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B+ Trees

Definition

A B+ tree of order M is a tree with the following structural properties: image-20240920155800064

  • 我们不能有一个根加一个孩子的结构
  • 这棵树是从下往上构建的,而非从上往下

Operation

Insertion

  • Simple spliting method
  • find a not full sibling(\(\times\))

image-20240920165325557

  • 从中我们可以看到,叶子节点元素个数最多有M

Deletion

与插入相似,但在一个节点失去两个孩子后,需要删掉它

Analysis

image-20240920165520696

因为在最坏的情况下,每个节点只有M/2个节点

image-20240920170023112

Problem

1

image-20240920192741785

D

Don't know.

2

image-20240920192922468

A

很简单,定义