Algorithm Discovery and Design

1. Chapter 2: Algorithm Discovery and Design Invitation to Computer Science, C++ Version, Third Edition

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

3. Introduction • This chapter discusses algorithms and algorithmic problem solving using three problems: • Searching lists • Finding maxima and minima • Matching patterns Invitation to Computer Science, C++ Version, Third Edition

4. Methods for Representing Algorithms • Natural language • Language spoken and written in everyday life • Examples: English, Spanish, Arabic, etc. • Problems with using natural language for algorithms • Verbose • Imprecise • Relies on context and experiences to give precise meaning to a word or phrase Invitation to Computer Science, C++ Version, Third Edition

5. Figure 2.1 The Addition Algorithm of Figure 1.2 Expressed in Natural Language Invitation to Computer Science, C++ Version, Third Edition

6. Methods for Representing Algorithms • 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, C++ Version, Third 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, C++ Version, Third Edition

8. Methods for Representing Algorithms Pseudocode • English language constructs modeled to look like statements available in most programming languages • Steps presented in a structured manner (numbered, indented, etc.) • No fixed syntax for most operations is required Invitation to Computer Science, C++ Version, Third Edition

9. 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, C++ Version, Third Edition

10. Algorithmic Operations • Types of algorithmic operations • Sequential • Conditional • Iterative Invitation to Computer Science, C++ Version, Third Edition

11. Sequential Operations • Computation operations • Example • Set the value of “variable” to “arithmetic expression” • Variable • Named storage location that can hold a data value Invitation to Computer Science, C++ Version, Third Edition

12. Sequential Operations (continued) • Input operations • To receive data values from the outside world • Example • Get a value for r, the radius of the circle • Output operations • To send results to the outside world for display • Example • Print the value of Area Invitation to Computer Science, C++ Version, Third Edition

13. An Algorithm Using Only Sequential Operations Figure 2.3: Algorithm for Computing Average Miles per Gallon Invitation to Computer Science, C++ Version, Third Edition

14. Conditional and Iterative Operations • Sequential algorithm ( example previous slide) • Also called straight-line algorithm • Executes its instructions in a straight line from top to bottom and then stops • Control operations • Conditional operations • Iterative operations Invitation to Computer Science, C++ Version, Third Edition

15. Conditional Operations • Conditional operations • Ask questions and choose alternative actions based on the answers • Example ( syntax vs semantics – show flow chart) • if x is greater than 25 then print x else print x times 100 Invitation to Computer Science, C++ Version, Third Edition

16. Figure 2.4: Second Version of the Average Miles per Gallon Algorithm(What types of operations ?) Invitation to Computer Science, C++ Version, Third Edition

17. Iterative Operations • Iterative operations • Perform “looping” behavior; repeating actions until a continuation condition becomes false • Loop • The repetition of a block of instructions Invitation to Computer Science, C++ Version, Third Edition

18. Iterative Operations (continued) • Examples (syntax) • while j > 0 do set s to s + aj set j to j - 1 • repeat do print ak print ak set k to k + 1 set k to k+1 until k > n while k ≤ n Invitation to Computer Science, C++ Version, Third Edition

19. 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, C++ Version, Third Edition

20. Figure 2.5: Third Version of the Average Miles per Gallon Algorithm(What type of operations are used ?) Invitation to Computer Science, C++ Version, Third Edition

21. Iterative Operations (continued) • Pretest loop ( semantics - show flow chart ) • Continuation condition tested at the beginning of each pass through the loop • It is possible for the loop body to never be executed • While loop Invitation to Computer Science, C++ Version, Third Edition

22. Conditional and Iterative Operations (continued) • Posttest loop ( semantics - show flow chart ) • Continuation condition tested at the end of loop body • Loop body must be executed at least once • Do/While loop ( or Repeat/Until loop ) Invitation to Computer Science, C++ Version, Third Edition

23. Figure 2.6 Summary of Pseudocode Language Instructions Invitation to Computer Science, C++ Version, Third Edition

24. Algorithm Development (1) • Algorithms have three basic phases • Input • Processing • Output Invitation to Computer Science, C++ Version, Third Edition

25. Algorithm Development (2) • Input - refers to the stage in which data and/or other processing information is given to the algorithm. • If calculating Area from Length and Width- values for L and W are provided • If summing the numbers from 1 to N- value for N is provided • If searching a list of names for a specific name- the list and the name to search for are given Invitation to Computer Science, C++ Version, Third Edition

26. Algorithm Development (3) • Processing – refers to the stage in which the data and/or other information is manipulated to obtain the desired result. • This is sometimes divided into two parts • Process Initialization (not always needed – give examples) • Set values of process parameters and/or, • Manipulate original data in some way • Process Execution • Algorithmic operations followed until the desired result is obtained. Invitation to Computer Science, C++ Version, Third Edition

27. Algorithm Development (4) • Output - The desired result is made available to the user or other computing agent • If calculating Area from Length and Width- the value of Area is displayed • If summing numbers from 1 to N- the value of N is displayed • If searching a list of names for a specific name- display info associated with name, or- report that name not found Invitation to Computer Science, C++ Version, Third Edition

28. Algorithm Development (5) • Algorithms are developed in order to solve a problem or accomplish a task. • The task or problem is usually expressed in: • words, as in a word problem, or a • specification document • How do I convert the problem description into an algorithm that can be programmed? Invitation to Computer Science, C++ Version, Third Edition

29. Algorithm Development (6) • Problem description → Algorithm • Read description until you grasp the problem. • Determine what data and other input information is required • Determine the desired output or outcome • Formulate a ‘high level’ description or plan for processing the input to get the desired result • Write a first draft of the algorithm • Refine the algorithm until it is in ‘pseudocode’ Invitation to Computer Science, C++ Version, Third Edition

30. Example 1: Looking, Looking, Looking • Examples of algorithmic problem solving • 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, C++ Version, Third Edition

31. Example 1: 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, C++ Version, Third Edition

32. Example 1: Looking, Looking, Looking (continued) • Algorithm discovery • Finding a solution to a given problem • Naïve sequential search algorithm ( example next slide ) • For each entry, write a separate section of the algorithm that checks for a match • Problems • Only works for collections of exactly one size • Duplicates the same operations over and over Invitation to Computer Science, C++ Version, Third Edition

33. Sequential Search – Attempt 1 (100 items) • Get values for list of Names, Numbers • Get target name • If Name1 equals target Then • Print Message “Found ”, Name1, “Phone Number”, Numbers1 • Endif • If Name2 equals target Then • Print Message “Found ”, Name2, “Phone Number”, Numbers2 • Endif • If Name3 equals target Then • Print Message “Found ”, Name3, “Phone Number”, Numbers3 • Endif • …. • If Name100 equals target Then • Print Message “Found ”, Name100, “Phone Number”, Numbers100 • Endif Invitation to Computer Science, C++ Version, Third Edition

34. Example 1: 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 (like 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, C++ Version, Third Edition

35. Figure 2.9: The Sequential Search Algorithm(flowchart next slide) Invitation to Computer Science, C++ Version, Third Edition

36. Invitation to Computer Science, C++ Version, Third Edition

37. Example 2: Big, Bigger, Biggest • Task • Find the largest value from a list of values • Algorithm outline • Keep track of the largest value seen so far and its location • Compare each value to the largest seen so far, and keep the larger as the new largest Invitation to Computer Science, C++ Version, Third Edition

38. Example 2: Big, Bigger, Biggest (continued) • Find Largest algorithm • Uses iteration and indices like previous example • Updates location and largest so far when needed in the loop Invitation to Computer Science, C++ Version, Third Edition

39. Figure 2.10 Algorithm to Find the Largest Value in a List Invitation to Computer Science, C++ Version, Third Edition

40. Find Largest Algorithm – Pseudo Code Simulator Version Steps for FindLargest With Array ASet Value of Size to A.lengthSet Value of LargestSoFar to A[0]Set Value of Location to 0Set Value of Counter to 1 While Value of Counter < Size Do If Value of A[Counter] > LargestSoFar Then Set Value of LargestSoFar to A[Counter] Set Value of Location to Counter Endif Set Value of Counter to Counter + 1 Endwhile Output Value of LargestSoFarOutput Value of Location Stop Input Initialization Processing Output Invitation to Computer Science, C++ Version, Third Edition

41. Example 3: Meeting Your Match • Task • Find if and where a pattern string occurs within a longer piece of text • Algorithm outline • Try each possible location of pattern string in turn • At each location, compare pattern characters against string characters Invitation to Computer Science, C++ Version, Third Edition

42. Example 3: Meeting Your Match (continued) • Concept of Abstraction • Separating high-level view from low-level details • Key concept in computer science • Makes difficult problems intellectually manageable • Allows piece-by-piece development of algorithms Invitation to Computer Science, C++ Version, Third Edition

43. Example 3: Meeting Your Match (continued) • Top-down design • When solving a complex problem: • Create high-level operations in first draft of an algorithm • After drafting the outline of the algorithm, return to the high-level operations and elaborate each one • Repeat until all operations are primitives Invitation to Computer Science, C++ Version, Third Edition

44. Example 3: Meeting Your Match (continued) • Pattern-matching algorithm (graphical example on board) • Contains a loop within a loop • External loop iterates through possible locations of matches to pattern • Internal loop iterates through corresponding characters of pattern and string to evaluate match Invitation to Computer Science, C++ Version, Third Edition

45. Pattern Matching • Pattern Matching Demonstration Invitation to Computer Science, C++ Version, Third Edition

46. Figure 2.12 Final Draft of the Pattern-Matching Algorithm Invitation to Computer Science, C++ Version, Third Edition

47. Problem solving with algorithms • The selection of an algorithm to solve a problem is greatly influenced by the way the data for that problem are organized • Searching is more efficient if list is sorted first • Once an algorithm has been developed, it may itself be used in the construction of other, more complex algorithms • Sorting may use find largest or find smallest Invitation to Computer Science, C++ Version, Third Edition

48. Problem solving with algorithms Library • A collection of useful algorithms • An important tool in algorithm design and development Invitation to Computer Science, C++ Version, Third Edition

49. Summary • Algorithm design is a first step in developing an algorithm • Must also: • Ensure the algorithm is correct • Ensure the algorithm is sufficiently efficient • Pseudocode is used to design and represent algorithms Invitation to Computer Science, C++ Version, Third Edition

50. Summary • Pseudocode is readable, unambiguous, and analyzable • Algorithm design is a creative process; uses multiple drafts and top-down design to develop the best solution • Abstraction is a key tool for good design Invitation to Computer Science, C++ Version, Third Edition