Question

Draw the diagrams on the file to be uploaded at the end of the exam. Please be neat, if it cannot be read, it cannot be graded. Label the diagrams Q2 part A and Q2 part B Q2 part A: Show the work and the resulting B+Tree after deleting data entry 17 Q2 part B: Using the tree derived from part (A) above, show the work and the resulting B+Tree after inserting data entry 7" B+ tree | 14 | 18 || 25 |4 33

Answer 1

Q2 PART A:

We are assuming that the maximum number of keys allowed is 4 and the minimum number of keys allowed is 2.

If this is the case then the after deleting 17 from the root, the node will be left with only one key i.e. 15 which violates the property of the B+ tree (underflow).

Thus we borrow one key from the siblings through the root.

As the left sibling of the root contains more number of keys than the right sibling, we will borrow from the left sibling.

As we are borrowing from the left sibling, so we will borrow the maximum key i.e. 8.

Now after shifting 8, the value of the root key 14 cannot be there as in B+ tree the right child keys should be >= the root key and left child keys should be < the root key.

So, we will replace the root key 14 with the minimum key of the right child i.e. 8.

So, the resulting key will be as follows:-

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Q2 PART B:

As the new tree from part A) has a space left for data entry 7* (no overflow) i.e. in the leftmost leaf, therefore, we need to do nothing and just insert 7 after 6 in the leftmost node. All the properties of the B+ tree will remain intact after the insertion. So, the new tree after inserting 7 will be as follows:-

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