Invitation to Computer Science 6th Edition

1. Invitation to Computer Science 6thEdition Chapter 2 The Algorithmic Foundations of Computer Science

2. Objectives In this chapter, you will learn about: • Representing algorithms • Examples of algorithmic problem solving Invitation to Computer Science, 6th Edition

3. Introduction • Chapter 1 • Introduced algorithms and algorithmic problem solving • This chapter • Develops more fully the notions of algorithm and algorithmic problem solving Invitation to Computer Science, 6th Edition

4. Representing Algorithms • Natural language • Language spoken and written in everyday life • Used to express algorithms • Examples: English, Spanish, Arabic, and so on Invitation to Computer Science, 6th Edition

5. Figure 2.1 The Addition Algorithm of Figure 1.2 Expressed in Natural Language Invitation to Computer Science, 6th Edition

6. Representing Algorithms(continued) • Problems using natural language to represent algorithms • Natural language can be extremely verbose • Lack of structure makes it difficult to locate specific sections of the algorithm • Natural language is too “rich” in interpretation and meaning Invitation to Computer Science, 6th Edition

7. Representing Algorithms(continued) • High-level programming language • Examples: C++, Java • Problem with using a high-level programming language for algorithms • During the initial phases of design, we are forced to deal with detailed language issues Invitation to Computer Science, 6th Edition

8. Figure 2.2 The Beginning of the Addition Algorithm of Figure 1.2 Expressed in a High-Level Programming Language Invitation to Computer Science, 6th Edition

9. Pseudocode • Pseudocode • Usedto design and represent algorithms • A compromise between the two extremes of natural and formal languages Invitation to Computer Science, 6th Edition

10. Pseudocode(continued) • English language constructs modeled to look like statements available in most programming languages • Steps presented in a structured manner (numbered, indented, and so on) • No fixed syntax for most operations is required Invitation to Computer Science, 6th Edition

11. Pseudocode(continued) • Less ambiguous and more readable than natural language • Emphasis is on process, not notation • Well-understood forms allow logical reasoning about algorithm behavior • Can be easily translated into a programming language Invitation to Computer Science, 6th Edition

12. Sequential Operations • Basic sequential operations • Computation, input, and output • Instruction for performing a computation and saving the result • Set the value of “variable” to “arithmetic expression” • Variable • Storage location that can hold a data value Invitation to Computer Science, 6th Edition

13. Sequential Operations (continued) • Pseudocode • Not a precise set of notational rules to be memorized and rigidly followed • Inputoperations • Submit to the computing agent data values from the outside world that it may then use in later instructions • Outputoperations • Send results from the computing agent to the outside world Invitation to Computer Science, 6th Edition

14. Figure 2.3 Algorithm for Computing Average Miles per Gallon Invitation to Computer Science, 6th Edition

15. Conditional and Iterative Operations • Sequential algorithm • Sometimes called a straight-line algorithm • Executes its instructions in a straight line from top to bottom and then stops • Control operations • Conditional and iterative • Allow us to alter the normal sequential flow of control in an algorithm Invitation to Computer Science, 6th Edition

16. Conditional and Iterative Operations (continued) • Conditional statements • Ask questions and choose alternative actions based on the answers • Example • if x is greater than 25 then print x else print x times 100 Invitation to Computer Science, 6th Edition

17. Figure 2.4 The If/Then/Else Pseudocode Statement Invitation to Computer Science, 6th Edition

18. Figure 2.5 Second Version of the Average Miles per Gallon Algorithm Invitation to Computer Science, 6th Edition

19. Conditional and Iterative Operations (continued) • Iterative operations • Perform “looping” behavior, repeating actions until a continuation condition becomes false • Loop • The repetition of a block of instructions • While statement Invitation to Computer Science, 6th Edition

20. Conditional and Iterative Operations (continued) • Examples • while j > 0 do set s to s + aj set j to j – 1 • repeat print ak set k to k + 1 until k > n Invitation to Computer Science, 6th Edition

21. Conditional and Iterative Operations (continued) • Components of a loop • Continuation condition • Loop body • Infinite loop • The continuation condition never becomes false • An error Invitation to Computer Science, 6th Edition

22. Figure 2.5 Second Version of the Average Miles per Gallon Algorithm Invitation to Computer Science, 6th Edition

23. Figure 2.6 Execution of the While Loop Invitation to Computer Science, 6th Edition

24. Conditional and Iterative Operations (continued) • Loop example Step Operation 1 Set the value of count to 1 2 While (count ≤ 100) do step 3 to step 5 3 Set square to (count x count) 4 Print the values of count and square 5 Add 1 to count Invitation to Computer Science, 6th Edition

25. Conditional and Iterative Operations (continued) • Pretest loop • Continuation condition is tested at the beginning of each pass through the loop • It is possible for the loop body to never be executed • While loop • Posttest loop • Continuation condition is tested at the end of the loop body, not the beginning • Loop body must be executed at least once • Do/While loop Invitation to Computer Science, 6th Edition

26. Figure 2.7 Third Version of the Average Miles per Gallon Algorithm Invitation to Computer Science, 6th Edition

27. Figure 2.8 Execution of the Do/While Posttest Loop Invitation to Computer Science, 6th Edition

28. Figure 2.9 Summary of Pseudocode Language Instructions Invitation to Computer Science, 6th Edition

29. Examples of Algorithmic Problem Solving • Example 1: Go Forth and Multiply Given 2 nonnegative integer values, a ≥ 0, b ≥ 0, compute and output the product (a * b) using the technique of repeated addition. That is, determine the value of the sum a + a + a + . . . + a (b times) Invitation to Computer Science, 6th Edition

30. Examples of Algorithmic Problem Solving((continued)) • Algorithm outline • Create a loop that executes exactly b times, with each execution of the loop adding the value of a to a running total Invitation to Computer Science, 6th Edition

31. Figure 2.10 Algorithm for Multiplication of Nonnegative Values via Repeated Addition Invitation to Computer Science, 6th Edition

32. Example 2: Looking, Looking, Looking • Task • Find a particular person’s name from an unordered list of telephone subscribers • Algorithm discovery • Finding a solution to a given problem • Naïve sequential search algorithm • For each entry, write a separate section of the algorithm that checks for a match Invitation to Computer Science, 6th Edition

33. Figure 2.11 First Attempt at Designing a Sequential Search Algorithm Invitation to Computer Science, 6th Edition

34. Example 2: Looking, Looking, Looking (continued)) • Problems of Naïve sequential search algorithm • Only works for collections of exactly one size • Duplicates the same operations over and over Invitation to Computer Science, 6th Edition

35. Figure 2.12 Second Attempt at Designing a Sequential Search Algorithm Invitation to Computer Science, 6th Edition

36. Figure 2.13 The Sequential Search Algorithm Invitation to Computer Science, 6th Edition

37. Example 2: Looking, Looking, Looking(continued) • Correct sequential search algorithm • Uses iteration to simplify the task • Refers to a value in the list using an index (or pointer) • Handles special cases (such as a name not found in the collection) • Uses the variable Found to exit the iteration as soon as a match is found Invitation to Computer Science, 6th Edition

38. Example 3: Big, Bigger, Biggest • Library • Collection of useful algorithms • Problem Given a value n ≥ 1 and a list containing exactly n unique numbers called A1, A2, . . . , An, find and print out both the largest value in the list and the position in the list where that largest value occurred Invitation to Computer Science, 6th Edition

39. Example 3: Big, Bigger, Biggest(continued) • Algorithm outline • Keep track of the largest value seen so far (initialized to be the first in the list) • Compare each value to the largest seen so far, and keep the larger as the new largest Invitation to Computer Science, 6th Edition

40. Example 3: Big, Bigger, Biggest(continued) • Find Largest algorithm • Uses iteration and indices as in previous example • Updates location and largest so far when needed in the loop Invitation to Computer Science, 6th Edition

41. Figure 2.14 Algorithm to Find the Largest Value in a List Invitation to Computer Science, 6th Edition

42. Example 4: Meeting Your Match • Pattern matching • Process of searching for a special pattern of symbols within a larger collection of information • Is assisting microbiologists and geneticists studying and mapping the human genome Invitation to Computer Science, 6th Edition

43. Example 4: Meeting Your Match (continued) • Pattern-matching problem You will be given some text composed of n characters that will be referred to as T1 T2 . . . Tn. You will also be given a pattern of m characters, m ≤ n, that will be represented as P1 P2 . . . Pm. The algorithm must locate every occurrence of the pattern within the text. The output of the algorithm is the location in the text where each match occurred. For this problem, the location of a match is defined to be the index position in the text where the match begins Invitation to Computer Science, 6th Edition

44. Example 4: Meeting Your Match (continued) • STEP 1 • The matching process: T1 T2 T3 T4 T5 … P1 P2 P3 • STEP 2 • The slide forward: T1 T2 T3 T4 T5 … • 1-character slide -> P1 P2 P3 Invitation to Computer Science, 6th Edition

45. Figure 2.15 First Draft of the Pattern-Matching Algorithm Invitation to Computer Science, 6th Edition

46. Example 4: Meeting Your Match (continued) • Examples of higher-level constructs • Sort the entire list into ascending order • Attempt to match the entire pattern against the text • Find a root of the equation • Abstraction • Use of high-level instructions during the design process • Top-down design • Viewing an operation at a high level of abstraction Invitation to Computer Science, 6th Edition

47. Figure 2.16Final Draft of the Pattern-Matching Algorithm Invitation to Computer Science, 6th Edition

48. Summary • Algorithm design • A first step in developing an algorithm • Algorithm design must: • Ensure the algorithm is correct • Ensure the algorithm is sufficiently efficient • Pseudocode • Used to design and represent algorithms Invitation to Computer Science, 6th Edition

49. Summary (continued) • Pseudocode • Readable, unambiguous, and able to be analyzed • Algorithm design • Uses multiple drafts and top-down design to develop the best solution • Abstraction • A key tool for good design Invitation to Computer Science, 6th Edition