Advanced Trees
Explore self-balancing trees, heaps for priority, and tries for efficient string searching.
Explore self-balancing trees, heaps for priority, and tries for efficient string searching. This hands-on tutorial focuses on practical implementation of advanced trees concepts.
Advanced Trees
Standard Binary Search Trees can become skewed (like a linked list) in the worst case. Advanced tree structures solve specific performance problems.
1. Self-Balancing Trees (AVL)
An AVL Tree is a BST where the heights of the two child subtrees of any node differ by at most one. If they differ by more, Rotations are performed to rebalance the tree.
2. Binary Heap
A Heap is a complete binary tree used to implement Priority Queues.
- Max-Heap: Parent is always $\ge$ children.
- Min-Heap: Parent is always $\le$ children.
3. Trie (Prefix Tree)
A Trie is used for efficient string storage and searching (e.g., auto-complete). Each node represents a character.
Stores: "ant", "and", "by"
Comparison: Tree Complexity
| Tree Type | Search | Insert | Best For |
|---|---|---|---|
| AVL Tree | O(log n) | O(log n) | Frequent Search |
| Binary Heap | O(n) | O(log n) | Priority Max/Min |
| Trie | O(L) | O(L) | Prefix Search |
L = length of the word
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Quiz
Quiz
Question 1 of 2Which tree structure is ideal for implementing an auto-complete feature?