Please include explanation and steps for each part. Thank you (Part a,d,e only)

3. B-tree as discussed in class splits a leaf when attempting to insert a new item into an already-full leaf but when the deletion of an item makes the leaf underloaded, the affected leaf first tries to grab an item from an adjacent sibling (either to the left or the right of the leaf), and only if this would make the sibling also underloaded, merges with the sibling. Consider a B-tree variation that we would call a "thrifty B-tree". A thrifty B-tree tries to reduce the number of node splits and merges whenever possible. That is: Before splitting an overflowing node, the node tries to move one of its items to an adjacent sibling and only splits if all of both its adjacent siblings (or only one if the node is a "boundary node" and has only one sibling) are full. An underloaded node only merges with a sibling if it cannot grab an item from either sibling in other words, it tries both its siblings - unless it only has one -- rather than just picking a sibling to "play with" and then either grab from it or merge with it as we discussed in class). Note that (a) the above modification also applies to upper-level nodes when they need to be split or merged and (b) thrifty B-trees still have logarithmic complexity for both insertion and deletion because the above actions are still localized to a vicinity of the affected node and require fixed amount of work at each level of the tree. Now consider the B-tree below with M=L=3. 12 || 3 || 6 | Assuming the "thrifty B-tree", draw the tree after the following operations: (a) Delete 4. Describe algorithmic steps involved (you can skip steps required to locate the item to be deleted). (2 pts) (b) In the original tree, delete "12". Describe algorithmic steps involved (you can skip steps required to locate the item to be deleted). (2 pts) (c) In the tree resulting from step (b), delete "2". Describe algorithmic steps involved (you can skip steps required to locate the item to be deleted). (2 pts) (d) In the original tree, add "9". Describe algorithmic steps involved (you can skip steps required to locate the leaf where the item needs to be inserted). (2 pts) (e) In the tree resulting from step (d), add "10". Describe algorithmic steps involved (you can skip steps required to locate the leaf where the item needs to be inserted). (2 pts)