Trees in Data Structures
A tree is a non-linear hierarchical data structure consisting of nodes connected by edges. It is widely used in search operations, hierarchical data storage, and decision-making processes.
What is a Tree?
A tree consists of:
- Root Node – The topmost node
- Child Node – Nodes connected to another node
- Parent Node – Node with children
- Leaf Node – Node with no children
- Edge – Connection between nodes
Properties of Trees
- One root node
- N nodes have N-1 edges
- Depth of a node = distance from root
- Height of a tree = maximum depth of a node
Types of Trees
1. Binary Tree
- Each node has at most two children
- Simplest form of a tree
2. Binary Search Tree (BST)
- Left child < parent
- Right child > parent
- Supports efficient search, insertion, deletion
3. Full Binary Tree
- Each node has 0 or 2 children
4. Complete Binary Tree
- All levels except last are full
- Nodes filled from left to right
5. AVL Tree
- Self-balancing BST
- Height difference between left and right subtrees ≤ 1
6. N-ary Tree
- Each node can have up to N children
Basic Operations on Trees
1. Traversal
- Inorder – Left → Root → Right
- Preorder – Root → Left → Right
- Postorder – Left → Right → Root
- Level Order – By levels using queue
2. Insertion
Add a node at the correct position (depends on tree type)
3. Deletion
Remove a node and maintain structure
4. Searching
Find a node based on value
Advantages of Trees
- Represents hierarchical data
- Efficient search and insertion (BST)
- Dynamic memory usage
- Forms the basis for advanced structures (heaps, tries)
Disadvantages of Trees
- Complex implementation
- Requires pointers
- Traversal can be time-consuming for large trees
Real-World Applications of Trees
- File system hierarchy
- Organizational charts
- Decision-making algorithms
- Database indexing (B-trees)
- Expression parsing in compilers
Tree vs Linked List
| Tree | Linked List |
|---|---|
| Non-linear | Linear |
| Hierarchical | Sequential |
| Faster search with BST | Linear search only |
| Complex implementation | Simple implementation |
Conclusion
Trees are a fundamental non-linear data structure used for hierarchical data storage and efficient searching. Mastering trees is crucial for understanding advanced structures like heaps, graphs, and tries, which are widely used in real-world applications.