Question

Consider the B+ tree shown in the following as an original tree. 73 85 1 2 5 6 8 1 32 39 41 45 52 58 73 91 99 Answer the following questions: 1) (2 marks) There are currently 18 records in this tree. How many additional records could be added to this tree without changing its height (give the maximum possible number)? (3 marks) Show the B+ tree after inserting a data entry with key 3 into the original tree. (3 marks) Show the B+ tree after deleting the data entry with key 91 from the original 2) 3)

Answer 1

B+ Tree is an extension of B Tree which allows efficient insertion, deletion, and searches operations.

1) 19 records could be added in this tree without changing its height.

Insertion in B+ Tree

Step 1: Insert the new node as a leaf node

Step 2: If the leaf doesn't have required space, split the node and copy the middle node to the next index node.

Step 3: If the index node doesn't have required space, split the node and copy the middle element to the next index page.

2) There is no such key in the tree (key 3).

Deletion in B+ Tree

Step 1: Delete the key and data from the leaves.

Step 2: if the leaf node contains less than minimum number of elements, merge down the node with its sibling and delete the key in between them.

Step 3: if the index node contains less than minimum number of elements, merge the node with the sibling and move down the key in between them.

3)