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Problem Solving and Algorithm Design: A Comprehensive Guide

This chapter focuses on problem-solving strategies, algorithm development, and the use of pseudocode. It also introduces top-down and object-oriented design methodologies.

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Problem Solving and Algorithm Design: A Comprehensive Guide

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  1. Chapter 6 Problem Solving and Algorithm Design

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

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

  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. Following an Algorithm Figure 6.4 A recipe for Hollandaise sauce

  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. 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. 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. Following Pseudocode 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 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

  19. Following Pseudocode Easier way to organize solution

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

  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. 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. 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. A Computer Example Prompt for and enter nameLevel 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. 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. A Computer Example Note: Insert information is within the loop

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

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

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

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

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

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

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