CUET PG 2021 — Computer PYQ

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Question

CUET PG 2021 — Computer PYQ

CUET PG | Computer | 2021

In a B* tree, If the search-key value is 8 bytes long, the block size is 512 bytes and the block pointer size is 2 bytes, then maximum order of the B* tree is

Choose the correct answer:

Explanation

1. Understanding the Parameters

Block Size ( $B$ ): $512$ bytes
Search-key Value Size ( $V$ ): $8$ bytes
Block Pointer Size ( $P$ ): $2$ bytes
Order ( $n$ ): The maximum number of child pointers a node can have.

2. The Node Structure Equation

In a B* tree (or B+ tree), an internal node of order $n$ contains:

$n$ block pointers (child pointers)
$(n - 1)$ search keys

The total memory occupied by a node must be less than or equal to the block size:

(n \cdot P) + ((n - 1) \cdot V) \le B

3. Step-by-Step Calculation

Substitute the given values into the equation:

(n \cdot 2) + ((n - 1) \cdot 8) \le 512

Expand the terms:

2n + 8n - 8 \le 512

Combine the terms containing $n$ :

10n - 8 \le 512

Add $8$ to both sides:

10n \le 520

Divide by $10$ :

n \le \frac{520}{10}

n \le 52

Final Solution

The maximum order ( $n$ ) of the B* tree is:

\mathbf{52}