问题
How many nodes does a resulting B-Tree(min degree 2) have if I insert numbers from 1 to n in order?
I tried inserting nodes from 1 to 20 there was a series for the number of nodes coming but i could not generalize it.
Can anyone please help me derive the formula for this.
回答1:
It will depend on the order of the B-Tree. The order of a BTree is the maximum number of children nodes a non-leaf node may hold (which is one more than the minimum number of keys such a node could hold).
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, and internal vertices carry no information.
So in your case when you are inserting 20 keys if the order is m then based on the conditions mentioned above you can derive a set of inequalities that describes the possible value of m. But there is no equality formula that says the number of internal nodes in a B-Tree.
来源：https://stackoverflow.com/questions/26238014/number-of-nodes-in-a-b-tree