---|---|
| Structure | Hierarchical | Linear |
| Access | Fast | Slow |
| Use case | Hierarchy | Sequential data |
1️⃣1️⃣ Real-Life Applications
✔ File systems
✔ Database indexing
✔ Expression parsing
✔ DNS systems
✔ AI decision trees
Interview Questions (Trees)
Q1. What is a tree?
👉 Non-linear hierarchical structure
Q2. Difference between tree & graph?
👉 Tree has no cycles
Q3. Why inorder traversal is special in BST?
👉 Gives sorted order
Q4. What is height of tree?
👉 Longest path from root to leaf
Final Summary
✔ Trees are hierarchical data structures
✔ Root-based node structure
✔ Many types (Binary, BST, Balanced)
✔ Traversals are key concepts
✔ Extremely important for DSA & interviews
