This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “B+ Tree”.
1. In a B+ tree, both the internal nodes and the leaves have keys.
Explanation: In a B+ -tree, only the leaves have keys, and these keys are replicated in non-leaf nodes for defining the path for locating individual records.
2. Which of the following is true?
a) B + tree allows only the rapid random access
b) B + tree allows only the rapid sequential access
c) B + tree allows rapid random access as well as rapid sequential access
d) B + tree allows rapid random access and slower sequential access
Explanation: The B+ -tree being a variation of B-tree allows rapid random access. In a B+ -tree the leaves are linked together, so it also provides rapid sequential access.
3. A B+ tree can contain a maximum of 7 pointers in a node. What is the minimum number of keys in leaves?
Explanation: Maximum number of pointers in a node is 7, i.e. the order of the B+ -tree is 7. In a B+ tree of order n each leaf node contains at most n – 1 key and at least ⌈(n − 1)/2⌉ keys. Therefore, a minimum number of keys each leaf can have = ⌈(7 – 1)/2⌉ = 3.
4. Which of the following is false?
a) A B+ -tree grows downwards
b) A B+ -tree is balanced
c) In a B+ -tree, the sibling pointers allow sequential searching
d) B+ -tree is shallower than B-tree
Explanation: A B+ -tree always grows upwards. And In a B+tree – i)The path from the root to every leaf node is of the same length, so the tree is balanced. ii) Leaves are linked, so allow sequential searching. iii) An index is built with a single key per block of data rather than with one key per data record, so it is shallower than B-tree.
6. Statement 1: When a node is split during insertion, the middle key is promoted to the parent as well as retained in right half-node.
Statement 2: When a key is deleted from the leaf, it is also deleted from the non-leaf nodes of the tree.
a) Statement 1 is true but statement 2 is false
b) Statement 2 is true but statement 1 is false
c) Both the statements are true
d) Both the statements are false
Explanation: During the split, the middle key is retained in the right half node and also promoted to parent node. When a key is deleted from the leaf, it is retained in non-leaves, because it can be still a valid separator between keys in nodes below.
7. Efficiency of finding the next record in B+ tree is ____
b) O(log n)
c) O(nlog n)
Explanation: In a B+ -tree finding the next recored (successor) involves accessing an additional leaf at most. So, the efficiency of finding the next record is O(1).
8. What is the maximum number of keys that a B+ -tree of order 3 and of height 3 have?
Explanation: A B+ tree of order n and height h can have at most nh – 1 keys. Therefore maximum number of keys = 33 -1 = 27 -1 = 26.
9. Which of the following is false?
a) Compared to B-tree, B+ -tree has larger fanout
b) Deletion in B-tree is more complicated than in B+ -tree
c) B+ -tree has greater depth than corresponding B-tree
d) Both B-tree and B+ -tree have same search and insertion efficiencies
Explanation: A B+ -tree has larger fanout and therefore have a depth smaller than that of corresponding B-tree.
10. Which one of the following data structures are preferred in database-system implementation?
a) AVL tree
c) B+ -tree
d) Splay tree
Explanation: The database-system implementations use B+ -tree data structure because they can be used for multilevel indexing.
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