ISRO | ISRO CS 2018 | Question 12

In a file which contains 1 million records and the order of the tree is 100, then what is the maximum number of nodes to be accessed if B+ tree index is used?

(A)

5

(B)

4

(C)

3

(D)

10

Answer: (B)

Explanation:

We have to find the maximum no. of nodes to be accessed in B+ tree so we have to consider the minimum fill factor. 
Here, 
number of record = 1 million = 10^6 (Given ) 
order of b+tree= number of pointers per node = p = 100 (Given ) 
Minimum pointers per node =⌈ p/ 2⌉ = ⌈ 100/ 2⌉ = 50 
number of nodes in last level of tree =10^6 / 50 = 2 * 10^4 
Number of nodes in Second last level of tree = 2*10^4 / 50 = 400 
Number of nodes in Third last level of tree = 400/50 =8 
number of node in Fourth last level of tree = 8/50 =1 
The maximum no. of nodes to be accessed = number pf B+ tree levels = 4 

Hence, option ( B ) is correct.

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