Trees with higher branching factors (e.g B+trees and B-trees) decreases what relative to the number of items stored in the tree?

Question

BlackTom AI · Accepted Answer

Question Restatement:
- Question: Trees with higher branching factors (e.g B+trees and B-trees) decreases what relative to the number of items stored in the tree?
- Options: ["None of the other answers are correct.", "the total number of nodes", "deletion speed only", "tree height", "the maximum number of children of a node"]

Option 1: None of the other answers are correct.
- This choice claims that all other options are incorrect. To assess it, we evaluate the other choices individually. Since at least one option (tree height) is actually affected by branching factor in B-trees/B+-trees, this statement cannot be true overall. Therefore, this option is not correct.

Option 2: the total number of nodes
- Higher branching factor means each node can point to more children, which can influence how many nodes are needed for a given number of items. However, for B-trees, increasing fan-out primarily reduces the height of the tree; the total node count does not consistently decrease simply due to a larger branching factor. In some configurations, you may even end up with more nodes due to more entries per node, even as height drops. Thus, saying it reliably decreases the total number of nodes is incorrect.

Option 3: deletion speed only
- Deletion speed is not the sole property governed by branching factor. While height can affect operation costs, deletion involves rebalancing and merging nodes, and the statement that branching factor only affects deletion speed is oversimplified and inaccurate. This option mischaracterizes the impact of branching on performance.

Option 4: tree height
- In B-trees and B+-trees, increasing the branching factor (fan-out) allows more keys and children per node, which reduces the overall height required to store a given number of items. This is a core and well-known property: higher branching factor lowers height, roughly logarithmically with respect to fan-out. This directly answers the question: the quantity that decreases when branching factor increases is the tree height.

Option 5: the maximum number of children of a node
- The maximum number of children of a node is a design parameter that actually increases as you raise the branching factor, not decreases. Saying higher branching decreases this maximum would be incorrect; it typically has the opposite effect. Therefore, this option is false.

Overall assessment:
- Option 4 (tree height) is the correct statement about what decreases when you increase branching factor in these trees. The other options either misstate the effect or claim effects that don’t align with how B-trees and B+-trees manage height, node counts, and structural parameters.

Trees with higher branching factors (e.g B+trees and B-trees) decreases what relative to the number of items stored in the tree?单项选择题

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