CSSE 230
Data Structures and Algorithm Analysis

Homework 7 - 70 points

To Be Turned In

Submit to the drop box.

1. Don’t forget: You should be keeping an individual log about your team project work so that you can write a performance evaluation for each of your teammates. You do not need to turn in this log, but I wanted to remind you while I had your attention.
2. (15 points) On paper, start with this red-black tree:

   (If it is hard to see, the two children of the root are red.) Insert the following nodes using the top-down insertion algorithm and show what happens (both rotations and re-colorings): 20, 10, 25, 27, 40. Please denote the red nodes very clearly, using red (best) or a key (acceptable). Work carefully - it will be hard to give partial credit if your answer is incorrect.

3. (15 points) Weiss exercise 20.5 [20.5]. In this problem you will check your understanding of collision resolution techniques in hash tables.
4. (40 points + up to 10 BONUS points) StringHashSet implementation. Check out the project from your individual repository. You will be implementing a HashSet using separate chaining. It implements many of the methods from Java's Set interface. Additionally:
   • It only needs to work for Strings.
   • You will implement a method to compute the String hash code.
   • You will also implement a toRawString function that dumps out the array of LinkedLists without formatting - this is to make sure it is putting everything in the right place.
   • You will implement many other methods. I did them in the order they appeared in the file, and the tests for later ones assume you passed the tests for the earlier ones. For example, to test remove(), we need to be able to add values first.
   • One cannot insert null
   • Java's HashSet has an initial capacity of 16 and rehashes when lambda reaches .75. To force more collisions earlier, we will use an initial capacity of 5, and rehash when lambda reaches 2.
   • The most challenging (fun) part of this was writing an iterator, since it needed to traverse a bunch of possibly empty linked lists. Once you have an iterator, it makes some other things (toString and rehashing) easier. But I recognize you are busy with your project, so am making that part optional, and worth a few bonus points as a reward if you get it working on your own.  

Optional practice problem - not to be turned in.

(xx points) Start with the following Binary Search Tree:

See the hint at the end!

1. Is this an AVL tree? ____ If not, rearrange it so that it is height-balanced.
2. Draw the tree after insertion of a node containing 11, using the usual BST insertion algorithm.
3. Is the new tree AVL? ______ If not, name the node where the rotation should be done, according to the algorithm from class. ______ Single or double rotation? ____________ If you need to do a rotation, draw the resulting tree.
4. Delete the element 5 from the original tree (not the one from part c), using the BST deletion algorithm described in class and in the textbook. Draw the new tree.
5. Is the new tree AVL? ______ If not, name the node where the rotation should be done, according to the algorithm from class. ______ Single or double rotation? ____________ If you need to do a rotation, draw the resulting tree.
6. Is your new tree (if any) AVL? ______ If not, name the node where the rotation should be done, according to the algorithm from class. ______ Single or double rotation? ____________ If you need to do a rotation, draw the resulting tree.
7. Add the element 5 to the tree from part (f) using the BST algorithm. Draw the new tree.
8. Is the new tree AVL? ______ If not, name the node where the rotation should be done, according to the algorithm from class. ______ Single or double rotation? ____________ If you need to do a rotation, draw the resulting tree.
9. Add the element 12 to the tree from part (h). Draw the new tree.
10. Is the new tree AVL? ______ If not, name the node where the rotation should be done, according to the algorithm from class. ______ Single or double rotation? ____________ If you need to do a rotation, draw the resulting tree.
11. Add the element 7 to the tree from part (j). Draw the new tree.
12. Is the new tree AVL? ______ If not, name the node where the rotation should be done, according to the algorithm from class. ______ Single or double rotation? ____________ If you need to do a rotation, draw the resulting tree.

Hint: In my solution, for all the sub-parts together, I did three single rotations and no double rotations. The first four leaf nodes in my final tree were 3, 5, 7, and 9. (In my first attempt, I misread part d) and deleted from the tree in part c) rather than the original tree. With that mistake, for all the sub-parts together, I did two single rotations and one double rotation and the first four leaf nodes in my final tree were also 3, 5, 7, and 9.)