1. Draw a binary balanced search tree without a balancing rotation mechanism for the following values, and explain your strategy to build such sorted n number of elements:

43 123 185 343 411 455 834 941 1310

2. Draw a new binary search tree that results from adding the following integers (14, 214, 33, 918, 15, 48, 56, 815, 134, 10, 131, 125, 45). Assume our simple implementation with no balancing mechanism.

3. Starting with the result from Exercise 2, draw the tree that results from removing (815 33 10, 15), again using our simple implementation with no balancing mechanism.

4. Draw a new AVL Balanced Tree that results from adding the following integers (14, 214, 33, 918, 15, 48, 56, 815, 134, 10, 131, 125, 45) and show each iteration.

5. Starting with the resulting tree from Exercise 4, draw the tree that results from performing a remove the root operation and show each iteration according to AVLTree remove process (remove root only one time).

6. Write a method to take a BinayTreeNode input (root) for level order, preOrder, postOrder, and inOrder methods.

7. Write a method to take a BinayTreeNode input (root) and determine whether the given tree is Binary Search Tree

8. Suppose you are given the following set of keys (111, 114, 118, 95, 99, 113, 128, 117, 115, 99) to insert into a hash table that holds exactly 11 values. Which index positions would those keys map to according to chaining?

9. Suppose you are given the following set of keys (111, 114, 118, 95, 99, 113, 128, 117, 115, 99) to insert into a hash table that holds exactly 11 values. Which index positions would those keys map to according to linear probing?

10. Suppose you are given the following set of keys (111, 114, 118, 95, 99, 113, 128, 117, 115, 99) to insert into a hash table that holds exactly 11 values. Which index positions would those keys map to according to quadratic probing?