Consider below statements – (I) Each non-leaf node in B⁺ tree has between…
2024
Consider below statements – (I) Each non-leaf node in B⁺ tree has between ⌈n/2⌉ and n children, where n is fixed for a particular tree. (II) The search key of a clustering index is always primary key. (III) Secondary indices must be dense. (IV) In a dense index, an index entry appears for only some of the search-key values. Which of the above statements are true?
- A.
I and IV
- B.
II and III
- C.
I and III
- D.
I and II
- E.
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Correct answer: C
Let's analyze each statement: Statement (I): In a B⁺ tree, each non-leaf node must have between ⌈n/2⌉ and n children, where n is the maximum number of children. This ensures the tree remains balanced and efficient. Hence, this statement is true. Statement (II): A clustering index is based on the order of the data, but it does not have to be the primary key. It can be any attribute that determines the physical order of records. Hence, this statement is false. Statement (III): Secondary indices can be either dense or sparse. They are not required to be dense. Hence, this statement is false. Statement (IV): In a dense index, there is an index entry for every search-key value. In a sparse index, entries exist only for some values. Hence, this statement is false. Therefore, only Statement (I) is true. The correct option is the one that includes only (I).