Question

Consider the following \(B^+\) tree with 5 nodes, in which a node can store at most 3 key values. The value 23 is now inserted in the \(B^+\) tree. Which of the following options(s) is/are CORRECT?

 

• A. None of the nodes will split.
• B. At least one node will split and redistribute.
• C. The total number of nodes will remain same.
• D. The height of the tree will increase.

Hint:

When a node in a \(B^+\) tree exceeds its key capacity, a split occurs, which might increase the height of the tree if the root is affected.

Answer 1

The Correct Option is B, D

In this \( B^+ \) tree, each node can hold at most 3 keys. Initially, the tree has 5 nodes. The insertion of 23 will cause a node split because adding this new value would exceed the capacity of the current node. When a node split occurs, a new node is created, and this may also cause the height of the tree to increase if the split affects the root.

Thus, options (B) and (D) are correct:
(B) At least one node will split and redistribute.
(D) The height of the tree will increase if the root node splits.

Why Other Options are Incorrect:
Option (A): Incorrect because the node will split due to the insertion of 23.
Option (C): Incorrect because the total number of nodes will increase when a node splits.