Overview
Tree structures provide hierarchical non-linear data organization optimized for logarithmic search, priority extraction, string prefix searching, and pattern mining. This directory covers foundational binary architectures, self-balancing search trees, probabilistic treaps, priority heaps, and digital tries.
Core Architectural Classifications
Foundational & Unbalanced Trees
- Binary Tree: The foundational non-linear node topology restricting child branching to at most 2 outgoing paths per node.
- Binary Search Tree (BST): A sorted tree structure enforcing left-to-right element ordering to enable high-speed value lookups.
Self-Balancing Search Trees
- AVL Tree: A strictly height-balanced search tree enforcing balance factor invariants () via localized single and double rotations.
- Red-Black Tree: A single-pass color-balanced BST that relaxes strict height constraints to achieve faster write operations with fewer total rotations.
- Randomized Search Trees (Treap, RST): A probabilistic structure assigning randomized priorities to simulate uniform random insertion orders, securing expected performance.
Digital & String Search Trees
- Multiway Trie: A character-path digital search tree mapping keys along edges rather than node bodies to achieve deterministic lookup times.
- Ternary Search Tree (TST): A space-efficient hybrid structure combining Trie prefix-matching logic with BST memory efficiency using 3 child pointers per node.
Priority & Array-Backed Trees
- Heap: A complete binary tree mapping directly onto contiguous flat arrays, providing constant-time root access for priority processing pipelines.
Pattern Mining Trees
- Frequent Pattern Tree (FP-Tree): A compact prefix tree compressing transaction logs to discover frequent itemsets without candidate pair generation.
Notes in This Section
| Note Link | Description |
|---|---|
| Binary Tree | Foundational non-linear hierarchical node network serving as the blueprint for search trees and heaps. |
| Binary Search Tree | Left-to-right sorted tree structure providing average search, insertion, and removal operations. |
| AVL Tree | Strictly height-balanced BST guaranteeing worst-case lookup bounds via structural rotations. |
| Red-Black Tree | Single-pass color-balanced BST optimizing write-heavy workloads with relaxed height rules. |
| Randomized Search Tree | Probabilistic Treap maintaining expected bounds regardless of input sorting patterns. |
| Multiway Trie | Digital search tree routing lookup queries along character-labeled edges for deterministic searches. |
| Ternary Search Tree | Memory-efficient hybrid trie replacing large node pointer arrays with Left/Middle/Right child pointers. |
| Heap | Array-backed complete binary tree powering priority queue dispatch pipelines with peek speed. |
| Frequent Pattern Tree (FP-Tree) | Dense prefix-tree structure optimizing transaction pattern mining in FP-Growth workflows. |