Problem $3.(40$ points$)$ Answer the following problems. For each problem, start with the

B$+-$tree in Figure $1.$

$($a$)(10$ points$)$ Draw the tree that would result from inserting $6$ into the tree in Figure $1.$ When

a node is split into two nodes, ensure that the right node has no more keys$/$pointers than the

left node. You may omit the parts of the tree that do not change.

$($b$)(10$ points$)$ Draw the tree that would result from deleting $8$ from the tree in Figure $1.$ When

node merging or redistribution is needed, if both the left and right sibling nodes are available,

use the left sibling node. You may omit the parts of the tree that do not change.

$($c$)(10$ points$)$ Draw the tree that would result from deleting $39$ from the tree in Figure $1.$ You

may omit the parts of the tree that do not change.

$($d$)(10$ points$)$ Draw the tree that would result from deleting $91,80,$ and $73$ from the tree in

Figure $1.$ You may omit the parts of the tree that do not change.

After solving the above problems, please state the amount of time spent for this assignment.

Feel free to add comments or suggestions if any.