This homework is due Mon. 14 Nov. at 2359

The assignment is graded out of 100 points. Deductions will be assessed based on the correctness and efficiency of your solution.

You will be provided with the following files in the base directory

• example.txt : an example set of inputs
• TopK.java : a java class with a main method to find the Top K input

The following relevant files are found in the ic312 package.

• MaxHeap.java : Starter code for a max-heap implementation of a priority queue. You will need to edit this file.
• MinHeap.java : Starter code for a min-heap. Complete this file for the Bonus!

Additionally, you will be provided with additional, useful data structures in the ic312 directory. In particular, Pair.java and ArrayList.java may be very useful!

Modern road races are "chip-timed", which means that competitors can start and finish at different times, and the winner is not necessarily the person who crosses the finish line first.

Your task for this homework will be to complete the implementation of a program that reads in a whole bunch of names and times, and prints out the names of the top K finishers with the lowest times, where the value of K is specified as a command-line argument. To do that, of course, you will be completing the implementation of a Heap.

The TopK.java program is already written for you. It creates a max-heap, reads in all the names and times, calling removeMax as necessary to maintain the heap size of K, and finally prints out the contents of the heap to show the top K finishers.

You just need to fill in the ic312/MaxHeap.java methods to implement the Priority Queue.

But wait, there is another way to do it! Instead of using a max-heap, whose size is always at most K+1, you could instead create one big min-heap with a "heapify" operation, then call removeMin K times to get the K smallest things. Instead of \(O(n \log K)\), this way would only have running time \(O(n + K\log n)\), which is potentially much better!

For this, you will create a min-heap instead of a max-heap. So your TimeHeap class will have a removeMin operation instead of removeMax. Oh, and you will also have to write a heapify method, and adjust the TopK.java program as necessary to make the appropriate calls.

This is harder, so I provide an incentive: *If you do it this way with a min-heap, your lowest HW grade from the first 7 homeworks will be overwritten with this HW grade.*

The fastest program in the class wins a tangible prize. Are you up to the challenge? I hope so. Good luck!

When everything works, if your program is run with java TopK 10 and then the following (found in example.txt) is typed into standard in (followed by ctrl-D):

Nathan     609601
Liam       707303
Logan      318344
Ethan       91286
Jacob      334328
William    631989
Samuel     592643
Sofia      492706
Sara       964558
Isabella   878226
Ava        613357
Emma       366389
Noah        60429
Emily      474105
Benjamin   645060
Chloe      481035
Lucas      502159
Maya       248729
Olivia     109154
Leah        28141

then the output should be

10. Chloe
9. Emily
8. Emma
7. Jacob
6. Logan
5. Maya
4. Olivia
3. Ethan
2. Noah
1. Leah

In fact, the example.txt file contains exactly this example, so for this one you could just run:

java TopK 10 < example.txt.

Note: Your code will be tested on more stringent examples than this using different test programs that make heaps larger than size 10. So you should test your own code like that as well!