1. PROBLEM SOLVING SKILLS
Computer Algorithms
PROBLEM SOLVING SKILLS

2. Fact: computers are dumb machines
Basic property of a computer (a machine):
Computers do what we tell them to do
Unfortunately, computer do not necessarily do what we want them to do....
(Because we can make mistake in telling the computer what we want to do... These mistakes are called "bugs")

3. Algorithm Definition: algorithm Dictionary definition:
Algorithm = a step-by-step procedure for solving a problem or accomplishing some task, especially by means of a computer

4. Computer Algorithms Computer Algorithm:
is an algorithm that can be executed by a computer

5. Computer Algorithms (cont.)
Properties of computer algorithms:
The steps in an algorithm must be consists of operations that can be executed by a computer
The step in an algorithm must be unambiguous
(Remember that a dumb machine like a computer will do what it is told to do.
Resolving ambiguity requires some thinking (intelligence) which computers cannot do !)
Computers cannot think.

6. Algorithm development
We will now illustrate the process of developing an algorithm
An algorithm always accomplishes some well- defined task or solves some well-defined problem
The task/problem that we will use to illustrate the process of developing an algorithm is:
Replacing a burned out light bulb

7. Instruction for humans on replacing a burned out light bulb
Typical instructions given to humans on how to replace a light bulb:
These brief instructions assume a lot of common sense knowledge that a machine does not have !!!
Remove the burned-out bulb
Insert a new bulb

8. Instruction for humans on replacing a burned out light bulb (cont.)
What can go wrong if a machine uses these instructions:
A machine does not know how to remove a bulb
It could yank the bulb out of its socket and damage the fixture in the process.
A machine does not know how to insert a bulb
A machine can replace the bulb with one that has an inadequate wattage (too bright or too dim)

9. Instructions for computers on replacing a burned out light bulb
Computers have no common sense knowledge (really dumb)
Instructions for computers must be given very explicitly (in "baby steps")

10. Example of how you would instruct a computer to change a light bulb:
[The following instructions will remove the burn-out bulb]
repeat until (bulb comes free of socket) {
turn bulb in counter-clockwise direction }
[The following instructions will find a suitable bulb]
select a new bulb
repeat until (wattage of bulb selected = wattage of old bulb)
discard the selected bulb select another bulb
[The following instructions will insert the new bulb]
repeat until (bulb is secure in socket)
turn bulb in clockwise direction

11. Algorithms and Problem Solving

12. Lecture Objectives Learn about problem solving skills
Explore the algorithmic approach for problem solving
Learn about algorithm development
Become aware of problem solving process

13. Problem Solving Programming is a process of problem solving
Problem solving techniques
Analyze the problem
Outline the problem requirements
Design steps (algorithm) to solve the problem
Algorithm:
Step-by-step problem-solving process
Solution achieved in finite amount of time

14. Problem Solving Process
Step 1 - Analyze the problem
Outline the problem and its requirements
Design steps (algorithm) to solve the problem
Step 2 - Implement the algorithm
Implement the algorithm in code
Verify that the algorithm works
Step 3 - Maintenance
Use and modify the program if the problem domain changes

15. Analyze the Problem Thoroughly understand the problem
Understand problem requirements
Does program require user interaction?
Does program manipulate data?
What is the output?
If the problem is complex, divide it into subproblems
Analyze each subproblem as above

16. What is an algorithm? The idea behind the computer program
Stays the same independent of
Which kind of hardware it is running on
Which programming language it is written in
Solves a well-specified problem in a general way
Is specified by
Describing the set of instances (input) it must work on
Describing the desired properties of the output

17. What is an algorithm? (Cont’d)
Before a computer can perform a task, it must have an algorithm that tells it what to do.
Informally: “An algorithm is a set of steps that define how a task is performed.”
Formally: “An algorithm is an ordered set of unambiguous executable steps, defining a terminating process.”
Ordered set of steps: structure!
Executable steps: doable!
Unambiguous steps: follow the directions!
Terminating: must have an end!

18. What is an algorithm? (Cont’d)

19. Important Properties of Algorithms
Correct
always returns the desired output for all legal instances of the problem.
Unambiguous
Precise
Efficient
Can be measured in terms of
Time
Space
Time tends to be more important

20. Representation of Algorithms
A single algorithm can be represented in many ways:
Formulas: F = (9/5)C + 32
Words: Multiply the Celsius by 9/5 and add 32.
Flow Charts.
Pseudo-code.
In each case, the algorithm stays the same; the implementation differs!

21. Representation of Algorithms (Cont’d)
A program is a representation of an algorithm designed for computer applications.
Process: Activity of executing a program, or execute the algorithm represented by the program
 Process: Activity of executing an algorithm.

22. Expressing Algorithms
English description
Pseudo-code
High-level programming language
More
precise
More easily expressed

23. Pseudocode
Pseudocode is like a programming language but its rules are less stringent.
Written as a combination of English and programming constructs
Based on selection (if, switch) and iteration (while, repeat) constructs in high-level programming languages
Design using these high level primitives
Independent of actual programming language

24. Pseudocode (Cont’d)
Example: The sequential search algorithm in pseudocode

25. Algorithm Discovery The Two Steps of Program Development:
1. Discover the algorithm.
2. Represent the algorithm as a program.
Step 2 is the easy step!
Step 1 can be very difficult!
To discover an algorithm is to solve the problem!

26. Problem Solving: A creative process
Problem solving techniques are not unique to Computer Science.
The CS field has joined with other fields to try to solve problems better.
Ideally, there should be an algorithm to find/develop algorithms.
However, this is not the case as some problems do not have algorithmic solutions.
Problem solving remains an art!

27. Problem Solving Strategies
Working backwards
Reverse-engineer
Once you know it can be done, it is much easier to do
What are some examples?
Look for a related problem that has been solved before
Java design patterns
Sort a particular list such as: David, Alice, Carol and Bob to find a general sorting algorithm
Stepwise Refinement
Break the problem into several sub-problems
Solve each subproblem separately
Produces a modular structure
K.I.S.S. = Keep It Simple Stupid!

28. Stepwise Refinement
Stepwise refinement is a top-down methodology in that it progresses from the general to the specific.
Bottom-up methodologies progress from the specific to the general.
These approaches complement each other
Solutions produced by stepwise refinement posses a natural modular structure - hence its popularity in algorithmic design.

29. Object-Oriented Design Methodology
Four stages to the decomposition process
Brainstorming
Filtering
Scenarios
Responsibility algorithms

30. Class-Responsibility-Collaboration (CRC) Cards

31. 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

32. 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

33. Scenarios Assign responsibilities to each class
There are two types of responsibilities
What a class must know about itself (knowledge)
What a class must be able to do (behavior)
Encapsulation is 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

34. 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

35. Computer Example
Let’s repeat the problem-solving process for creating an address list
Brainstorming and filtering
Circling the nouns and underlining the verbs

36. Computer Example (Cont’d)
First pass at a list of classes

37. Computer Example (Cont’d)
Filtered list

38. CRC Cards

39. Responsibility Algorithms