Consider the following sequence of $16$ operations on an initially empty search tree:

Insert Bob

Insert Tim

Insert Fred

Insert Peter

Insert Jane

Insert Willow

Remove Tim

Insert Laura

Insert Nancy

Insert Hank

Insert Samson

Remove Peter

Insert Rhea

Insert David

Remove Rhea

Remove Nancy

The above sequence of operations is to be performed in the same exact manner into each

of the following trees $-$

BST

AVLTree

$2-3$ Tree

Max Heap

Draw how each tree is structured at the following $3$ steps:

After 'Remove Tim' step $($step $6)$

After 'Remove Peter' step $($step $10)$

After 'Remove Nancy' step $($step $14)$

For the insertion steps $-$ follow the 'smaller node to the left subtree $/$ greater or equal

node to the right subtree' algorithm, except for the heap where you should follow the

conventional method for inserting nodes into a heap.

For the removal steps $-$ follow the $\text{'}$in$-$order successor replacement' algorithm, except for

the heap where you should follow the conventional method for removing nodes from a

heap or sub$-$heap.

There should be a total of $3$ diagrams per tree $-$ do not include any intermediate

diagrams.

Try to finish one tree fully before starting on a different tree, otherwise you may have

confusion and errors.

Draw and sequence your diagrams clearly $-$ if I can't understand them then you lose

points.

If you need to make any assumptions or encounter any limitations$,$ state them clearly.