CSCE 156

Final Exam

April 30, 2007

Name:

NUID:

This examination consists of 7 questions and you have 120 minutes to complete the test. Show all steps (including any computations/explanations) that lead you to the answers. Since I will not be able to meet with you to discuss your exam scores before I turn in your course grades, it is important to provide your answers to the questions clearly.

Please read every question carefully. If you have questions, please raise your hand and I will come to you.

Since most of the questions are open-ended, that means you could spend too much time than necessary for some of the questions. Please manage your time well. Answer questions that are more straightforward first.

Including this page, there are 8 pages.

1. (20 points) Pointers.

(a) (10 points) Given the following code, what are the output statements? Explain.

1. int *p;

2. p = new int;

3. *p = 28;

4. int *q;

5. q = p; 

6. cout << q; //??

7. cout << *q; //??

8. int x;

9. x = 10;

10. p = &x;

11. cout << p; //??

12. cout << *p; //??

13. cout << *q; //??

(b) (10 points) For classes with data members, we normally implement three methods to deal with potential problems of shallow copy. Identify these three methods. Describe the underlying strategies for the implementation of these methods.

2. (20 points) Abstract Data Type – Linked Lists, Stacks, Queues.

(a) (10 points) Describe how (i) access, (ii) removal, and (iii) insertion are done in each of the above abstract data types.

(b) (10 points) Breadth-first traversal of a graph can be implemented using a queue. Describe how this can be done clearly.

3. (20 points) Search.

(a) (15 points) Find a hash function that will be able to hash UNL students into a hash table of about N buckets, where N is the number of students at UNL. You may use their names, NUID, or other attributes as the key, X, or a combination of those attributes as the key, X. Describe your hash function clearly. (Hint: Keep in mind of the two main objectives of choosing a good hash function.)

(b) (5 points) Since collisions are unavoidable, how do you resolve collisions for your hash function above?

4. (20 points) Sorting

(a) (10 points) Describe the algorithm of quicksort clearly.

(b) (10 points) Describe the algorithm of mergesort clearly.

5. (20 points) Binary Trees.

(a) (10 points) What is the definition of a binary search tree?

(b) (10 points) Describe clearly the algorithm that deletes a node that has nonempty left and right subtrees such that the binary search tree after deletion is still a binary search tree.

6. (20 points) Graphs.

(a) (15 points) Describe clearly the Prim’s algorithm that finds a minimal spanning tree of a graph.

(b) (5 points) Describe an application or a problem that a minimal spanning tree can be used to solve.

7. (20 points) General. Short answer questions.

(a) (5 points) Explain why AVL (height-balanced) trees are useful.

(b) (5 points) What is the performance lowerbound on comparison-based search algorithms? What is the performance lowerbound on comparison-based sorting algorithms?

(c) (5 points) Draw the directed graph G of the following adjacency matrix.

(d) (5 points) Identify a minimal spanning tree of the following graph and compute the total weights of the edges in the minimal spanning tree.