Chapter 6 discusses problem-solving and algorithm design, outlining the steps and methodologies involved in computer problem-solving, such as understanding the problem, devising a plan, and testing algorithms. It emphasizes the importance of pseudocode in expressing algorithms and presents top-down and object-oriented design approaches to tackle complex problems through abstraction and collaboration among objects. Key themes include information hiding, abstraction, and the necessity for clear and structured instructions in algorithm development.

1. Chapter 6
Problem Solving
and Algorithm Design

2. 2
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

3. 3
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

4. 4
Problem Solving
Problem solving
The act of finding a solution to a perplexing,
distressing, vexing, or unsettled question
How do you define problem solving?

5. 5
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!

6. 6
Problem Solving
How do you solve problems?
Understand the problem
Devise a plan
Carry out the plan
Look back

7. 7
Strategies
Ask questions!
– 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?

8. 8
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?

9. 9
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
subtask is manageable

10. 10
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?

11. 11
Computer Problem-Solving
Analysis and Specification Phase
Analyze
Specification
Algorithm Development Phase
Develop algorithm
Test algorithm
Implementation Phase
Code algorithm
Test algorithm
Maintenance Phase
Use
Maintain
Can you
name
a recurring
theme?

12. 12
Phase Interactions
Should we
add another
arrow?
(What happens
if the problem
is revised?)

13. 13
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

14. 14
Following an Algorithm
Figure 6.4 A recipe for Hollandaise sauce

15. 15
Following an Algorithm
Algorithm for preparing a Hollandaise sauce
If concerned about cholesterol
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

16. 16
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

17. 17
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

18. 18
Following Pseudocode
What is 93 in base 8?
93/8 gives 11 remainder 5
11/6 gives 1 remainder 3
1/ 8 gives 0 remainder 1
answer 1 3 5
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

19. 19
Following Pseudocode
Easier way to organize solution

20. 20
Pseudocode for Complete
Computer Solution
Write "Enter the new base"
Read newBase
Write "Enter the number to be converted"
Read decimalNumber
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
Write "The answer is "
Write answer

21. 21
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

22. 22
Pseudocode Functionality
Output
Printing a value on an output device
Write, Print
Input
Getting values from the outside word and
storing them into variables
Get, Read

23. 23
Pseudocode Functionality
Repetition
Repeating a series of statements
Set count to 1
While ( count < 10)
Write "Enter an integer number"
Read aNumber
Write "You entered " + aNumber
Set count to count + 1
How many values were read?

24. 24
Pseudocode Functionality
Selection
Making a choice to execute or skip a statement (or
group of statements)
Read number
If (number < 0)
Write number + " is less than zero."
or
Write "Enter a positive number."
Read number
If (number < 0)
Write number + " is less than zero."
Write "You didn't follow instructions."

25. 25
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"

26. 26
Pseudocode Example
Write "How many pairs of values are to be entered?"
Read numberOfPairs
Set numberRead to 0
While (numberRead < numberOfPairs)
Write "Enter two values separated by a blank; press return"
Read number1
Read number2
If (number1 < number2)
Print number1 + " " + number2
Else
Print number2 + " " number1
Increment numberRead

27. 27
Walk Through
Data Fill in values during each iteration
3 numberRead number1 number2
55 70
2 1
33 33
numberOfPairs
What is the output?

28. 28
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

29. 29
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
Figure 6.5
An example
of top-down
design

30. 30
A General Example
Planning a large party
Figure 6.6 Subdividing the party planning

31. 31
A Computer Example
Problem
Create a list that includes each person’s
name, telephone number, and e-mail
address
– 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

32. 32
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
Enter email address
Insert information into list
Which steps are abstract? Which steps are concrete?
What is missing?

33. 33
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."
Read response
If (response = 0)
Set moreNames to false
Which steps are concrete? Which steps are abstract?

34. 34
A Computer Example
Prompt for and enter name Level 2
Write "Enter last name; press return."
Read lastName
Write "Enter first name; press return."
Read firstName
Prompt for and enter telephone number Level 2
Write "Enter area code and 7-digit number; press return."
Read telephoneNumber
Prompt for and enter email address Level 2
Write "Enter email address; press return."
Read emailAddress

35. 35
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
addresses follows:"
Get first item from the list
While (more items)
Write item's firstName + " " + lastName
Write item's telephoneNumber
Write item's emailAddress
Write a blank line
Get next item from the list

36. 36
A Computer Example
Note: Insert information is within the loop

37. 37
Testing the Algorithm
Important distinction
Mathematics
We tests the answer
Programs
We test the process

38. 38
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

39. 39
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

40. 40
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!

41. 41
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

42. 42
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)

43. 43
Object-Oriented Design
Top-Down Design
decomposes problems into tasks
Object-Oriented Design
decomposes problems into
collaborating objects
Yes, but how?

44. 44
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

45. 45
Object-Oriented Design
Think of design as a mapping from real
world objects to classes of objects
birth
date
marriage
date
dog's
birth date
Date class
Objects Classes of objects

46. 46
Object-Oriented Design
Program World simulates these groups
class Date
dogBirthdate
birthdate
marriageDate
Description Instances

47. 47
Object-Oriented Design
Date's
Actions in
real world
?
We call an object's interactions
with other objects its
responsibilities
Create itself
Know the state of its fields
Compare itself to another date
Return a date #days hence

48. 48
Object-Oriented Design
Responsibilities become methods in the
Program World
class Date
getMonth
getDay
getYear
dogBirthdate
birthdate
marriageDate

49. 49
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

50. 50
CRC Cards
CRC cards are a notational device to record information
about a class, what is must do and with whom it must
collaborate

51. 51
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

52. 52
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

53. 53
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)

54. 54
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

55. 55
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

56. 56
Computer Example
Let’s repeat the problem-solving process for
creating an address list
Brainstorming and filtering
– Circling the nouns and underlining the verbs
is a good way to begin

57. Computer Example
First pass at a list of
classes
list
name
telephone number
email address
list
order
names
list
scraps
paper
cards
Filtered List
list, name, telephone number email address

58. 58
CRC Cards
Can you think of any other useful responsibilities?

59. 59
CRC Cards
Can you think of any other useful responsibilities?

60. 60
CRC Cards
How is this class different from Name and Person?

61. 61
Responsibility Algorithms
Person Class
Initialize
name.initialize()
Write "Enter phone number; press return."
Get telephone number
Write "Enter email address; press return."
Get email address
Print
name.print()
Write "Telephone number: " + telephoneNumber
Write "Email address: " + emailAddress
Tells name to initialize itself
Tells name to print itself

62. 62
Responsibility Algorithms
Name Class
Initialize
"Enter the first name; press return."
Read firstName
"Enter the last name; press return."
Read lastName
Print
Print "First name: " + firstName
Print "Last name: " + lastName

63. 63
Important Threads
Information Hiding
The practice of hiding the details of a module with
the goal of controlling access to it
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

64. 64
Important Threads
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

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

66. 66
Important Threads
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

67. 67
Importhat Threads
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
task
Syntax
The formal grammar rules governing the construction of
valid instructions
Semantics
The rules that give meaning to the instructions

68. 68
Ethical Issues
Licensing Computer Professionals
Are computer professionals licensed?
What is the ACM and why is it opposed
to licensing?
What is the IEEE and what is its
position on licensing?
Should computer professionals be licensed?

69. 69
Who am I?
I am a
mathematician.
Why is my
picture in a
book about
computer
science?

70. 70
Do you know?
What does TNDM stand for and what is it?
How is a computer data base being used
to help endangered species?
What is forensic computing?
What techniques does it use?
How is physical evidence protected?