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Consider a B+-tree in which the maximum number of keys in a node is 5. What is the minimum number of child pointers in any non-root internal node?

Question

Consider a B+-tree in which the maximum number of keys in a node is 5. What is the minimum number of child pointers in any non-root internal node?

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Solution

To determine the minimum number of child pointers in any non-root internal node of a B+-tree with a maximum of 5 keys in a node, we need to consider the properties of a B+-tree.

In a B+-tree, each internal node (excluding the root) must have at least ⌈(n+1)/2⌉ child pointers, where n is the maximum number of keys in a node.

In this case, n is 5, so the minimum number of child pointers in any non-root internal node would be ⌈(5+1)/2⌉ = ⌈6/2⌉ = ⌈3⌉ = 3.

Therefore, the minimum number of child pointers in any non-root internal node of this B+-tree is 3.

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