Computer Algorithms

1. 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 problemoraccomplishing 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. • Resolvingambiguity requires some thinking (intelligence) which computers cannot do !) • Computers cannotthink.

6. Algorithm development • We will now illustrate the process of developing an algorithm • An algorithmalways 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. [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 } • Example of how you would instruct a computer to change a light bulb:

11. Algorithms andProblem Solving

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

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 musthave 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 algorithmdesigned 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