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# GATE | GATE CS 2008 | Question 41

• Difficulty Level : Expert
• Last Updated : 28 Jun, 2021

A B-tree of order 4 is built from scratch by 10 successive insertions. What is the maximum number of node splitting operations that may take place?

(A)

3

(B)

4

(C)

5

(D)

6

Explanation:

Insertion of 3 keys
10 20 30

Insertion of 4th key (1st split)
30
/   \\
10*20   40

Insertion of 5th key no split
To maximize splits, let us insert a value in a node that has
key in access. Let us insert 5
30
/     \\
5*10*20   40

Insertion of 6th key (2nd Split)
To maximize splits, let us insert a value in a node that has
key in access. Let us insert 8
8*30
/   |   \\
5    10*20   40

Insertion of 7th key
To maximize splits, let us insert a value in a node that has
key in access. Let us insert 15
8*30
/     |    \\
5    10*15*20   40

Insertion of 8th key (3rd Split)
To maximize splits, let us insert a value in a node that has
key in access. Let us insert 12
8*12*30
/   /   \\  \\
5   10 15*20  40

Insertion of 9th key
To maximize splits, let us insert a value in a node that has
key in access. Let us insert 17
8*12*30
/  /   \\   \\
5  10 15*17*20 40

Insertion of 10th key (4th and 5th Splits)
To maximize splits, let us insert a value in a node that has
key in access. Let us insert 13
12
/      \\
8       15*30
/   \\     /  |  \\
5    10  13 17*20   40

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