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# 8.1 alogorithm & prolem solving

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### 8.1 alogorithm & prolem solving

1. 1. Problem Solving Algorithms
2. 2. PSPD Using C Design Topic & Structure of the lesson In this chapter you will learn about: • Problem Solving • Algorithm • Pseudocodes • Flowcharts
3. 3. PSPD Using C Design Key Terms you must be able to use If you have mastered this topic, you should be able to use the following terms correctly in your assignments and exams: • program • pseudocode • flowchart • algorithm
4. 4. PSPD Using C Design Problem Solving Techniques In this chapter you will learn about:  What problem solving is  The software development method of problem solving using computers  Basic algorithm control structures  The sequence structure  The selection structure  The repetition structure
5. 5. PSPD Using C Design Problem Solving Techniques By the time you have completed this chapter,you will have acquired the ability to:  Apply the software development method to solve problems  Difference between the Algorithm & the Flowchart  Knowing about the control structures
6. 6. PSPD Using C Design Problem Solving First: You have to understand the problem. UNDERSTANDING THE PROBLEM What is the unknown? What are the data?What is the condition? Is it possible to satisfy the condition?Is the condition sufficient to determine the unknown?Or is it sufficient?Or Redundant? Or Contradictory? Draw a figure.Introduce suitable notation.Separate the various parts of the condition.Can you write them down?
7. 7. PSPD Using C Design Problem Solving Second: Find the connection between the data and the unknown. Auxiliary problems may be devised if needed. You should obtain eventually a plan of the solution. DEVISING A PLAN Have you seen it before? Or have you seen the same problem in slightly different form? Do you know a related problem? Look at the unknown! Try to think of a familiar problem having the same or similar unknown. Split the problem into smaller, simple sub-problems. If you cannot solve the proposed problem try to solve first some related problem. Or solve more general problem. Or special case of the problem. Or solve the part of the problem.
8. 8. PSPD Using C Design Problem Solving Third: Carry out your plan. CARRYING OUT THE PLAN Carrying out your plan of the solution,check each step. Can you see clearly that step is correct? Can you prove that it is correct? Fourth: Examine the solution obtained. LOOKING BACK Can you check the result? Can you derive the result differently? Can you use the result, or the method, for some other problem?
9. 9. PSPD Using C Design Problem Solving The software development method The software development method consists of the following steps:  Requirements specification  Analysis  Design  Implementation  Testing and verification  Documentation
10. 10. PSPD Using C Design Algorithmic Problem Solving Algorithmic problem: Any problem whose solution can be expressed as a set of executable instructions. Algorithm: A well defined computational procedure consisting of a set of instructions, that takes some value or set of values, as input, and produces some value or set of values, as output.
11. 11. PSPD Using C Design Algorithmic Problem Solving Derived from the name of Mohammed al- khowarizmi, a Persian mathematician in the ninth century. Al-khowarizmi--Algorismus(in Latin)--Algorithm  An algorithm is like a recipe, that converts the ingredients into some culinary dish.  The formal written version is a program.  Algorithms/programs are the software.The machine that runs the programs is the hardware.
12. 12. PSPD Using C Design Algorithmic Problem Solving Ingredient Recipe (software) Cooking utensils (hardware) Al-gong Bah-kut-the
13. 13. PSPD Using C Design Characteristics of an Algorithm  Each step of an algorithm must be exact, preciously and ambiguously described.  It must terminate, i.e. it contains a finite number of steps.  It must be effective, i.e.., produce the correct output.  It must be general, i.e.. to solve every instance of the problem.
14. 14. PSPD Using C Design Characteristics of an Algorithm  An Algorithm is implemented in some programming language. program = Algorithm + Data Structures.  Data Structures refer to the types of data used and how the data are organized in the program.  An algorithm is usually presented in the form of some pseudo-code, which is a mixture of English statement,some mathematical notations,and selected keywords from a programming language.
15. 15. PSPD Using C Design Characteristics of an Algorithm PROBLEM: You are required to design a complete system which will enable the sum of two values to be calculated.  An Algorithm should emphasize the WHAT’s and not the HOW’s. Consider the problem below:
16. 16. PSPD Using C Design Problem Solving To grapple with this problem, we have to understand the problem from the human perspective. A question to ask yourself is this, “How Would You Calculate the Sum of Two Values?”
17. 17. PSPD Using C Design Problem Solving As the computer is also a device similar to the way in which the human brain functions, the process of calculating the sum of two values can also be easily performed by the computer. =
18. 18. PSPD Using C Design Problem Solving Input Processing (Brains) Output
19. 19. PSPD Using C Design Problem Solving Input Device Output Device CPU (Brains)
20. 20. PSPD Using C Design Problem Solving 5 10 15 5 + 10 = 15 Input Processing Output Let us assume we are interested in calculating the sum of 5 and 10.
21. 21. PSPD Using C Design Problem Solving As shown previously, the example values (5 and 10) have been specified explicitly. As the brain is flexible enough in calculating a wide range of numbers, the two input values have to be generalised.
22. 22. PSPD Using C Design Problem Solving Value1 Value2 Sum Sum = Value1 + Value2 Notice that instead of using specific numbers, variables are used to represent these values.
23. 23. PSPD Using C Design What Are Variables? Variables are memory locations within the computer which allows pieces of data to be stored. The word variable comes from the word vary, which means that whatever you place within a variable can be changed. A variable can be viewed as a container used to store things. Data (for example, name, age, salary) can be stored in these containers.
24. 24. PSPD Using C Design What Are Variables?
25. 25. PSPD Using C Design Problem Solving Now that we have an exact idea about how the problem is solved, let us represent this in a clearer manner, using the defining diagram. Input Processing Output Value1 Value2 Sum
26. 26. PSPD Using C Design Problem Solving The next step is to identify the actual processing steps required to convert the input to become the output. Input Processing Output Value1 Value2 Sum1) Read Value1, Value2 2) Calculate Sum 3) Display Sum
27. 27. PSPD Using C Design Algorithm Development Once the defining diagram has been developed, the next logical step is to develop the algorithm (which is much more detailed). Input Processing Output Value1 Value2 Sum1) Read Value1, Value2 2) Calculate Sum 3) Display Sum The developed processing steps have to be more detailed in the algorithm.
28. 28. PSPD Using C Design Algorithm Development The basic mathematical operators used in algorithms are as follows:- + addition - subtraction * multiplication / division = assignment ( ) brackets for grouping calculations
29. 29. PSPD Using C Design Algorithm Development Example of an algorithm (using pseudocodes) which can be used to carry out the tasks outlined in the defining diagram is as follows:- 1) Read Value1, Value2 2) Calculate Sum = Value1 + Value2 3) Display Sum
30. 30. PSPD Using C Design Pseudocoding A Pseudocode language is semiformal, English- like language with a limited vocabulary that can be used to design and describe algorithms. The pseudocode language can be used for:  Designing algorithms  Communicating algorithms as programs  Implementing algorithms as programs  Debugging logic errors in program
31. 31. PSPD Using C Design Pseudocode for the Control Structures The Sequence Control Structure: The sequence control structure is a series of steps or statements that are executed in the order in which they are written in an algorithm. For Example: read taxable income read filing status compute income tax
32. 32. PSPD Using C Design Cont’d The Selection Control Structure: The selection control structure defines two courses of action, depending on the outcome of a condition. A condition is an expression that, when evaluated, computes to either true or false. Syntax is: if condition then-part else else-part end-if
33. 33. PSPD Using C Design Decision Making Being able to mimic the way the human brain works, the computer also has the ability to make decisions. Decision making can be represented in pseudocodes using the IF...THEN construct. IF (expression) THEN : : ENDIF
34. 34. PSPD Using C Design Decision Making IF (expression) THEN : : ENDIF The expression is a comparison between two values which evaluates to either true of false. Statements are placed here.
35. 35. PSPD Using C Design Decision Making Example:- We are looking for a job which pays more than RM4000. IF (Salary>4000) THEN Say "I Will Take The Job!!" ENDIF Example of an Expression
36. 36. PSPD Using C Design Decision Making Commonly used relational operators in expressions:- > Greater Than < Less Than = Equals To < > Not Equals To >= Greater Than or Equals To <= Less Than or Equals To ( ) Brackets used for prioritising certain calculations
37. 37. PSPD Using C Design Decision Making Since all expressions works out to be either true or false, what the IF..THEN statement represents is a two-state condition. For example, A potential employer is waiting for you to give a reply (on the spot) about the job offer with a salary of RM2000. Your decision would be to only take a job worth more than RM4000. What would you say? IF (Salary>4000) THEN Say “YES!” ELSE Say “NO!” ENDIF
38. 38. PSPD Using C Design Decision Making Certain conditions may give rise to more than one expression being evaluated. These are known as compound expressions. Example:- You are interested in taking up a job which pays more than RM4000 and that the company must also provide a credit card. IF (Salary>4000) And (CreditCard=YES) THEN Take Job!! ENDIF
39. 39. PSPD Using C Design Decision Making Compound expressions can be represented using the following operators:- AND Every expression must evaluate to be true in order for the whole expression to be true. OR As long as any one of the expression can be true, the entire IF statement will be true. NOT The inverse (opposite) of the entire expression.
40. 40. PSPD Using C Design Decision Making IF statements can be nested, that is, placed within another IF statement. This is used in situations when the expression is more complex than the simple decisions (as seen earlier).
41. 41. PSPD Using C Design Decision Making IF (Salary>4000) And (CreditCard=YES) THEN Say “Yes I Will Take The Job!!” ENDIF For example, this statement......... can be represented like this......... IF (Salary>4000) THEN IF (CreditCard=YES) THEN Say “Yes I Will Take The Job!!” ELSE Say “No Credit Card?” Say “Sorry!!” ENDIF ELSE Say “Not Enough Pay!!” ENDIF ........ whereby more possibilities can be represented.
42. 42. PSPD Using C Design Decision Making For good practice........... IF (Salary>4000) THEN IF (CreditCard=YES) THEN Say “Yes I Will Take The Job!!” ELSE Say “No Credit Card?” Say “Sorry!!” ENDIF ELSE Say “Not Enough Pay!!” ENDIF ........ ensure that statements are properly indented to indicate block of statements which belong together.
43. 43. PSPD Using C Design Cont’d For Example: if a is greater than b then print “A is greater” else print “B is greater” end if
44. 44. PSPD Using C Design Cont’d Repetition Control Structure: The repetition control structure specifies a block of one or more statements that are repeatedly executed until a condition is satisfied. Syntax is: while condition loop-body end-while
45. 45. PSPD Using C Design Looping Constructs Looping constructs (also known as repetition or iteration constructs) are a kind of construct found in pseudocodes which allows statements (or a group of statements) to be repeated. The main reason why looping constructs are provided is because most of the problems which we encounter everyday requires some degree of repetition.
46. 46. PSPD Using C Design Looping Constructs An example of a process which is iterative:- Payroll processing is very much an iterative process as the person processing the payroll applies the same calculations for each employee to produce the pay slip.
47. 47. PSPD Using C Design Looping Constructs The looping constructs available in pseudocodes are as follows:- DOWHILE...ENDDO FOR…NEXT REPEAT...UNTIL
48. 48. PSPD Using C Design Looping Constructs The format of the DOWHILE...ENDDO construct is shown below:- DOWHILE (expression) : : : ENDDO Group of statements An expression which determines whether the loop will continue.
49. 49. PSPD Using C Design Looping Constructs The format of the FOR...NEXT construct is shown below:- FOR (initialze TO expression) STEP increment : : : ENDDO Group of statements An expression which determines whether the loop will continue.
50. 50. PSPD Using C Design Looping Constructs The format of the REPEAT...UNTIL construct is shown below:- REPEAT : : : UNTIL (expression) Group of statements An expression which determines whether the loop will continue.
51. 51. PSPD Using C Design Looping Constructs Take a look at the following example:- You are required to develop a complete system which will allow the total payroll to be calculated. The system is required to read in the amount to be paid for each employee. The moment the system receives an input value of -99, the system is required to stop and display the total payroll.
52. 52. PSPD Using C Design Looping Constructs Input Processing Output Salary Total1) Read Salary 2) Calculate Total 3) Display Total The Defining Diagram
53. 53. PSPD Using C Design Looping Constructs Algorithm (Using Pseudocodes) 1) Display "Enter Salary" 2) Read Salary 3) Total = 0 4) DOWHILE (Salary<>-99) Total = Total + Salary Display "Enter Salary" Read Salary ENDDO 5) Display "Total Payroll = ", Total
54. 54. PSPD Using C Design Cont’d Example: Dowhile (income is less than 50000) print “Enter taxable income;should be greater than or equal to 50000” read income Enddo
55. 55. PSPD Using C Design Desk Check Table A desk check table is used to verify the correctness of the design. This is to ensure that the program which will eventually be developed is going to produce the answer which is required. The desk check table is developed based on the following steps:- 1) Identify the data sets. 2) Identify the expected results. 3) Trace through the algorithm with the data sets using a trace table. 4) Analyse & compare the results produced in step (3) and the expected results in step (2).
56. 56. PSPD Using C Design Desk Check Table Identify Data Sets Input Processing Output Value1 Value2 Sum1) Read Value1, Value2 2) Calculate Sum 3) Display Sum Focus on the input section of the defining diagram and identify some possible values (data sets) which can be used to test the system.
57. 57. PSPD Using C Design Desk Check Table Identify Expected Results Input Processing Output Value1 Value2 Sum1) Read Value1, Value2 2) Calculate Sum 3) Display Sum Focus on the output section of the defining diagram and identify some possible values which the system will produce based on the data sets.
58. 58. PSPD Using C Design Desk Check Table Trace Table - Data Set 1 Read Value1 Value2 5 3 Sum Calculate 8 Display  Do the results match the expected results?
59. 59. PSPD Using C Design Desk Check Table Trace Table - Data Set 2 Read Value1 Value2 8 13 Sum Calculate 21 Display  Do the results match the expected results?
60. 60. PSPD Using C Design Desk Check Table Trace Table - Data Set 3 Read Value1 Value2 15 9 Sum Calculate 24 Display  Do the results match the expected results?
61. 61. PSPD Using C Design Program Flowcharts As humans are more inclined towards understanding diagrams and pictures rather than words, pseudocodes tends to become tedious to understand if too lengthy. Program flowcharts, because they are represented graphically, makes understanding easier.
62. 62. PSPD Using C Design Program Flowcharts The following are the commonly used symbols for drawing program flowcharts. terminator off-page connector process storage decision making document input/output connector arrowheads
63. 63. PSPD Using C DesignBegin Read Value1, Value2 Program Flowcharts Calculate Sum = Value1 + Value2 Display Sum End
64. 64. PSPD Using C DesignBegin Read Amount Program Flowcharts End Amount>20.00? Calculate Actual=Amount * 0.80 Calculate Actual=Amount NOYES
65. 65. PSPD Using C Design Flowcharting        Another technique used in designing and representing  algorithms.  Alternative to pseudocoing  A pseudocode description is verbal, a flowchart is graphical in nature. Definition:  A flowchart is a graph consisting of geometrical shapes that are connected by flow lines.
66. 66. PSPD Using C Design Sequence Structure       Pseudocode: Flowchart: statement_1 statement_2 ------------ statement_n Statement -1 Statement -2 Statement -n
67. 67. PSPD Using C Design Selection Structure       Pseudocode: Flowchart: if condition then-part else else-part end_if condition else-part then-part truefalse
68. 68. PSPD Using C Design Selection Structure       Pseudocode: Flowchart: if condition then-part end_if condition then-part true false Y N
69. 69. PSPD Using C Design Repetition Structure Pseudocode: Flowchart: while condition loop-body end-while condition loop-body F T Y N
70. 70. PSPD Using C Design Summary  Problem Solving– the process of transforming the description of a problem to its solution.  To Solve complex problems, we use computers as a tool and develop computer programs that give us solutions.  A commonly used method for problem solving using computers is the software development method,which consists of six steps.
71. 71. PSPD Using C Design Summary 1. The Requirements specification, provides us with a precise definition of the problem.  2. In the analysis phase we identify problem inputs,outputs,special constraints, and formulas and equations to be used. 3. The design phase is concerned with developing an algorithm for the solution of the problem.
72. 72. PSPD Using C Design Summary 4. The implementation of an algorithm is a computer program.When executed, it should produce the solution to the problem. 5. Program Verification is the process of ensuring that a program meets user requirements. 6. Program testing, on the other hand, is the process of executing a program to demonstrate its correctness. 7. Program Documentation facilitates the use of the program,future program maintenance efforts,and program debugging.
73. 73. PSPD Using C Design Summary  An algorithm is a sequence of a finite number of steps arranged in a specific logical order that, when executed, produce the solution for a problem.  A pseudocode language is a semiformal,English-like language with a limited vocabulary that can be used to design and describe algorithms.
74. 74. PSPD Using C Design Summary  Any algorithm can be described in terms of three basic control structures.They are the sequence,selection and repetition structures.  The top-down stepwise refinement of algorithms is a fundamental problem-solving strategy.  A Flowchart is a graphical representation of an algorithm.
75. 75. PSPD Using C Design Quick Review Question 1. State the difference between the Dowhile – Enddo structure and the Repeat – Until structure. 2. Write an algorithm that will display the first hundred even numbers using the Do-While loop.
76. 76. PSPD Using C Design Follow Up Assignment • This is an individual piece of work. • Your source code will be discussed at the end of the next lesson.
77. 77. PSPD Using C Design Summary of Main Teaching Points • Problem Solving • Pseudocodes • Flowcharts • Basic control structures • The sequence structure • The selection structure • The repetition structure