# Problem Solving and Algorithm Design - PowerPoint

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```					     Chapter 6
Problem Solving
and Algorithm Design
Chapter Goals

• Determine whether a problem is suitable for a
computer solution
• Describe the computer problem-solving process
and relate it to Polya’s How to Solve It list
• Distinguish between following an algorithm and
developing one
• Describe the pseudocode constructs used in
expressing an algorithm
• Use pseudocode to express an algorithm
2
Chapter Goals

• Apply top-down design methodology to develop
an algorithm to solve a problem
• Define the key terms in object-oriented design
• Apply object-oriented design methodology to
develop a collection of interacting objects to
solve a problem
• Discuss the following threads as they relate to
problem solving: information hiding, abstraction,
naming things, and testing

3
Problem Solving

Problem solving
The act of finding a solution to a perplexing,
distressing, vexing, or unsettled question

How do you define problem solving?

4
Problem Solving

How to Solve It: A New Aspect of
Mathematical Method by George Polya
"How to solve it list" written within the
context of mathematical problems
But list is quite general

We can use it to solve computer
related problems!

5
Problem Solving

How do you solve problems?

Understand the problem
Devise a plan
Carry out the plan
Look back
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Strategies

– What do I know about the problem?
– What is the information that I have to process
in order the find the solution?
– What does the solution look like?
– What sort of special cases exist?
– How will I recognize that I have found
the solution?
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Strategies

Ask questions! Never reinvent the wheel!
Similar problems come up again and again
in different guises
A good programmer recognizes a task or
subtask that has been solved before and
plugs in the solution
Can you think of two similar problems?
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Strategies

Divide and Conquer!
Break up a large problem into smaller units
and solve each smaller problem
– Applies the concept of abstraction
– The divide-and-conquer approach can be
applied over and over again until each

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Algorithms

Algorithm
A set of unambiguous instructions for solving a
problem or subproblem in a finite amount of time
using a finite amount of data

Why must instructions be unambiguous?
Why must time and data be finite?

10
Computer Problem-Solving

Analysis and Specification Phase   Can you
Analyze                      name
Specification                a recurring
Algorithm Development Phase        theme?
Develop algorithm
Test algorithm
Implementation Phase
Code algorithm
Test algorithm
Maintenance Phase
Use
Maintain

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Phase Interactions

Should we
arrow?

(What happens
if the problem
is revised?)

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Pseudocode

Pseudocode
A mixture of English and formatting to
make the steps in an algorithm explicit
Algorithm to Convert base-10 number to other bases

While ( the quotient is not zero )
Divide the decimal number by the new base
Make the remainder the next digit to the left in the answer
Replace the original decimal number with the quotient

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Following an Algorithm

Figure 6.4 A recipe for Hollandaise sauce
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Following an Algorithm

Algorithm for preparing a Hollandaise sauce
Put butter substitute in a pot
Else
Put butter in a pot
Turn on burner
Put pot on the burner
While (NOT bubbling)
Leave pot on the burner
Put other ingredients in the blender
Turn on blender
While (more in pot)
Pour contents into lender in slow steam
Turn off blender

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Developing an Algorithm

Two methodologies used to develop
computer solutions to a problem
– Top-down design focuses on the tasks to be
done
– Object-oriented design focuses on the data
involved in the solution

But first, let's look at a way to express
algorithms: pseudocode

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Pseudocode

Pseudocode
A way of expressing algorithms that uses a
mixture of English phrases and indention to
make the steps in the solution explicit
There are no grammar rules in pseudocode
Pseudocode is not case sensitive

17
Following Pseudocode
While ( the quotient is not zero )
Divide the decimal number by the new base
Make the remainder the next digit to the left in the answer
Replace the original decimal number with

What is 93 in base 8?
93/8 gives 11 remainder 5
11/6 gives 1 remainder 3
1/ 8 gives 0 remainder 1

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Following Pseudocode

Easier way to organize solution

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Pseudocode for Complete
Computer Solution
Write "Enter the new base"
Write "Enter the number to be converted"
Set quotient to 1
While (quotient is not zero)
Set quotient to decimalNumber DIV newBase
Set remainder to decimalNumber REM newBase
Make the remainder the next digit to the left in the answer
Set decimalNumber to quotient

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Pseudocode Functionality

Variables
Names of places to store values
quotient, decimalNumber, newBase

Assignment
Storing the value of an expression into a
variable
Set quotient to 64
quotient <-- 64
quotient <-- 6 * 10 + 4
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Pseudocode Functionality

Output
Printing a value on an output device
Write, Print

Input
Getting values from the outside word and
storing them into variables

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Pseudocode Functionality

Repetition
Repeating a series of statements
Set count to 1
While ( count < 10)
Write "Enter an integer number"
Write "You entered " + aNumber
Set count to count + 1

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Pseudocode Functionality

Selection
Making a choice to execute or skip a statement (or
group of statements)
If (number < 0)
Write number + " is less than zero."
or
Write "Enter a positive number."
If (number < 0)
Write number + " is less than zero."
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Pseudocode Functionality

Selection
Choose to execute one statement (or group of
statements) or another statement (or group of
statements)
If ( age < 12 )
Write "Pay children's rate"
Write "You get a free box of popcorn"
else If ( age < 65 )
Write "Pay regular rate"
else
Write "Pay senior citizens rate"

25
Pseudocode Example
Write "How many pairs of values are to be entered?"
Write "Enter two values separated by a blank; press return"
If (number1 < number2)
Print number1 + " " + number2
Else
Print number2 + " " number1

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Walk Through

Data            Fill in values during each iteration
55 70
21
33 33
numberOfPairs

What is the output?
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Top-Down Design

Top-Down Design
Problem-solving technique in which the problem is divided
into subproblems; the process is applied to each subproblem
Modules
Self-contained collection of steps, that solve a problem or
subproblem
Abstract Step
An algorithmic step containing unspecified details
Concrete Step
An algorithm step in which all details are specified
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Top-Down Design

Figure 6.5
An example
of top-down
design

Process continues for as many levels as it takes to make every step
concrete
Name of (sub)problem at one level becomes a module at next lower
level
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A General Example

Planning a large party

Figure 6.6 Subdividing the party planning

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A Computer Example

Problem
Create a list that includes each person’s
name, telephone number, and e-mail
– This list should then be printed in alphabetical
order
– The names to be included in the list are on
scraps of paper and business cards
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A Computer Example
Main                                            Level 0

Enter names and numbers into list
Put list into alphabetical order
Print list

Enter names and numbers into list               Level 1

While ( more names)
Enter name
Enter telephone number
Insert information into list

Which steps are abstract? Which steps are concrete?
What is missing?
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A Computer Example
Enter names and numbers into list (revised)             Level 1

Set moreNames to true
While (moreNames)
Prompt for and enter name
Prompt for and enter telephone number
Prompt for and enter email address
Insert information into list
Write "Enter a 1 to continue or a 0 to stop."
If (response = 0)
Set moreNames to false

Which steps are concrete? Which steps are abstract?

33
A Computer Example
Prompt for and enter name                                   Level 2

Write "Enter last name; press return."
Write "Enter first name; press return."

Prompt for and enter telephone number                       Level 2

Write "Enter area code and 7-digit number; press return."

Prompt for and enter email address                          Level 2

Write "Enter email address; press return."

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A Computer Example
Put list into alphabetical order

Concrete or abstract?

Print the list                                      Level 1

Write "The list of names, telephone numbers, and email
Get first item from the list
While (more items)
Write item's firstName + " " + lastName
Write item's telephoneNumber
Write a blank line
Get next item from the list

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A Computer Example

Note: Insert information is within the loop
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Testing the Algorithm

Important distinction

Mathematics
Programs
We test the process

37
Testing the Algorithm

Desk checking
Working through a design at a desk with a pencil and paper
Walk-through
Manual simulation of the design by team members, taking
sample data values and simulating the design using the
sample data
Inspection
One person (not the designer) reads the design (handed
out in advance) line by line while the others point out errors

38
Object-Oriented Design

Object-oriented Design
A problem-solving methodology that
produces a solution to a problem in terms of
self-contained entities called objects
Object
A thing or entity that makes sense within
the context of the problem
For example, a student, a car, time, date
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Object-Oriented Design

World View of OOD
Problems are solved by
– isolating the objects in a problem,
– determining their properties and actions
(responsibilities), and
– letting the objects collaborate to solve a
problem
What? Say again!

40
Object-Oriented Design

An analogy: You and your friend fix dinner
Objects: you, friend, dinner
Class: you and friend are people
People have name, eye color, …
People can shop, cook, …
Instance of a class: you and friend are instances of
class People, you each have your own name and
eye color, you each can shop and cook
You collaborate to fix dinner
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Object-Oriented Design

Class (or object class)
A description of a group of similar objects
Object (instance of a class)
A concrete example of the class
Classes contain fields that represent the
properties (name, eye color) and
behaviors (responsibilities) (shop, cook) of the class
Method
A named algorithm that defines behavior (shop,
cook)
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Object-Oriented Design

Top-Down Design
Object-Oriented Design
decomposes problems into
collaborating objects
Yes, but how?

43
Object-Oriented Design

Steps
– isolate the real-world objects in the
problem
– abstract the objects with like properties
into groups (classes)
– determine the responsibilities of the group
in interacting with other groups

44
Object-Oriented Design

Think of design as a mapping from real
world objects to classes of objects
birth
date

marriage    Date class
date

dog's
birth date

Objects                      Classes of objects
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Object-Oriented Design

Program World simulates these groups

dogBirthdate

class Date                birthdate

marriageDate

Description               Instances
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Object-Oriented Design

Date's                 We call an object's interactions
Actions in                   with other objects its
real world                      responsibilities
?

Create itself
Know the state of its fields
Compare itself to another date
Return a date #days hence

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Object-Oriented Design

Responsibilities become methods in the
Program World
dogBirthdate

class Date
getMonth
getDay               birthdate
getYear

marriageDate

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Object-Oriented Design
Methodology
Four stages to the decomposition process
– Brainstorming to locate possible classes
– Filtering the classes to find duplicates or
remove unnecessary ones
– Scenarios are tried to be sure we understand
collaborations
– Responsibility algorithms are designed for all
actions that classes must exhibit
49
CRC Cards
CRC cards are a notational device to record information
about a class, what is must do and with whom it must
collaborate

50
Brainstorming

A group problem-solving technique that
involves the spontaneous contribution of
ideas from all members of the group
– All ideas are potential good ideas
– Think fast and furiously first, and ponder later
– A little humor can be a powerful force

Brainstorming is designed to produce a list
of candidate classes
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Filtering

Determine which are the core classes in the
problem solution
There may be two classes in the list that
have many common attributes and
behaviors
There may be classes that really don’t
belong in the problem solution

52
Scenarios

Assign responsibilities to each class
There are two types of responsibilities
– What a class must know about itself
(knowledge responsibilities)
– What a class must be able to do (behavior
responsibilities)

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Scenarios

Encapsulation
The bundling of data and actions in such a
way that the logical properties of the data
and actions are separated from the
implementation details
Each class encapsulates its data but
shares their values through knowledge
responsibilities
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Responsibility Algorithms

The algorithms must be written for the
responsibilities
– Knowledge responsibilities usually just return
the contents of one of an object’s variables
– Action responsibilities are a little more
complicated, often involving calculations

55
Computer Example

Let’s repeat the problem-solving process for
Brainstorming and filtering
– Circling the nouns and underlining the verbs
is a good way to begin

56
Computer Example

First pass at a list of               list
name
classes                               telephone number
list
order
names
list
scraps
paper
cards

Filtered List

list, name, telephone number email address
CRC Cards

Can you think of any other useful responsibilities?

58
CRC Cards

Can you think of any other useful responsibilities?

59
CRC Cards

How is this class different from Name and Person?

60
Responsibility Algorithms

Person Class
Initialize                                     Tells name to initialize itself

name.initialize()
Write "Enter phone number; press return."
Get telephone number
Write "Enter email address; press return."
Tells name to print itself
Print

name.print()
Write "Telephone number: " + telephoneNumber

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Responsibility Algorithms
Name Class

Initialize

"Enter the first name; press return."
"Enter the last name; press return."

Print

Print "First name: " + firstName
Print "Last name: " + lastName

62

Information Hiding
The practice of hiding the details of a module with
Abstraction
A model of a complex system that includes only
the details essential to the viewer

Information Hiding and Abstraction are two
sides of the same coin
63

Data abstraction
Separation of the logical view of data from their
implementation
Procedural abstraction
Separation of the logical view of actions from their
implementation
Control abstraction
Separation of the logical view of a control structure from its
implementation

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Abstraction is the most powerful tool people have for
managing complexity!
65

Identifiers
Names given to data and actions, by which
– we access the data and
Read firstName, Set count to count + 1
– execute the actions
name.initialize(), name.print()

Giving names to data and actions is a form
of abstraction
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Programming language
A set of grammar rules, symbols, and special words used
to construct a program
Program
A sequence of instructions written to perform a specified
Syntax
The formal grammar rules governing the construction of
valid instructions
Semantics
The rules that give meaning to the instructions
67

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