对于B-tree
,并没有一个明确的定义. 依据规则,大致可以按照 最重要参数 - order
的不同解释,分为两种
1. Bayer & McCreigt 1972
用 order 规定每个节点容纳的键值数量
d
:order
h
: depth ,深度,树高
k
: 节点的 健值数
N
: 一棵 B-tree 能储存的总键值
- 对于跟节点,
1 <= k <= 2d
- 对于其他的普通节点:
d <= k <= 2d
- 一个非叶 节点,有
k+1
个子节点 - 2(d+1)^h -1 <= N <= (2d + 1)^(h+1) - 1
2. Knuth 1998
用 order 规定每个非叶节点能引申的子节点数量。这个更为常见一些。
According to Knuth's definition, a B-tree of order m is a tree which satisfies the following properties:
- Every node has at most m children.
- Every non-leaf node (except root) has at least ⌈m⁄2⌉ children.
- The root has at least two children if it is not a leaf node.
- A non-leaf node with k children contains k−1 keys.
- All leaves appear in the same level
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