木構造アルゴリズムAdvanced

AVL Tree

First self-balancing binary search tree invented in 1962 by Adelson-Velsky and Landis. Maintains height balance through rotations, guaranteeing O(log n) operations. Stricter balancing than red-black trees makes it ideal for lookup-heavy applications like databases and file systems.

#tree#self-balancing#rotation#binary-search-tree

Complexity Analysis

Time (Average)

O(log n)

Expected case performance

Space

O(n)

Memory requirements

Time (Best)

O(log n)

Best case performance

Time (Worst)

O(log n)

Worst case performance

📚 CLRS Reference

Introduction to Algorithms•Chapter 13•Section Notes

Values to Insert (comma-separated, max 10)

Watch rotations maintain balance!

Example Sets:

Rotation Types

• LL: Right rotation (left-heavy)
• RR: Left rotation (right-heavy)
• LR: Left-Right rotation
• RL: Right-Left rotation
• Balance factor: height(left) - height(right)
• O(log n) for insert, delete, search

Step: 1 / 0

Animation Speed500ms

SlowFast

Keyboard Shortcuts

Space Play/Pause← → StepR Reset1-4 Speed

Real-time Statistics

Algorithm Performance Metrics

Progress0%

Comparisons

Swaps

Array Accesses

Steps

1/ 0

Algorithm Visualization

Step 1 of 0

Initialize array to begin

Default

Comparing

Swapped

Sorted

Code Execution

Currently executing

Previously executed

Implementation

Related Algorithms

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Trie (Prefix Tree)

Intermediate

Tree-based data structure that stores strings efficiently by sharing common prefixes. Each path from root to leaf represents a word or key. Excels at autocomplete, spell checking, IP routing tables, and dictionary implementations with O(m) operations where m is key length.

O(m)

O(ALPHABET_SIZE × N × M)

treestring-algorithms

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Lowest Common Ancestor (LCA)

Intermediate

Finds the deepest node that is an ancestor of two given nodes in a tree. Fundamental operation in tree queries with applications in computational biology (species evolution), network routing, and version control systems. Various algorithms offer different time-space tradeoffs.