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Chapter 2

Chapter 2. Algorithm Discovery and Design. Objectives. In this chapter, you will learn about: Representing algorithms Examples of algorithmic problem solving. Introduction. This chapter discusses algorithms and algorithmic problem solving using three problems: Searching lists

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Chapter 2

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  1. Chapter 2 Algorithm Discovery and Design

  2. Objectives In this chapter, you will learn about: • Representing algorithms • Examples of algorithmic problem solving

  3. Introduction • This chapter discusses algorithms and algorithmic problem solving using three problems: • Searching lists • Finding maxima and minima • Matching patterns

  4. Representing Algorithms Natural Language - too verbose, ambiguous and lacks structure. Formal programming languages – forces low level details, punctuation, grammar syntax. Pseudocode - English like statements, very readable, no grammatical rules, etc., is easily translated into a programming language.

  5. 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

  6. 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

  7. The Beginning of the Addition Algorithm Expressed in a High-Level Programming Language

  8. 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

  9. Representing Algorithms • 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

  10. Types of algorithmic operations • Sequential • Conditional • Iterative

  11. Sequential Operations • Sequential algorithm • Also called straight-line algorithm • Executes its instructions in a straight line from top to bottom and then stops • Computation Set the value of “variable” to “arithmetic expression” where a Variable is a named storage location that can hold a data value For Example: Set the value of c to a+b or Add a and b to get c

  12. Sequential Operations • Input operations • To receive data values from the outside world • Examples: Get values for “variable1”, ‘variable2”,... Get a value for r, the radius of the circle • Output operations • To send results to the outside world for display • Examples: Print values for “variable1”, “variable2”,... Print the value of Area

  13. Algorithm for Computing Average Miles per Gallon

  14. Conditional and Iterative Operations • Control operations • Conditional operations • “Question asking” operations • Often use “if” • Iterative operations • Looping operations • Often use while or repeat

  15. Conditional Operations • Conditional operations • Ask questions and choose alternative actions based on the answers • Also called branch or decision operations • Example • if x is greater than 25 then print x else print x times 100

  16. Iterative Operations • Iterative operations • Perform “looping” behavior; repeating actions until a continuation condition becomes false • Loop • The repetition of a block of instructions

  17. Iterative Operations [loops] Pseudocode ( Counting Loop – For Loop) Repeat step I to step J until the “True/False” condition becomes true Step I: operation …….. Step J :operation

  18. Iterative Operations [loops] Pseudocode ( While loop) Repeat while a “True/False” Condition is false operation ….. operation End of the loop

  19. Iterative Operations [loops] Pseudocode (Repeat Until Loop) Repeat until a “True/False” Condition becomes true operation ….. operation End of the loop

  20. Iterative Operations (loops) • Examples • For J = 1 to 10 print J • 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

  21. Second Version of the Average Miles per Gallon Algorithm

  22. Iterative Operations [ loops] • Components of a loop • Continuation condition • Loop body • Infinite loop • The continuation condition never becomes false • An error

  23. Iterative Operations [ loops] • Pretest loop • 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

  24. Iterative Operations [ loops] • Posttest loop • Continuation condition tested at the endof loop body • Loop body must be executed at least once • Do/While loop

  25. Third Version of the Average Miles per Gallon Algorithm

  26. Summary of Pseudocode Language Instructions

  27. Example 1: Go Forth and Multiply A Simple looping problem Multiply two numbers using repeated addition • Get values for a and b • Determine the value of a+a+a+… a+ (b times) • Use a loop that executes b times and adds the value of a to a total each time • Print the value of the product

  28. Example 2: 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

  29. 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

  30. Example 2: Looking, Looking, Looking (continued) • 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 • Problems • Only works for collections of exactly one size • Duplicates the same operations over and over

  31. 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 (like a name not found in the collection) • Uses the variable Found to exit the iteration as soon as a match is found

  32. The Sequential Search Algorithm

  33. 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 are organized

  34. Example 3: Big, Bigger, Biggest • Task • Find the largest value from a list of values • 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

  35. Example 3: Big, Bigger, Biggest (continued) • Once an algorithm has been developed, it may itself be used in the construction of other, more complex algorithms • Algorithms can be used as the building blocks of software • Library • A collection of useful algorithms • An important tool in algorithm design and development

  36. Example 3: 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

  37. Algorithm to Find the Largest Value in a List

  38. Example 4: 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

  39. Example 4: Meeting Your Match (continued) • 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

  40. Example 4: 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

  41. Example 3: Meeting Your Match (continued) • Pattern-matching algorithm • 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

  42. Final Draft of the Pattern-Matching Algorithm

  43. 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

  44. Pattern Matching • Some applications • Matching phrases in Literature or text • Find a pattern and replace it with another • Web search ( “Google”)- matching strings • Patterns in X-rays, CAT scans, etc. • Patterns in the human genome – whole new field of bioinformatics

  45. 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

  46. Important Algorithms • Sequential search • ( Get values) and Start at the beginning of list • Set found = false • Repeat until found or end of list • Look at each element • If element = target • set found = true and • print desired element else move pointer to next element • End loop • If found = false then print message “not on list” • Stop

  47. Important Algorithms • Find Largest • ( Get values) and Start at the beginning of list • Set found = false and Largest to first element • Repeat until end of list • Look at each element • If element > largest • set (found = true) and • (largest = element) and (location = i) • move pointer to next element • End loop • Print largest and location • Stop

  48. Important Algorithms Pattern matching in text • Location 123456789………………. • Text A manand a woman • Pattern an • Output There is a match at position 4, etc. Patterns in genes • Gene: TCAGGCTAATCGGAAGT • Probe: TAATC • Match: Yes!

  49. Definitions • Algorithm Discovery – finding a correct and efficient solution to a problem • Library – collection of useful algorithms • Iteration – repeated operations • Index – the position of an element in a list

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