Chapter 2: Algorithm Discovery and Design

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Chapter 2 Algorithm Discovery and Design

• Invitation to Computer Science,
• Java Version, Second Edition

2
Objectives

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

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Introduction

• This chapter discusses algorithms and algorithmic
  problem solving using three problems
• Searching lists
• Finding smallest and largest items in lists
• Matching patterns

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Representing Algorithms

• What is an algorithm?
• A series of steps to perform a task thats it.
• A recipe is an algorithm for how to cook chicken
  enchiladas
• Directions are an algorithm for how to get to
  someones house

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Representing Algorithms

• Natural language
• Language spoken and written in everyday life
• English, Spanish
• Problems with using natural language for
  algorithms
• Imprecise
• Relies on context and experience of the person
  you are talking to
• I saw the man looking through the telescope

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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

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Pseudocode

• English language constructs modeled to look like
  statements available in most programming
  languages
• Ex ADD X Y
• No fixed syntax for most operations is required
• Everyone knows what you are talking about

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Pseudocode (continued)

• Less ambiguous and more readable than natural
  language
• Emphasis is on the process, not the specific
  notation
• Can be easily translated into a programming
  language

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Operations

• Types of algorithmic operations
• Sequential input / output, assignment,
  printing, etc.
• Conditional doing one thing or another based on
  a certain condition
• Iterative looping doing something more than
  once

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Sequential Operations (continued)

• Computation operations
• Example
• Set the value of variable to arithmetic
  expression
• X 10 (set x equal to 10)
• Variable
• Named storage location that can hold a data value
• X in the above example

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Sequential Operations (continued)

• Input operations
• To receive data values from the outside world
• Get a value for r, the radius of the circle
• Output operations
• To send results to the outside world for display
• Print the value of Area

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1. Go to gas station
2. Take out loan

• Figure 2.3
• Algorithm for Computing Average Miles per Gallon

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Conditional and Iterative Operations

• Sequential algorithm
• Executes its instructions in a straight line from
  top to bottom and then stops
• Control operations allow us to get more complex
• Conditional operations
• IF X10 THEN do some stuff
• Iterative operations
• WHILE X lt 100 do some other stuff

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Conditional and Iterative Operations (continued)

• Conditional operations
• 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

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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

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Conditional and Iterative Operations (continued)

• Examples
• while j gt 0 do
• set s to s aj
• set j to j - 1
• repeat
• print ak
• set k to k 1
• until k gt n

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• Figure 2.4
• Second Version of the Average Miles per Gallon
  Algorithm

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Conditional and Iterative Operations (continued)

• Components of a loop
• Continuation condition when do we stop?
• Loop body what we want to repeat
• Infinite loop
• The continuation condition never becomes false
  and the loop runs forever
• This is usually an error

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• Figure 2.5
• Third Version of the Average Miles per Gallon
  Algorithm

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Conditional and Iterative Operations

• 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
• Ex While loop

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Conditional and Iterative Operations (continued)

• Post-test loop
• Continuation condition tested at the end of loop
  body
• Loop body must be executed at least once
• Ex Do - While loop

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• Figure 2.6
• Summary of Pseudocode Language Instructions

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One other operation - functions

• Someone (possibly not you) writes a function.
• This function performs some action, like
  averaging three numbers, and returns a result to
  you.
• You call the function, and it returns a result
• A function accepts parameters (the numbers to
  average in this case) and you include these
  parameters when you call the function.

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One other operation - functions

• Average (98, 77, 100) then gives me the average
  of the 3 numbers
• Assuming the function was written correctly ?
• Essential for creating re-usable code, not
  reinventing the wheel, etc.
• Many, many built in functions (methods) in Java.

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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

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Example 1 Looking, Looking, Looking (continued)

• Task
• Find a particular persons 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

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Example 1 Looking, Looking, Looking (continued)

• Correct sequential search algorithm
• Uses iteration (loops) to simplify the task
• Handles special cases (like a name not found in
  the collection)

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Uses the variable Found to exit the iteration as
soon as a match is found

• Figure 2.9
• The Sequential Search Algorithm

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Example 1 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

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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
  (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

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Example 2 Big, Bigger, Biggest (continued)

• Once an algorithm has been developed, it may
  itself be used in the construction of other, more
  complex algorithms
• Library
• A collection of useful algorithms created
  (usually) by someone else.
• Dont reinvent the wheel many solutions to
  common problems are available, particularly in
  Java
• An important tool in algorithm design and
  development

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• Figure 2.10
• Algorithm to Find the Largest Value in a List

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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

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Example 3 Meeting Your Match (continued)

• Abstraction
• Separating high-level view from low-level details
• Key concept in computer science LAYERS
• Makes difficult problems intellectually
  manageable
• Allows piece-by-piece development of algorithms

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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

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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

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• Figure 2.12
• Final Draft of the Pattern-Matching Algorithm

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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

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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