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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 keys in any non-root node?

(a) 1
(b) 2
(c) 3
(d) 4.

User Denix
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Final answer:

The minimum number of keys in any non-root node of a B+-tree with a maximum of 5 keys per node is 2. In a B+ tree with a maximum of 5 keys in a node, the minimum number of keys in any non-root node is 3, ensuring the tree remains balanced. the correct answer is B.

Step-by-step explanation:

In a B+-tree, the minimum number of keys in any non-root node is 2. A B+-tree is a self-balancing search tree in which all the keys are stored in the leaf nodes and the internal nodes act as intermediaries to guide the search process. In a B+-tree, each node, except for the root node, must contain at least half of the maximum number of keys allowed in the node. Since the maximum number of keys in a node is 5, the minimum number of keys in any non-root node is 2 (half of 5 is 2.5, but the number of keys must be a whole number).

In a B+ tree with a maximum of 5 keys in a node, the minimum number of keys in any non-root node is 3, ensuring the tree remains balanced.

When considering a B+ tree where the maximum number of keys in a node is 5, the minimum number of keys in any non-root node, according to the properties of B+ trees, would be half the maximum number of keys. Since the maximum is 5 and B+ trees have the property that all non-root nodes must be at least half full, we calculate the minimum as half of 5, rounded up. Therefore, the minimum is 3. So, in a B+ tree with a maximum of 5 keys in a node, the minimum number of keys in any non-root node is 3. This enforces the properties of the tree that keeps it balanced.

User Ajith Kumar
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