b-tree# Why do some btree diagrams have multiple nodes at the same level?

Why do some diagrams have no value for each node and instead have 2 values? What are they trying to represent?

The second diagram makes sense if 8 has a left and right node of 6 and 7. I don't understand why in the first diagram 100 has 2 left and 2 right nodes.

What am I missing here?

Solution

I don't understand why in the first diagram 100 has 2 left and 2 right nodes.

First of all, a B-tree is not a binary (search) tree: a node in a B-tree is designed to allow for more than one key up to a fixed maximum. In the first image, a box represents a *single* node with potentially multiple keys. In the second image there are separation lines between the keys, but it is the same principle. So in usual terminology the first diagram shows a root node with only two children, not four.

Why do some diagrams have no value for each node and instead have 2 values?

You are referring to the *keys* contained within a single node. Each node has a fixed number of slots that can be occupied by keys, but this is dynamic. During the lifetime of a node, it may have a varying number of keys, but within certain limits.

The images depict B-trees of order 3 (using Knuth's definition of order, which is the maximum branching factor).

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