1.) Start with an empty binary search tree, and insert each of these values in the order shown:

50, 75, 25, 40, 10, 90, 60, 80, 30, 70, 20. Draw the binary search tree after the final insert.

2.) Write the nodes of the above BST in the order they are visited by each of these traversals:

In order:

Preorder:

Postorder:

3.) Remove each of these values in the order shown: 10, 90, 50. Re-draw the binary search tree after completing these remove operations.

4.) Draw a binary search tree whose preorder traversal is 60, 30, 10, 0, 20, 50, 40, 90, 70, 80, 100.

5.) Draw the heap that results from inserting the same values as on the first page into an initially empty min ordered heap. 50, 75, 25, 40, 10, 90, 60, 80, 30, 70, 20

6.) Perform two extract-min operations on the heap above. Draw the heap after each operation.

7.) Draw the min-ordered heap that results from using the bottom-up heap building method. Start with an initial array containing the values: 50, 75, 25, 40, 10, 90, 60, 80, 30, 70, 20.