Homework 1 - Thinking About Algorithms
Due in class September 14th, 2005.
This homework is intended to get you thinking about
algorithms. Recall that an algorithm is just an ordered series of steps
that can be used to accomplish a particular task.
- It is late at night, and you are hungry. You want to order
a pizza. You have two flyers advertising cheap (but oh so
delicious) pizzas. One is from Hoya Pizza, which sells a 9 inch
square pizza for $9.99. One is from Saxa Pizza, which sells a
10 inch round pizza for $8.99. Which pizza is the better buy?
- The steps you took to find the best pizza buy above
constitutes an algorithm, albeit a very specific algorithm. A
limitation is that it only works for 9 inch square pizzas that cost
$9.99 and for 10 inch round pizzas that cost $8.99. What we
would like to do is generalize this algorithm to work with
different sizes and costs of pizzas.
Instead of using the actual numbers provided, rewrite your
previous algorithm' using variables or symbols that
represent the numbers. For example, instead of writing 9.99,
write roundPizzaCost, and instead of writing 10, write
For example, if we had a triangle pizza, we may write something like:
- trianglePizzaCost = 7.99
- trianglePizzaBase = 6
- trianglePizzaHeight = 9
- trianglePizzaArea = 0.5 x trianglePizzaBase x trianglePizzaHeight
- trianglePriceSqIn = trianglePizzaCost / trianglePizzaArea
The advantage of doing this is that we've separated the procedure for
calculating the price per square inch of a pizza from any set of
specific numbers. To compute a new price per square inch, we simply
reassign the variables that correspond to the cost and the size of
the pizza, and apply the algorithm.
- Assume that you are restricted to four actions: INPUT,
CALCULATE, DECISION, and OUTPUT. Express your algorithm for
deciding which pizza is the better buy in terms of these
actions. Do not invent or add your own actions, use only
these four, and every step must use one of these actions.
For our triangle pizza example, we may write something like:
- INPUT trianglePizzaCost
- INPUT trianglePizzaBase
- INPUT trianglePizzaHeight
- CALCULATE trianglePizzaArea = 0.5 x trianglePizzaBase x trianglePizzaHeight
- CALCULATE trianglePriceSqIn = trianglePizzaCost / trianglePizzaArea
- OUTPUT trianglePriceSqIn
- There are many different ways of expressing
algorithms. A graphical method that shows the order that
things execute is called a flowchart. While not an
endorsement of their product, the first two pages give a
simple example of what a flowchart looks like. Draw a
flowchart of the algorithm you developed for the last
- In this class, we will need to be able to read and
follow algorithms as well as developing and writing our
own. Do problems 29 through 32 in Chapter 1 of the text, and include the
answers in your homework submission.