December 2016
Intermediate to advanced
440 pages
9h 44m
Japanese
Content preview from アルゴリズムクイックリファレンス 第2版
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146
■
5
章 探索
5.5.4
分析
平衡
AVL
木の探索の平均時性能は、
二分探索
と同じであり、
O(log n)
となる。
探索では回転が決して生じないことに注意する。
自己平衡二分木は、単純な二分探索木よりも挿入削除にずっと複雑なコードを必
要とする。回転メソッドを調べれば、いずれも固定個数の演算なので、定数時間の
振る舞いとして扱うことができる。平衡
AVL
木の高さは、回転により常に
O(log n)
なので、要素の挿入削除に際しても、
O(log n)
より多くの回転が行われることは決
してない。そこで、挿入削除が
O(log n)
時間だと確信を持てる。実行時性能の利得
という点でのトレードオフは常に検討の価値があるが、
AVL
木の各節点に高さ情報
を追加で格納すると、ストレージの要求が増える。
5.5.5
変形
二分木の自然な拡張は、
n
分木であり、各節点が
2
つ以上の値を持ち、
3
つ以上の
子を持つ。そのような木でよく使われるものが
B
木で、関係データベースの実装で
優れた性能を示す。
B
木の完全な分析は、（
Cormen et al., 2009
）にあり、例を含
めたオンラインのチュートリアル（
http:
//
www.bluerwhite.org
/
btree
/
）もある。
もう
1
つの自己平衡二分木として初版で紹介した赤黒木（
red-black tree
）があ
る。赤黒木は近似的に平衡しており、どの分岐も他の分岐の倍以上の高さにな
らないことが保証される。実装をリポジトリの
JavaCode.src.algs.model.tree. ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.