Consider the following sequence of 14 operations on an initially empty search tree:

Consider the following sequence of 14 operations on an initially empty search tree:

1. Insert Bob
2. Insert Tim
3. Insert Fred
4. Insert Peter
5. Insert Jane
6. Remove Tim
7. Insert Laura
8. Insert Nancy
9. Insert Hank
10. Remove Peter
11. Insert Rhea
12. Insert David
13. Remove Rhea
14. Remove Nancy

1. The above sequence of operations is to be performed in the exact manner into each of the following trees –
   • BST
   • AVL Tree
   • 2-3 Tree
   • Max Heap
2. 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)
3. 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.
4. For the removal steps – follow the ‘in-order successor replacement’ algorithm, except for the heap where you should follow the conventional method for removing nodes from a heap.
5. There should be a total of 3 diagrams per tree – finish one tree fully before starting on a different tree. Draw and sequence your diagrams clearly – if I can’t understand them then you lose points.
6. If you need to make any assumptions or encounter any limitations, state them clearly.

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