1. Algorithms and Problem Solving

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

3. 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

4. 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

5. 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

6. 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

7. 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!

8. What is an algorithm? (Cont’d)

9. 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

10. 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!

11. 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.

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

13. 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

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

15. 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!

16. 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!

17. 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!

18. 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.

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

20. Class-Responsibility-Collaboration (CRC) Cards

21. 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

22. 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

23. 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

24. 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

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

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

27. Computer Example (Cont’d)
Filtered list

28. CRC Cards

29. Responsibility Algorithms