CS99 Fall 2001
Prelim2 Sample Problems:

1. DIS.com needs you to simulate the number of boxes a worker can stack 
   on eight carts in one day.  A chute issues one box at a time for
   the worker to place on a cart.  The boxes have random sizes, which
   are ranked from 1 to 5.  A box of size 5(#5) must be at the bottom
   of the stack on each cart.  All other boxes may be stacked in any
   order.  Since the worker does not want to bother with removing
   boxes from a cart, the simulation has these assumptions: 

   + A cart has no limit to the number of boxes it can store
   + The worker will not shuffle the boxes
   + Each time a #5 box appears, the worker starts stacking a new cart
     with the #5 box at the bottom   
   + Another worker has already filled the first and second carts with
     three and seven boxes, respectively
   + The third cart currently has two boxes stacked on it, so far
   + The first cart has a #5 box at the bottom

   Since the company is very cheap, it has only five more empty carts
   for the worker to use.  So, when the ninth#5 box appears, the
   worker cannot continue stacking boxes.  However, the company will
   only produce forty boxes in one day. So, the worker might not need
   to use all of the carts.

1a. Write a brief algorithm that describes how to simulate this problem.  
    Ultimately, the program must report the following:
    + the total number of carts needed
    + the total number of boxes stacked on all of the carts, which is
      the sum of all boxes on all carts.

1b. Write a program that determines the number of carts used and the 
    number of boxes that the worker stacked on all of the carts by
    doing the following:
    + Initilize the following variables: maximum number of boxes that the 
      company produces (maxBoxes), total number of boxes placed on the
      carts (totalBoxes), total number of carts for storing
      boxes (cartTotal), current count of cart that is being
      used (cartCount), and the current box size that worker will attempt
      to stack (currentBox).
    + Use a loop with selection statements inside of it to simulate
      whether or not the current box gets stacked and if a new cart
      must be chosen.  Boxes of size#5 must be placed on a new cart,
      assuming that the carts have not been exhausted.
    + Report the number of carts that were used and the total number
      of boxes stored on all carts.

2. Probelm 4.21 (no need to plot) from Matlab Programming for Engineers 
   by Chapman  

3. Problem 4.24 from Matlab Programming for Engineers by Chapman  

4. For character graphics, draw a circle. You could use the equation
   x^2+y^2=r^2, along with x=r*cos(theta), y=r*sin(theta).

5. Write a program that converts a 1-D array into a 2D array with the
   1D array on the diagonal and "reverse diagonal". 
   For example, 

       [1 2 3]
 
   becomes

       [1 0 3]
       [0 2 0]
       [1 0 3]