Data Structures - Introduction
- Abstract data types
- Linear Data Structures
- Linked List Introduction
- Single Linked List
- Stacks using Array
- Stacks using linkedlist
- Queues using array
- Queues using linkedlist
- Stack Applications
- Infix to Postfic Converstion
- Postfix Evaluation
- Dictionaries
- Introduction to Dictionaries
- Linear list representation
- Skip list representation
- Hash Table
- Introduction Hash Table
- Hash functions
- Collision Resolution
- Separate chaining
- Open addressing
- Rehashing
- Extendible hashing
- Trees
- Introduction to Tree
- Binary trees Representation
- Binary tree traversals
- Binary Search Tree
- AVL Tree
- Red Black Tree
- Splay Tree
- B Tree
- B+ Tree
- Comparison of Trees
- Graphs
- Introduction to Graph
- Graph Representation
- Breadth-First Search
- Depth-First Search
- Sorting
- Quick Sort
- Merge Sort
- Heap Sort
- Pattern Matching
- Introduction to pattern Matching
- Brute force Pattern Matching
- Boyer–Moore Pattern Matching
- KMP Pattern Matching
- Tries
- Introduction to Tries
- Standard Trie
- Compressed tries
- Suffix Trie
Comparison of Trees
Binary Search Trees (BSTs), AVL Trees, Red-Black Trees, B-Trees, and B+ Trees are all types of self-balancing tree data structures that are used to store, retrieve, modify, and delete data in an efficient manner. Each has its unique characteristics, advantages, and disadvantages. Here's a comparison
| Feature | BST | AVL Tree | Red-Black Tree | B-Tree | B+ Tree |
|---|---|---|---|---|---|
| Structure | Binary tree with ordered keys | Balanced binary tree with rotation operations | Self-balancing binary tree with red and black nodes | Multi-level tree with ordered keys at each level | Multi-level tree with data stored only at leaf nodes |
| Balancing | No automatic balancing | Guaranteed height balance (log n) | Probabilistically balanced with O(log n) height | Guaranteed height balance (log m N) | No internal node data, balanced using pointer adjustments |
| Space complexity | O(n) | O(n) | O(n) | O(n) | O(n) |
| Good for | Simple searches and insertions, basic data structures | Efficient searches and insertions with guarantees on worst-case performance | Efficient searches and insertions with probabilistically good performance | Large datasets, efficient search and range queries | Efficient storage and search of large datasets with frequent updates |
| Disadvantages | Unbalanced trees can lead to slow performance | More complex than BST, overhead of balance operations | Slightly more complex than AVL tree, no guarantee of balance | Not suitable for small datasets, higher space complexity | Less flexibility than B-tree, data not stored in internal nodes |
Comparison of trees based on the Time complexity
| Tree Types | Average Case | Worst Case | ||||
|---|---|---|---|---|---|---|
| Insert | Delete | Search | Insert | Delete | Search | |
| Binary Search Tree | O(log n) | O(log n) | O(log n) | O(n) | O(n) | O(n) |
| AVL Tree | O(log2 n) | O(log2 n) | O(log2 n) | O(log2 n) | O(log2 n) | O(log2 n) |
| B - Tree | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) |
| Red - Black Tree | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) |
| Splay Tree | O(log2 n) | O(log2 n) | O(log2 n) | O(log2 n) | O(log2 n) | O(log2 n) |
Choosing the right data structure depends on your specific needs:
- BST: Use it for basic operations on small datasets or if simplicity is more important than performance.
- AVL Tree: Choose it if you need guaranteed good performance for searches and insertions even on unbalanced data.
- Red-Black Tree: Opt for it if you want probabilistic good performance and a simpler implementation than AVL trees.
- B-Tree: Select it when dealing with large datasets on disk or other secondary storage due to its efficient search and range queries.
- B+ Tree: Use it for scenarios similar to B-trees, but when data size matters, as it stores data only in leaf nodes, optimizing space usage.
Next Topic :Introduction to Graph