定義
A B-tree is a self-balancing tree data structure that maintains sorted data and allows for search, sequential access, insertions, and deletions in logarithmic time. B-trees are a generalization of binary search trees in that a node can have more than two children. They are commonly used in databases and file systems to store and manage large amounts of data while minimizing disk I/O operations.
構造
Each node in a B-tree contains a number of keys and child pointers. The keys are stored in a sorted order, and the children of a node are pointers to its child nodes. The number of children is determined by the order of the B-tree, denoted as m. A B-tree of order m can have at most m 子を持つことができ、少なくとも⌈m/2⌉ children (except for the root node, which can have fewer). Each node can store up to m – 1 個のキーを持つことができます。
操作
B木における一般的な操作は以下の通りです：
- 探索： 木内で効率的にキーを見つける。
- 挿入： Adding a new key while maintaining the tree’s balance.
- 削除： キーを削除し、必要に応じて木を再バランスさせる。
応用例
B木は広く使用されています database systems and filesystems due to their ability to handle large blocks of data efficiently. They reduce the number of disk accesses required for operations, which is crucial for performance in systems that handle large datasets.