木構造アルゴリズム

データベース、ファイルシステム、検索操作を支える階層的データ構造の扱い方を学びます。二分探索木を理解し、O(log n)の操作を保証するAVL木や赤黒木などの自己平衡木を探求し、データ処理や式の評価に不可欠な木の走査技法（中順、前順、後順）をマスターします。

3 アルゴリズム

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

Start Learning

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.

AVL Tree

Advanced

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.

💡 学習のヒント

基礎を固めるために初級レベルのアルゴリズムから始め、中級および上級のトピックに進んでください。各アルゴリズムには、インタラクティブな可視化、複雑度分析、複数の言語でのコード例が含まれています。