Please just do problem $2!!!$ Problem $1(20$ points$)$

Construct a B$+$ tree for the following set of key values:

$(2,3,5,7,11,17,19,23,29,31)$

Assume that the tree is initially empty and values are added in ascending order.

Construct B$+-$trees for the cases where the number of pointers that will fit in

one node is $4.($n$=4)$

Note: Please illustrate the final structure of the B$+$ tree, showing the key

distribution in each node after all insertions.

Problem $2(60$ points$)$

For the tree in Problem $1,$ show the form of the tree after each of the following

series of operations:

Insert $9$

Insert $10$

Insert $8$

Delete $23$

Delete $19$

Note: Draw the updated B$+$ tree after each operation, showing changes in node

structures and any necessary rebalancing.