The Algorithmic Foundations of Computer Science

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Chapter 2 The Algorithmic Foundations of Computer
Science
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Objectives

• After studying this chapter, students will be
  able to
• Explain the benefits of pseudocode over natural
  language or a programming language
• Represent algorithms using pseudocode
• Identify algorithm statements as sequential,
  conditional, or iterative
• Define abstraction and top-down design, and
  explain their use in breaking down complex
  problems

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Objectives (continued)

• After studying this chapter, students will be
  able to
• Illustrate the operation of sample algorithms
• multiplication by repeated addition
• sequential search of a collection of values
• finding the maximum element in a collection
• finding a pattern string in a larger piece of text

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Introduction

• Algorithms for everyday may not be suitable for
  computers to perform (as in Chapter 1)
• Algorithmic problem solving focuses on algorithms
  suitable for computers
• Pseudocode is a tool for designing algorithms
• This chapter will use a set of problems to
  illustrate algorithmic problem solving

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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

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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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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
• Less ambiguous, 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

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Representing Algorithms

• Pseudocode is used to design algorithms
• Natural language is
• expressive, easy to use
• verbose, unstructured, and ambiguous
• Programming languages are
• structured, designed for computers
• Formal syntax, grammar
• grammatically fussy, cryptic
• Pseudocode lies somewhere between these two

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Types of algorithmic operations

• Sequential step by step
• Conditional if
• Iterative - loop

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Representing Algorithms (continued)

• Sequential operations perform a single task
• Input gets data values from outside the
  algorithm
• Computation a single numeric calculation
• Output sends data values to the outside world
• A variable is a named location to hold a value
• A sequential algorithm is made up only of
  sequential operations
• Example computing average miles per gallon

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Representing Algorithms (continued)

• Control operation changes the normal flow of
  control
• Conditional statement asks a question and
  selects among alternative options
• Evaluate the true/false condition
• If the condition is true, then do the first set
  of operations and skip the second set
• If the condition is false, skip the first set of
  operations and do the second set
• Example check for good or bad gas mileage

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Representing Algorithms (continued)

• Iteration an operation that causes looping,
  repeating a block of instructions
• While statement repeats while a condition remains
  true
• continuation condition a test to see if while
  loop should continue
• loop body instructions to perform repeatedly
• Example repeated mileage calculations

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Iterative Operations loops

• Components of a loop
• Continuation condition
• Loop body
• Infinite loop (avoid)
• The continuation condition never becomes false
• An error

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Representing Algorithms (continued)

• Do/while, repeat/until alternate iterative
  operation
• continuation condition appears at the end
• loop body always performed at least once
• post-test loop
• Primitive operations sequential, conditional,
  and iterative are all that is needed

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Examples of Algorithmic Problem SolvingExample
1 Go Forth and Multiply

• Given two 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).

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Examples of Algorithmic Problem SolvingExample
1 Go Forth and Multiply (continued)

• Get input values
• Get values for a and b
• Compute the answer
• Loop b times, adding each time
• Output the result
• Print the final value
• steps need elaboration

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Examples of Algorithmic Problem SolvingExample
1 Go Forth and Multiply (continued)

• Loop b times, adding each time
• Set the value of count to 0
• While (count lt b) do
• the rest of the loop
• Set the value of count to count 1
• End of loop
• steps need elaboration

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Examples of Algorithmic Problem SolvingExample
1 Go Forth and Multiply (continued)

• Loop b times, adding each time
• Set the value of count to 0
• Set the value of product to 0
• While (count lt b) do
• Set the value of product to (product a)
• Set the value of count to count 1
• End of loop
• Output the result
• Print the value of product

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Example 2 Looking, Looking, Looking

• Examples of algorithmic problem solving
  Searching
• 2. Sequential search find a particular value in
  an unordered collection
• 3. Find maximum find the largest value in a
  collection of data
• 4. Pattern matching determine if and where a
  particular pattern occurs in a piece of text

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Examples of Algorithmic Problem SolvingExample
2 Looking, Looking, Looking

• Assume that we have a list of 10,000 names that
  we define as N1, N2, N3, . . . , N10,000,
• along with the 10,000 telephone numbers of
  those individuals, denoted as
• T1, T2, T3, . . . , T10,000.
• To simplify the problem, we initially assume
  that all names in the book are unique and that
  the names need not be in alphabetical order.

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Examples of Algorithmic Problem SolvingExample
2 Looking, Looking, Looking (continued)

• Finding the correct solution to a problem is
  called algorithm discovery and is the most
  challenging and creative part of the
  problem-solving process.
• Three versions here illustrate algorithm
  discovery, working toward a correct, efficient
  solution
• A sequential algorithm (no loops or conditionals)
• An incomplete iterative algorithm
• A correct algorithm

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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

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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

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Examples of Algorithmic Problem SolvingExample
3 Big, Bigger, Biggest

• A building-block algorithm used in many
  libraries
• Library A collection of pre-defined useful
  algorithms
• 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.

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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

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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

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Examples of Algorithmic Problem SolvingExample
4 Meeting Your Match

• Pattern-matching common across many applications
• word processor search, web search, image
  analysis, human genome project
• 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 given pattern within the text.
  The output of the algorithm is the location in
  the text where each match occurred.

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Examples of Algorithmic Problem SolvingExample
4 Meeting Your Match (continued)

• Algorithm has two parts
• Sliding the pattern along the text, aligning it
  with each position in turn
• Given a particular alignment, determine if there
  is a match at that location
• Solve parts separately and use
• Abstraction, focus on high level, not details
• Top-down design, start with big picture,
  gradually elaborate parts

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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

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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

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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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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

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Summary

• Pseudocode is used for algorithm design
  structured like code, but allows English and math
  phrasing and notation
• Pseudocode is made up of sequential,
  conditional, and iterative operations
• Algorithmic problem solving involves
• Step-by-step development of algorithm pieces
• Use of abstraction, and top-down design

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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

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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 gt largest
• set (found true) and
• (largest element) and (location i)
• move pointer to next element
• End loop
• Print largest and location
• Stop

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Important Algorithms

• Pattern matching in text
• Location 123456789.
• Text A man and a woman
• Pattern an
• Output There is a match at position 4,
  etc.
• Patterns in genes
• Gene TCAGGCTAATCGGAAGT
• Probe TAATC
• Match Yes!

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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
• Abstraction- ability to separate the high level
  view of an object from the low level details
• Top-Down Design viewing an operation at a high
  level of abstraction and later adding the details
  in steps
• ( stepwise refinement)

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Research

• Write an algorithm that generates a Caesar cipher
  (See p. 86, 21) and Chapter 13
• Investigate the field of bioinformatics
• Basic Explanations
• htthttp//en.wikipedia.org/wiki/Bioinformatics
• http//biotech.icmb.utexas.edu/pages/bioinfo.html
• BLAST tool used to search protein databases
• http//www.ncbi.nlm.nih.gov/Education/BLASTinfo/in
  formation3.html