Invitation to Computer Science 6 th 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 • Pseudocode • Natural language: used to express algorithms • 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

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) • 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

7. 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

8. Pseudocode (continued) • Natural languages • Not sufficiently precise to represent algorithms • High-level programming language • During the initial phases of design, we are forced to deal with detailed language issues 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. Figure 1.2 Algorithm for Adding Two m-digit Numbers Invitation to Computer Science, 6th Edition

11. 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

12. 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

13. 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

14. 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

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

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17. 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

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

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

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

21. Conditional and Iterative Operations (continued) • Loop • The repetition of a block of instructions • While statement • Continuation condition • Determines if statement is true or false • Infinite loop • Continuation condition never becomes false Invitation to Computer Science, 6th Edition

22. Conditional and Iterative Operations (continued) • Examples • while j > 0 do set s to s + aj set j to j – 1 • do print ak set k to k + 1 while k < n 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 • Posttest loop • Continuation condition is tested at the end of the loop body, not the beginning • Primitives • Instructions that computing agent understands and is capable of executing without further explanation 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

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

30. Examples of Algorithmic Problem Solving • Go Forth and Multiply: Multiply two numbers using repeated addition • Sequential search: Find a particular value in an unordered collection • Find maximum: Find the largest value in a collection of data • Pattern matching: Determine if and where a particular pattern occurs in a piece of text Invitation to Computer Science, 6th Edition

31. 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 3 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

32. 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

33. Get values for a and b • Set the values of count to 0 • Set the value of product to 0 • While (count < b) do • Set the value of product to (product + a) • Set the value of count to (count + 1) • End of loop • Print the value of product Invitation to Computer Science, 6th Edition

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

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37. Modified version of Multiply • Devise an algorithm that uses a loop to take in a positive integer n and a real number x as the input and computes and print xn . Assume that the computing agent knows how to multiply but do not know how to calculate exponential. Hint: x0 = 1; x1 = x; x2 = x*x; x3= x*x*x; etc. Make sure you stop the algorithm at some point. Invitation to Computer Science, 6th Edition

38. Example 2: Looking, Looking, Looking • Algorithm discovery • Finding a solution to a given problem • Sequential search • Standard algorithm for searching an unordered list of values • Binary Search (extended example) • In computer science, a binary search or half-interval search algorithm finds the position of a specified value (the input “key”) within a sorted array. Invitation to Computer Science, 6th Edition

39. Example 2: Looking, Looking, Looking (Continued) • Task • Find a particular person’s name from an unordered list of telephone subscribers • Algorithm outline • Start with the first entry and check its name, then repeat the process for all entries Invitation to Computer Science, 6th Edition

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

41. Example 2: Looking, Looking, Looking (continued)) • For each entry, write a separate section of the algorithm that checks for a match • 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

42. 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

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

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

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46. Example 2: Looking, Looking, Looking (continued) • The selection of an algorithm to solve a problem is greatly influenced by the way the data for that problem is organized Invitation to Computer Science, 6th Edition

47. 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

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

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