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Algorithms

PROGRAMMING PAPER 2 AS. Algorithms. What it’s all about. Problem Solving Algorithm Pseudo codes Flowcharts. At the end of this you should be able to :. Understand Problem definitions Solve these using Algorithms Solve these using Flowcharts

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Algorithms

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  1. PROGRAMMING PAPER 2 AS Algorithms

  2. What it’s all about • Problem Solving • Algorithm • Pseudo codes • Flowcharts

  3. At the end of this you should be able to : • Understand Problem definitions • Solve these using Algorithms • Solve these using Flowcharts • Be able to identify, define and understand various programming terms

  4. Key Terms • You should know what these terms are and when to use them • program • pseudocode • flowchart • algorithm

  5. Problem Solving Techniques Here 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

  6. Problem Solving Techniques What do they translate to : • Apply the software development method to solve problems • Difference between the Algorithm & the Flowchart • Knowing about the control structures

  7. What do you do first

  8. Problem Solving

  9. Problem Solving

  10. Slightly off track… • The software development method • The software development method consists of the following steps: • Requirements specification • Analysis • Design • Implementation • Testing and verification • Documentation

  11. 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.

  12. Characteristics of an Algorithm • Each step of an algorithm must be exact, preciously and unambiguously 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.

  13. 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.

  14. Characteristics of an Algorithm • An Algorithm should emphasize the WHAT’s and not the HOW’s. Consider the problem below: PROBLEM: You are required to design a complete system which will enable the sum of two values to be calculated.

  15. 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?”

  16. 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.

  17. Defining diagram 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

  18. LIST THE STEPS The next step is to identify the actual processing steps required to convert the input to become the output. Input Processing Output Value1 Value2 1) Read Value1, Value2 2) Calculate Sum 3) Display Sum Sum

  19. 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 1) Read Value1, Value2 2) Calculate Sum 3) Display Sum Sum The developed processing steps have to be more detailed in the algorithm.

  20. Algorithm Development The basic mathematical operators used in algorithms are as follows:- + addition - subtraction * multiplication / division = assignment ( ) brackets for grouping calculations

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. Decision Making The expression is a comparison between two values which evaluates to either true of false. IF (expression) THEN : : ENDIF Statements are placed here.

  27. Decision Making Example:- We are looking for a job which pays more than Rs. 4000. Example of an Expression IF (Salary>4000) THEN Say "I Will Take The Job!!" ENDIF

  28. 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

  29. 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 Rs.2000. 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

  30. 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 Rs.4000 and that the company must also provide a credit card. IF (Salary>4000) And (CreditCard=YES) THEN Take Job!! ENDIF

  31. 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.

  32. 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).

  33. Decision Making For example, this statement......... IF (Salary>4000) And (CreditCard=YES) THEN Say “Yes I Will Take The Job!!” ENDIF 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.

  34. 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.

  35. Cont’d For Example: if a is greater than b then print “A is greater” else print “B is greater” end if

  36. 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

  37. ITERATIVE STATEMENTS 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.

  38. ITERATION EXAMPLE An example of a process which is iterative:- Processing Pay of teachers by the school is very much an iterative process as the person processing the payroll applies the same calculations for each employee to produce the pay slip.

  39. TYPES OF LOOPS The looping constructs available in pseudocodes are as follows:- DOWHILE...ENDDO FOR…NEXT REPEAT...UNTIL

  40. DO WHILE LOOP 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.

  41. FOR LOOP 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.

  42. REPEAT…UNTIL 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.

  43. 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.

  44. Looping Constructs The Defining Diagram Input Processing Output Salary 1) Read Salary 2) Calculate Total 3) Display Total Total

  45. 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

  46. Cont’d Example: Dowhile (income is less than 50000) print “Enter taxable income;should be greater than or equal to 50000” read income Enddo

  47. 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.

  48. Program Flowcharts The following are the commonly used symbols for drawing program flowcharts. off-page connector terminator process storage decision making document input/output connector arrowheads

  49. Program Flowcharts Begin Read Value1, Value2 Calculate Sum = Value1 + Value2 Display Sum End

  50. Program Flowcharts Begin Read Amount NO YES Amount>20.00? Calculate Actual=Amount * 0.80 Calculate Actual=Amount End

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