Algorithms

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Algorithms

• CS139 Aug 30, 2004

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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?

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Algorithm Development Objectives

• At the end of this unit the student will
• 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.

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References for this lecture

• Schaums Outline Chapter 2

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Problem Solving

1. Understand the problem (and the audience)
2. Are you making a pie?
3. Needing directions?
4. Putting together a piece of equipment?
5. Trying to solve a mathematical puzzle?
6. Devise a plan
7. Is this similar to something else?
8. Who is the audience for the solution?
9. What are the required steps?

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Problem Solving ( Contd )

• Carry out the plan (implement)
• Does it work?
• Is each step correct? Necessary?
• Is the solution accurate? (Correct)
• Will it always lead to a solution

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Algorithm Definition

• A logical sequence of steps for solving a
  problem,
• From http//Dictionary.msn.com
• Dale and Lewis
• 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.

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Algorithm Definition, cont

• Shackelford, Russell L. in Introduction to
  Computing and Algorithms
• An algorithm is a specification of a behavioral
  process. It consists of a finite set of
  instructions that govern behavior step-by-step.

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Notice

• Notice the term finite. Algorithms should lead
  to an eventual solution.
• Step by step process. Each step should do one
  logical action.

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Algorithms

• Algorithms are addressed to some audience.
  Consider
• A set of instructions for building a childs
  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 GPAs.

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Audience

• 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 dont know.
• An audience might include people or a computer.

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Good vs. Bad Algorithms

• All algorithms will have input, perform a
  process, and produce output.
• A good algorithm should be
• 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

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Precision

• 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.

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Simplicity

• 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.
• Avoid something like Take 2nd right after you
  exit at King Street

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It has Levels of Abstraction.

• From the Oxford English Dictionary, abstraction
  is defined as
• 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.

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Or in other words

• The abstraction property lets us view an
  algorithm as a series of high level aggregate
  steps, with the detail hidden in a lower level.

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Abstraction, cont.

• 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.

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Diagrammatically
Drive the car to school
Get directions
Turn left out of your driveway
Start the car
At the next light, turn right.
Follow the directions
At the intersection with I-66, take the on-ramp
for I-66 West
Get parking pass
Drive to the destination

Level 1
Level 3
Find a place to park
Stop the car
Level 2
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Other algorithm attributes

• 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.

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Steps from Schaums

• Analyze the problem and develop the
  specification.
• Design the solution
• 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.

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In class exercise

• In your group, create an algorithm to calculate a
  semester GPA. You may use a calculator.
• Recall
• GPA is based on the letter grade achieved in the
  class and the number of credit hours for the
  class.
• Generally QPs A 4.0, B 3.0, C2.0, D1.0,
  F0.0 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.

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For example

• For example, a student is taking 4 classes
• CS139 4 credits C
• CS110 1 credit A
• GWRIT103 3 credits B
• GHIST101 3 credits C-
• What is the students semester average?
• How did you figure it out?
• How can you describe that process for others in
  the class?

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Now trade papers with another group
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Look at the GPA calculation algorithm

• 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 Fs? All As
  (limits)?
• What about different numbers of classes? One or 6?

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Next up

• 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.
• Tomorrow is the last day to bring in folders for
  credit. Check blackboard to see if you have
  given me a folder.
• Be sure to read Chapter 2 in Schaums for
  Wednesdays class.