Definição
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.
Estrutura
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 filhos e pelo menos ⌈m/2⌉ children (except for the root node, which can have fewer). Each node can store up to m – 1 chaves.
Operações
Operações comuns em árvores B incluem:
- Busca: Encontrar eficientemente uma chave dentro da árvore.
- Inserção: Adding a new key while maintaining the tree’s balance.
- Exclusão: Remover uma chave e reequilibrar a árvore, se necessário.
Aplicações
As árvores B são amplamente utilizadas em 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.