56. Chapter 6: Problem Solving and Algorithm Design
In general, how are problems solved on a computer?
Analysis & Specification
Understand the problem
Specify what the program needs to do
Algorithm Development
Formulate sequence of steps for solving problem
Test that the steps work for certain key cases
Implementation
Translate the algorithm into a programming language
Test whether the program produces correct results
Maintenance
Deliver the program and have real users use it
Debug and upgrade the program as needed
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Problem Solving and Algorithm Design
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57. Problem Solving and Algorithm Design
Algorithms
An algorithm is an ordered set of unambiguous, executable steps that ultimately terminate if followed.
Ambiguous:
Not executable:
Lather
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Problem Solving and Algorithm Design
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No termination:
Rinse
Repeat

58. Problem Solving and Algorithm Design
Computer Algorithms
In computer programming, an algorithm is the sequence of steps (i.e., the “recipe”) for accomplishing a task.
Every step in an algorithm has two basic components:
Semantics: The meaning of the step
Syntax: The format of the step
Semantics
Get a value from the user
Double that value
Return the result to the user
Syntax
Program DoubleIt;
var x, y integer;
begin
write(“Input your number: ”);
read(x);
y = 2*x;
writeln(“The doubled number is ”, y);
end.
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Problem Solving and Algorithm Design
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59. Pseudocode
Pseudocode is an informal notation for expressing an algorithm.
Procedure Sat1231A
Set year to 2001
Set month to January
Set day to first Saturday in January 2001
While (year < 2021) Do {
Increment day by 7
If date is New Year’s Eve
Then display year as having a Saturday New Year’s Eve
If day > (number of days in month)
Then
Adjust day by subtracting the number of days in month
If month is December
Increment year by 1 }
Else
Increment month by one
Example: Which years in have New Year’s Eve on Saturday?
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Problem Solving and Algorithm Design
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60. Problem Solving and Algorithm Design
Algorithm Alternatives
It’s possible to devise many algorithms to solve the same problem.
Procedure Sat1231B
Set day_of_week to 12/31/2000
Set year to 2001
While (year < 2021) Do {
If year is a leap year
Then increment day_of_week by 2
Else increment day_of_week by 1
If day_of_week is Saturday
Then display year as having a Saturday New Year’s Eve
Increment year by 1 }
Alternative pseudocode to determine which years in have New Year’s Eve on Saturday.
Both algorithms work, but which is better?
Which is easier to code?
Which runs more efficiently?
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Problem Solving and Algorithm Design
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61. Networking Capability Artificial Intelligence
Program Modularity
The software development process usually involves a team of developers, so the software is often designed as a hierarchical system of modules, which can be viewed as easily modified interdependent entities.
Video Game
Networking Capability
Data Security
Server Access
Customer Billing
Game Play
Animation
Character Animation
Special Effects
Backgrounds
Artificial Intelligence
Sound
Music
Voice
Sound Effects
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Problem Solving and Algorithm Design
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62. Problem Solving and Algorithm Design
Advantages of Modular Programming
Modifiability
It’s easier to alter or upgrade the program if changes can be segregated to particular modules
Debuggability
It’s easier to diagnose and pinpoint problems with the program if it’s split into logically distinct modules
Reusability
Generic modules can be developed and then reused in other programs, eliminating the need to “reinvent the wheel”
Readability
It’s easier to read someone else’s program or refresh you memory about your own program if it’s broken into self-contained units
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63. Computer Graphics Modularity Example
Initially, set the program up to calculate the scene with simple lighting.
Replace the simple lighting with more sophisticated reflective surfaces.
Add a module to smooth out the silhouettes of objects.
main
generate
polygons
torus
cube
teapot
sphere
cone
draw
shade
polygon
pixels
main
generate
polygons
torus
cube
teapot
sphere
cone
draw
blend
compute
reflect
pixels
main
generate
polygons
torus
cube
teapot
sphere
cone
draw
blend
compute
reflect
pixels
curved
surfaces
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Problem Solving and Algorithm Design
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64. Top-Down Design
One common approach for designing programs is the top-down methodology.
Design a high-level solution to the programming problem.
Consider each complicated subproblem as a separate programming problem.
Return to step #1 with each subproblem.
Process Payroll
Get Input Data
Retrieve Timecard Data
Retrieve Salary Information
Retrieve Dependent Records
Retrieve Retirement Plans
Retrieve Tax Rates
Perform Calculations
Compute Gross Pay
Compute Deductions
Produce Output
Generate Paychecks
Update YTD Records
This approach lends itself to modularity.
However, it may impose an artificial hierarchy on the tasks being performed.
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Problem Solving and Algorithm Design
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65. Bottom-Up Design
A newer approach for designing programs is the bottom-up methodology.
Separate each major task in the overall problem into an individual programming problem.
Develop cooperative programming solutions to the separate problems.
Video Game Engine
Physics Engine
Fluid Dynamics Engine
Particle Systems Engine
Collision Detection Engine
Math Engine
Rotational Calculation Engine
Fractal Engine
Artificial Intelligence Engine
Intelligent Agent Engine
Behavior Prediction Engine
This approach produces reusable modules.
However, those modules may prove difficult to cobble together to solve bigger problems.
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