1. Muhammad Adnan Talib Lec#4 27 th Sep,2012 Computer Science Department COMSATS Institute of Information Technology Sahiwal Introduction to Computer Programming Problem Solving & Algorithms

2. Problem Solving Problem Solving is a key factor of human intelligence Consider the example

3. Problem Solving From our daily life experience we know that the best way to solve a problem is to divide it into small steps, then to carry out these steps one by one to achieve the desired goal. If look at a cheff following a recipe to make a meal we will observe that he is following certain steps.

4. Problem Solving How we give solution to a given problem? Algorithms

5. 5 Algorithm A concept that pervades all areas of computer science. Algorithm is a process that a computer could carry out to complete a well defined task within finite time and resources. The objective of computer science is to solve problems by developing, analyzing, and implementing algorithmic solutions.

6. 6 Al-Khwarizmi Principle All complex problems can be broken into simpler sub- problems. Solve a complex problem by breaking it down into smaller sub-problems and then solve them (in a specified order), one at a time. When all the steps are solved, the original problem itself has also been solved. This process is called Algorithm.

7. 7 Computer Programming Computer is a powerful tool It is not intelligent! In order to use computer to solve our problems, we must tell it what we want done and the order in which we want it done. These instructions are called computer program. This process is called computer programming. The person giving these instructions is called a computer programmer.

8. 8 Computer Programming Analyze the problem Develop a sequence of instructions for solving the problem. Communicate it to the computer.

9. 9 Phases of the software life cycle Requirement definition Analysis and design Coding Testing Implementation Maintenance

10. 10 Problem Solving Techniques Ask questions Look for things that are similar Means-ends analysis Divide and Conquer Merging solutions

11. 11 Ask Questions Ask questions until you have developed a clear understanding of the problem. Who, What, Why, Where, When. What do I have to work with? (my data or input) How much data is there? What should my output look like? How many times is the process going to be repeated? What are the exceptions to the main course? What special error condition might come up?

12. 12 Look for things that are Similar Do not reinvent the wheel! Draw Analogies

13. 13 Means-Ends analysis Starting point and ending state are known. You need to devise the transformation function. Ends are defined – you need to analyze your means of getting between them. Lahore to Islamabad What are the options? Narrow down the options? Figure out the details?

14. 14 Divide and Conquer Same as the Al-khwarizmi Principle. Breakup the large problem into smaller units and then solve them one at a time. Building block approach.

15. 15 Divide and Conquer Hard Problem Hard Sub-problemEasy Sub-problem

16. 16 Merging Solution Sometimes merging two independent solutions solves the problem more efficiently? Calculate Average Count values Sum Values Divide sum by count

17. 17 Problem Solving Techniques What is the unknown? What is required? What are the data? What is given? What is the condition? By what condition the unknown is linked to the data?

18. 18 Conversion from Fahrenheit to Celsius Output Temperature in Celsius (C) Inputs Temperature in Fahrenheit (F) Process

19. 19 Calculate and print the average grade of 3 tests for the entire class Input 3 test scores for each student output Average of 3 tests for each student Process 1. Get three scores 2. Add them together 3. Divide by three to get the average 4. Print the average 5. Repeat step 1 to 4 for next student 6. Stop if there are no more students

20. 20  A flowchart is a visual or graphical representation of an algorithm.  The flowchart employs a series of blocks and arrows, each of which represents a particular operation or step in the algorithm.  The arrows represent the sequence in which the operations are implemented. Flow Charts

21. 21 Flowcharts – Most Common Symbols SymbolName Function TerminalRepresents the beginning or end of a program. Flow-lineRepresents the flow of logic. ProcessRepresents calculations or data manipulation. Input/OutputRepresents inputs or outputs of data and information. DecisionRepresents a comparison, question, or decision that determines alternative paths to be followed.

22. 22 Flowcharts – An Example Find the solution of a quadratic equation Ax 2 +Bx+C=0, given A, B and C. START INPUT A, B, C Calculate R = SQRT(B 2 -4AC) A A X1 = (-B+R)/(2A) X2 = (-B-R)/(2A) PRINT A, B, C, X1, X2 END

23. 23 Flow Charting Expresses the flow of processing in a structured pictorial format. Processing Steps Input and Output Steps Decision Flow of data Connectors Terminator

24. 24 Flow chart for Converting Fahrenheit into Celsius Get temp. in ‘F’ Print ‘C’ Calculate Stop Begin

25. 25 Add them together Divide the result by three More students? Yes Stop No Flow chart for calculating average of three scores Get three scores Print the average

26. 26 START INPUT A, B Add A to B and store in C OUTPUT C END Comparison of Algorithm representations in Natural language, flowchart and Pseudo-code Step 1: Begin the calculations Step 2: Input two values A and B Step 3: Add the values Step 4: Display the result Step 5: End the calculation BEGIN Adder Input A and B C = A + B PRINT C END Adder Natural language FlowchartPseudo-code

27. 27 Algorithm Representation (Natural Languages) English or some other natural language. Are not particularly good: too verbose unstructured too rich in interpretation (ambiguous) imprecise

28. 28 Algorithm Representation (Using Programming Language) { int I, m, Carry; int a[100], b[100], c[100]; cin >> m; for ( int j = 0 ; k <= m-1 ; j++ ) { cin >> a[j]; cin >> b[j]; } Carry = 0; i = 0; while ( i < m ) { …

29. 29 Programming Languages Are not particularly good either Too many implementation details to worry about Too rigid syntax Easy to lose sight of the real task

30. 30 Pseudo-code We need a compromise between the two:  Pseudo-code Computer scientists use pseudo-code to express algorithms: English like constructs (or other natural language), but modeled to look like statements in typical programming languages.

31. 31 Pseudo-code Primitives Three basic kind of operations: Sequential Computation ( Set … ) Input/Output ( Get... / Print... ) Conditional If … Else If … Iterative / looping Repeat... While...

32. 32 Performs a computation and stores the result. Computation Example: Set the value of C to (A + B) Set the value of location to 0 Set the value of GPA to (sum / count) General format: General format: Set the value of to

33. 33 Variables A variable is a named storage. - A value can be stored into it, overwriting the previous value - Its value can be copied Examples : Set the value of A to 3 The variable A holds the value 3 after its execution Set the value of A to (A+1) Same as: add 1 to the value of A ( A is now 4)

34. 34 Not too Strict on Syntax Pseudo-code is kind of a programming language without a rigid syntax, for example we can write: Set the value of A to (B+C) as Set A to (B+C) or even: Set the value of sum to 0 Set the value of GPA to 0 as Set sum and GPA to 0

35. 35 Sequential Operations - Input/Output Outside world InputOutput The Computer needs to communicate with the outside world:  INPUT operations allow the computing agent to receive from the outside world data values to use in subsequent computations.  OUTPUT operations allow the computing agent to communicate results of computations to the outside world.

36. 36 Input General format: The computing agent (computer) suspends executions and waits for an input value. Get a value for

37. 37 Input - Examples Examples: Get value for grade Get values for N, M Can write: Get value for N 1... Get value for N 100 as Get value for N 1,..., N 100

38. 38 Output General format: The computing agent (computer) displays the value of the variable(s). Print the value of Print the message, " "

39. 39 Output - Examples Examples: Print the value of grade Print the message, "Hello" Can write: Print the value of N 1... Print the value of N 100 as Print the values of N 1,..., N 100

40. 40 Example Write an algorithm to calculate the average of three numbers. Steps Operations 1 Get values for N1, N2, and N3 2 Set the value of Average to (N1+N2+N3)/3 3 Print the value of Average 4 Stop

41. 41 Conditional Operations If then operations for the then-part Else operations for the else-part 1.Evaluate expression to see whether it is true or false. 2.If true, then execute operations in then-part 3.Otherwise, execute operations in else-part.

42. 42 Conditions, or Boolean Expressions A condition is one whose value is true or false, for example:  3 > 2is greater than (true)  3 = 2 is equal to (false)  A > 2is true if A’s value is greater than 2 (at the time this is executed), false otherwise.

43. 43 E1 or E2 true if at least one of them is true; false otherwise. E.g. 3 > 2 or 2 > 3 is true E.g. 3 > 2 or 2 > 3 is true E1 and E2 true if both are true; false otherwise true if both are true; false otherwise E.g. 3 > 2 and 2 > 3 is false E.g. 3 > 2 and 2 > 3 is false not E true if E is false, false if E is true Conditions may be compounded

44. 44 1. Get a value for A 2. If A = 0 then 3. Print the message, “The input is zero” Else 4. Print the message, “The input is not zero”Example 1. Get a value for grade 2. If grade 9 then 3. Print the message, “Invalid grade” Else 4. Set the value of total to (grade + total)

45. 45 Iterative Operation - While While remains true do steps i to j step i:operation step i+1:operation … step j:operation 1.Evaluate 1.Evaluate 2.If condition is true, execute steps i to j, then go back to i. 3. Otherwise, if condition is false,continue execution from step j+1.

46. 46 1 Get a value for count 2 While count < 10 do 3 Set square to (count * count) 4 Print the values of count and square 5 Add 1 to count 6 Stop Example

47. 47 What happens when it gets executed? If count starts with 7, we get printout 7 49 8 64 9 81 What if count starts with 11? Nothing is printed, loop is executed 0 times. While Loops

48. 48 Set value of A equal to 1 While A > 0 Print message, “Enter an integer” Get a value for A End of the loop Stop What does the following algorithm do? Exercise

49. 49 Tracing an algorithm The current values of algorithm variables at various points during execution can be known by tracing the algorithm with a table called Trace Table

50. 50 Trace Table Problem: Determine the value of the variable x and y after the following algorithm is executed Pseudocode: x = 5 Y = 7 If x = 5 then y= 8 else y= 0 if y = 7 then x = 6 else x = 3 if x = y then y = 0 Nesting???

51. 51 … Continued 834.3 834.2 854.1 853 752 -51 yXStep No. Trace table for algorithm

52. 52 Find the phone number of a given Name in an (unsorted) list of names and their phone numbers Names Phone numbers N 1 T 1 N 2 T 2 … N 1000 T 1000 Sequential Search: an Example

53. 53 Sequential Search: an Example 1 2 3 4 5 6 7 8 9 10 11 553614 442563 521463 541236 452361 442563 551123 441155 521364 528975 541258 Name to find: Smith, John

54. 54 1. Get value for Name 2. Get values for N1,…,N1000 3. Get values for T1,…,T1000 4. If Name = N1 then print the value of T1 5. If Name = N2 then print the value of T2 … 1002. If Name = N999 then print the value of T999 1003. If Name = N1000 then print the value of 1000 1005. Stop Sequential Search: 1st Attempt

55. 55 Get values for Name, N1,…, N1000, T1,…, T1000 Set the value i to 1 and the value of Found to 0 While Found = 0 AND i <= 1000 do If Name = Ni then Print the value of Ti Set the value of Found to 1 Else Add 1 to the value of I EndIF End of While loop Stop Sequential Search: Using a Loop

56. 56 The largest is 8 at location 3 Idea (sketch): Go through the entire list, at each iteration find the largest-so-far and record its location Given a list of variables A1, A2, …, An, find the largest value and its (first) location Selection: Find the Largest Number

57. 57 To begin with, set largest-so-far to (the value of) A1 set location to 1 set i to 2 i

58. 58 Compare A1 and A2 largest-so-far still holds the value of A1 set i to i +1 i

59. 59 Compare A1 and A3 largest-so-far now holds the value of A3 location is 3 set i to i +1 i

60. 60 Continue the similar process until i = 8 i

61. 61 Get a value for n, the size of the list Get values for A 1, A 2, …, A n, the list to be searched Set largest_so_far to A 1 and set location to 1 Set the value of i to 2 While i is less or equal to n do If A i > largest_so_far then Set the value of largest_so_far to A i Set the value of location to I EndIF Add 1 to the value of i End of While loop Print the values of largest_so_far and location Selection: Find The Largest Number