Question

A B-tree of minimum degree \( t \) can have a maximum of _________ pointers in a node.

• A. \( t - 1 \)
• B. \( 2t - 1 \)
• C. \( 2t \)
• D. \( t \)

Hint:

In a B-tree of minimum degree \( t \):
- Maximum keys per node: \( 2t - 1 \).
- Maximum child pointers per node: \( 2t \).

Answer 1

The Correct Option is C

Step 1: Understanding B-Trees
- A B-tree is a self-balancing search tree that maintains sorted data for efficient insertion, deletion, and search operations.
- The minimum degree \( t \) of a B-tree defines the minimum number of children a node can have.

Step 2: Maximum Number of Pointers in a Node
- A node in a B-tree of minimum degree \( t \) can have:
- At most \( 2t - 1 \) keys.
- At most \( 2t \) children (pointers to subtrees).
Step 3: Evaluating the Options
- (A) Incorrect: \( t - 1 \) is the minimum number of keys, not pointers.
- (B) Incorrect: \( 2t - 1 \) is the maximum number of keys, not pointers.
- (C) Correct: \( 2t \) is the maximum number of child pointers a node can have.
- (D) Incorrect: \( t \) is the minimum number of child pointers in an internal node.