computer science homework

CPS 350: Assignment 4 Due 11:55 pm, 3/27/2017 (100 pts) This is NOT a team project. No late submission will be accepted.

Receive 5 bonus points if turn in the complete work without errors at least one day before deadline.

Receive an F for this course if any academic dishonesty occurs 1. Purpose The purpose of this assignment is to implement prio rity queues.

2. Description 2.1. Implementation (30 points for BinaryHeap.java, 45 f or ThreeHeap.java) Your main task is to implement two priority queues. All two implementations should implement the provided PriorityQueue interface (include imple ments PriorityQueue in your Java code), which means they should work with priorities that h ave type double and there are no corresponding items attached to the priorities. You r implementations should be as follows: A class BinaryHeap that implements a binary min-heap as we discussed in class, using an array to store the conceptual complete tree. A class ThreeHeap that implements a min-heap where each non-leaf node has 3 children.

You should still use a contiguous portion of an arr ay to store the conceptual complete tree. We suggest you make a copy of your BinaryHeap class and make changes as necessary.

Put your two implementations in two separate Java f iles, BinaryHeap.java and ThreeHeap.java.

Your priority queues should allow duplicates. That is, two or more copies of the same value should be allowed to exist in the heap at the same time. For example, if you call deleteMin and you have {3.0, 3.0, 6.0, 7.0} in the heap, it would just return one of the 3.0 values, then on the next deleteMin it would return the other 3.0. It do es not matter "which" 3.0 is returned first.

According to our definition of priority queue, what must be guaranteed is that both 3.0 values will be returned before a 6.0 or 7.0 is returned, a nd that the 6.0 would be returned before the 7.0.

Your implementations should automatically grow as n ecessary. (If interested, you may also have them shrink when appropriate; this is optional.) Fo r any arrays, you should start with a small array (say, 10 elements) and resize to use an array twice as large whenever the array becomes full, copying over the elements in the smaller arra y. Do the copying with a for loop rather than any Java library methods (even though using the lib rary is how one would normally do it). You may use the length field of an array as needed. Be sure to test your solutions thoroughly and to turn in your testing code. For instance, you may generate 1000 random numbers, insert them into a priority queue, and keep deleteMin() as long as the priority queue is not empty. Part of th e grading will involve thorough testing including any difficult cases. For this assignment, we will be grading more strictly for things like style and efficiency.

2.2. Questions (25 points) The questions include comparing the actual run-time of your implementations. We would expect the reports to be at least a couple of pages long, quite possibly longer to have room for relevant graphs or tables. Submit a report.pdf file, answering the questions i n this template report.docx file: 1. (5pts) What is the worst case asymptotic running ti me of isEmpty, size, insert, findMin, and deleteMin operations on all your heap implement ations? For this analysis you should ignore the cost of growing the array. That is, assu me that you have enough space when you are inserting a value.

2. (5pts) Which of your two implementations would you recommend to someone who needs to use a heap? Why is that one preferred? Are there any conditions under which you might suggest using your other implementations?

3. (5pts) Briefly discuss how you went about testing y our two heap implementations. Feel free to refer to your testing files, which you shou ld submit.

4. (10pts) You implemented a binary-heap and a three-h eap. Now think if you can implement a four-heap, a five-heap, etc.

a. In a short table, indicate for a binary heap, a thr ee-heap, a four-heap and a five- heap, where the children for the node at array inde x i are. For example, the first row of the table would indicate that for a binary h eap, the two children would be at i*2 and i*2+1.

b. For a d-heap where d is a variable representing the number of children (like two, three, four, five, ...), give an arithmetic formula for calculating where the left- most child for the node at array index i are. For e xample, a wrong answer in the right format would be i*d+14. Naturally, your formu la should produce the right answer for all the rows in your table from part (a) .

2.3. Bonus Components (10 points) The following suggestion is meant for you to try if you finish the requirements early. 1. (5pts) Implement a d-heap where d is the number of children for non-leaf nodes. Your class should implement the same priority queue inte rface and it should use a contiguous array portion as in your first two implementations. It should include an empty constructor and additional constructor that takes d as an argument, work correctly for any d greater than or equal to 2, and use d as the number of children for nodes. 2. (5pts) Implement a binary heap that works for any t ype (not just doubles). It should use Java generic types to allow any priority type that implements an appropriate interface for comparing two priorities and your heap should allow items of a second generic type that are "attached" to each priority. That is, each node contains a key-value pair, where key is the priority. Note this implementation will not imp lement the provided interface, so provide any additional comments necessary to explai n how your class should be used. 3. Grading notes If your program does not compile, you receive zero points for that program. Additional deductions: 1. (5 points) Your code does not follow the style guid e discussed in class/textbook.

2. (30 points) Your code does not have author name, da te, purpose of this program, comments on the variables and methods, etc.

4. Turn in You should ZIP the following files and submit the ZIP to isidore.

BinaryHeap.java ThreeHeap.java Any additional Java files needed, if any. The Java files you used to test your implementation s. The Java files you used to time your implementation s. report.pdf, containing answers to Questions in 2.2. Any additional files for the bonus credits in a zip file named extracredit.zip. Please make sure that this zip file decompresses its contents i nto a folder called extracredit and not into a bunch of individual files.

Do not turn in PriorityQueue.java and EmptyPQExcept ion.java. You must not change these files.

Your implementations must work with the code as pro vided to you.