COSC 311 Homework 9/27/2018   

Test Big Oh for queue ops

Distributed: R 9/27/2018       Due: R 10/4/2018

In class on 9/25, I averred that to insert or delete one element to a queue
of size n was O(1), and *not* O(n).  This homework will test
that assertion.

Create and populate a circular queue, implemented on 1D array, with n elements.
Measure the time it takes to insert/delete K operations.

Fixing K, vary the size n.

Graph the times to execute K queue operations versus n (the size of the
array). 

If I am right (and I am) the time to perform K queue operations will not vary
based on the size of the queue.

Using your timing results and the resulting graph, make a statement, that you
justify, about whether or not your result support O(1) or O(n) for a queue operation.


Constraints:
(1) You must determine the value K (number of queue operations) dependent on
your computer's performance. A reasonable first guess is K=10,000. The longest time
you should need to execute should be approximately something between 100 and 300 seconds. 

(2) You will determine, based on your computer's performance, the various values
of n for the size of the queue. These values must give a reasonable spread of
timing results. You will need at least 6 values for n.

(3) The queue operations, insert and delete, must be in random order,
with equal probability (the probability of insert is 50%, the probability of 
delete is 50%).

(4) Once you have an idea of the values of n and the value of K, then use
the same 1D array size for all experiments. Allocate 1.5 times the space for the
largest value of n to avoid possible queue overflow. 

(5) The size of the 1D array must be the same for all experiments.

(6) Appropriately modify the pseudo-code given in 
https://emunix.emich.edu/~haynes/CommonCourseMaterial/311/circularQueue.txt
Do not use a Java supplied collection such as List, Queue, etc.
Do not cannabalize code from another source -- even if cited correctly.

(7) Write one program for all the experiments. Hardcode the values of n.

(8) Obviously, you must time *only* the queue operations. You should include
tests for isEmpty() or isFull() in the timing.

(9) Also, the value of the actual data element is not used; therefore you shouldn't
generate a random value for the data. 
 
 
Points taken off for:
(1) Doesn't work
(2) Failure to meet style constraints
(3) Failure to meet coding constraints
(4) Code does not match output
(5) Ugly or difficult to understand code
(6) Results:  sloppy graph
              sloppy, weasely, or wrong concluding statement

Turn in:
  -- Hard copy of code
  -- Header must include your last name, homework identifier (hw0927), URL
     of source code.
  -- Screen shot showing timing results
  -- Graph of timing results
  -- Concluding statement: Your results support what Big Oh function and why.