Transcript What is an Algorithm? - James Madison University

Algorithms
CS139 – Aug 30, 2004
Problem Solving
Your roommate, who is taking CS139, is in a
panic. He is worried that he might lose his
financial aid if his GPA goes under 2.0
How can he figure out what his current GPA is?
How can you build a process that any student
can use to tell them what GPA they have
based on grades provided thus far?
Algorithm Development Objectives
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At the end of this unit the student will:
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define the term algorithm
state 5 properties of a good algorithm
from a given problem and stated audience, create
an appropriate algorithm using the properties
stated above.
use the concept of abstraction and top-down
design in creating an algorithm.
begin to think about the kinds of problems that
have a computing solution.
References for this lecture
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Schaum’s Outline – Chapter 2
Problem Solving
1.
Understand the problem (and the audience)
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4.
2.
Are you making a pie?
Needing directions?
Putting together a piece of equipment?
Trying to solve a mathematical puzzle?
Devise a plan
1.
2.
3.
Is this similar to something else?
Who is the audience for the solution?
What are the required steps?
Problem Solving ( Cont’d )
3. Carry out the plan (implement)
1. Does it work?
2. Is each step correct? Necessary?
4. Is the solution accurate? (Correct)
1. Will it always lead to a solution
Algorithm Definition
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A logical sequence of steps for solving a
problem, …
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From http://Dictionary.msn.com
Dale and Lewis:
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a plan of solution for a problem
Algorithm – An unambiguous (and precise) set of steps
for solving a problem (or sub-problem) in a finite
amount of time using a finite amount of data.
Algorithm Definition, cont
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Shackelford, Russell L. in Introduction to
Computing and Algorithms –
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“An algorithm is a specification of a behavioral
process. It consists of a finite set of instructions
that govern behavior step-by-step.”
Notice
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Notice the term finite. Algorithms should
lead to an eventual solution.
Step by step process. Each step should do one
logical action.
Algorithms
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Algorithms are addressed to some audience.
Consider:
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A set of instructions for building a child’s bicycle.
A diagnostic checklist for a failure of some system on the
space shuttle.
The algorithm for what to do when a nuclear reactor
begins to overheat.
An algorithm that will run on a computer system to
calculate student GPA’s.
Audience
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Each audience will have its own “rules” that
govern how we will address them, the
language that they speak.
Each audience will have certain assumptions
about what they know and don’t know.
An audience might include people or a
computer.
Good vs. Bad Algorithms
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All algorithms will have input, perform a
process, and produce output.
A good algorithm should be:
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Simple - relative
Complete – account for all inputs & cases
Correct (Right)
should have appropriate levels of Abstraction. –
grouping steps into a single module
Precise
Mnemonic - SCRAP
Precision
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Precision means that there is only one way to
interpret the instruction. Unambiguous
Words like “maybe”, “sometimes” and
“occasionally” have no business in a well developed
algorithm.
Instead of “maybe”, we can specify the exact
circumstances in which an action will be carried out.
Simplicity
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Simple can be defined as having no
unnecessary steps and no unnecessary
complexity. (You may lose points if your
algorithm contains unnecessary steps)
Each step of a well developed algorithm
should carry out one logical step of the
process.
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Avoid something like: “Take 2nd right after you
exit at King Street”
It has Levels of Abstraction.
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From the Oxford English Dictionary,
abstraction is defined as:
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“The act or process of separating in thought, of
considering a thing independently of its
associations; or a substance independently of its
attributes; or an attribute or quality independently
of the substance to which it belongs.”
Example: Add all the scores then divide the sum
by the number of students to get the average.
Or in other words
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The abstraction property lets us view an
algorithm as a series of high level aggregate
steps, with the detail hidden in a lower level.
Abstraction, cont.
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Instead of approaching a problem and worrying
about each and every thing you must do to solve the
problem, you can begin to look at the major steps.
(Top down design)
After the major steps, you can begin to fill in how
you would accomplish the major step.
That fill in may lead to the need for additional levels
to fill in those details, etc.
Top down design.
Diagrammatically
Get directions
Drive the car to
school
Start the car
At the next light, turn right.
Follow the directions
Get parking pass
Drive to the
destination
Level 1
Turn left out of your
driveway
Find a place to park
Stop the car
Level 2
At the intersection with I66, take the on-ramp for
I-66 West
…
Level 3
Other algorithm attributes
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A good algorithm should be correct.
A good algorithm should be complete.
Shackelford again, “To be correct, an
algorithm must produce results that are
correct and complete given any and all sets
of appropriate data.”
And to be correct, an algorithm must proceed
through to a conclusion.
Steps from Schaum’s
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Analyze the problem and develop the specification.
Design the solution
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Test the solution as part of the design steps.
Implement the program (code the program)
Test the program
Validate the program (further extensive testing) to
insure it works under all circumstances.
In class exercise
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In your group, create an algorithm to calculate a
semester GPA. You may use a calculator.
Recall:
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GPA is based on the letter grade achieved in the class and
the number of credit hours for the class.
Generally QP’s – A = 4.0, B = 3.0, C=2.0, D=1.0, F=0.0
and a + adds .3 to the grade and a – subtracts .3 from the
QP.
The semester GPA is then the average QP for each credit
hour attempted.
For example:
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For example, a student is taking 4 classes:
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CS139 – 4 credits – C
CS110 – 1 credit – A
GWRIT103 – 3 credits – B+
GHIST101 – 3 credits – C-
What is the student’s semester average?
How did you figure it out?
How can you describe that process for others in the
class?
Now trade papers with another
group
Look at the GPA calculation algorithm
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What properties does the testing algorithm display?
Is is simple, precise, etc.
Test the solution using a couple of different test
cases. Does the algorithm work for those different
cases?
What happens if the grades are all F’s? All A’s
(limits)?
What about different numbers of classes? One or 6?
Next up
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You will create some other algorithms in lab.
Please be on time for your selected section.
Focus on the 5 principles as you are building your
algorithms.
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Tomorrow is the last day to bring in folders for
credit. Check blackboard to see if you have given
me a folder.
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Be sure to read Chapter 2 in Schaum’s for
Wednesday’s class.