C Programming: From Problem Analysis to Program Design, Fifth Edition

1
C Programming From Problem Analysis to Program
Design, Fifth Edition

• Chapter 10
  Applications of Arrays and the class vector

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Objectives

• In this chapter, you will
• Explore how to sort an array using the bubble
  sort, selection sort, and insertion sort
  algorithms
• Learn how to implement the binary search
  algorithm
• Become familiar with the vector type

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List Processing

• List a collection of values of the same type
• Basic list operations
• Search the list for a given item
• Sort the list
• Insert an item in the list
• Delete an item from the list
• Print the list

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Searching

• Sequential search algorithm

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Searching (cont'd.)

• List with 1000 elements
• Search item is the second item
• Sequential search makes two key comparisons
• Search item is the 900th item
• Sequential search makes 900 key comparisons
• Search item is not in the list
• Sequential search makes 1000 key comparisons

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Searching (cont'd.)

• Sequential search
• Not very efficient for large lists
• On average, number of key comparisons equal to
  half the size of the list
• Does not assume that the list is sorted

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Bubble Sort

• list0...listn - 1
• List of n elements, indexed 0 to n - 1

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Bubble Sort (cont'd.)

• Series of n - 1 iterations
• Successive elements listindex and listindex
  1 of list are compared
• If listindex gt listindex 1
• Elements listindex and listindex 1 are
  swapped
• Smaller elements move toward the top
• Larger elements move toward the bottom

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Bubble Sort (cont'd.)
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Bubble Sort (cont'd.)
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Bubble Sort (cont'd.)
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Bubble Sort (cont'd.)
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Bubble Sort (cont'd.)
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Bubble Sort (cont'd.)

• List of length n
• Exactly n(n - 1) / 2 key comparisons
• On average n(n - 1) / 4 item assignments
• n 1000
• 500,000 key comparisons
• 250,000 item assignments

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Selection Sort

• Rearrange the list by selecting an element in the
  list and moving it to its proper position
• Finds the location of the smallest element in the
  unsorted portion of the list
• Moves it to the top of the unsorted portion of
  the list

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Selection Sort (cont'd.)
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Selection Sort (cont'd.)
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Selection Sort (cont'd.)

• In the unsorted portion of the list
• Find the location of the smallest element
• Move the smallest element to the beginning of the
  unsorted list

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Selection Sort (cont'd.)
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Selection Sort (cont'd.)

• List of length n
• Exactly n(n - 1) / 2 key comparisons
• 3(n - 1) item assignments
• n 1000
• 500,000 key comparisons
• 3000 item assignments

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Insertion Sort

• Sorts the list by moving each element to its
  proper place

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Insertion Sort (cont'd.)

• Consider the element list4
• First element of unsorted list
• list4 lt list3
• Move list4 to proper location
• At list2

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Insertion Sort (cont'd.)
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Insertion Sort (cont'd.)
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Insertion Sort (cont'd.)

• During the sorting phase
• Array containing the list is divided into two
  sublists sorted and unsorted

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Insertion Sort (cont'd.)
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Insertion Sort (cont'd.)

• List of length n
• About (n2 3n 4) / 4 key comparisons
• About n(n 1) / 4 item assignments
• n 1000
• 250,000 key comparisons
• 250,000 item assignments

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Binary Search

• Much faster than a sequential search
• List must be sorted
• Divide and conquer
• Compare search item with middle element
• Less than middle search only upper half of list
• More than middle search only lower half of list

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Binary Search (cont'd.)
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Binary Search (cont'd.)
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Binary Search (cont'd.)
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Performance of Binary Search

• L is a sorted list of size 1024
• Every iteration of the while loop cuts the size
  of the search list by half
• At most, 11 iterations to determine whether x is
  in L
• Binary search will make 22 comparisons at most
• L has1048576 elements
• Binary search makes 42 item comparisons at most

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Performance of Binary Search (cont'd.)

• List of length n
• Maximum number comparisons 2log2n 2

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vector type (class)

• Only a fixed number of elements can be stored in
  an array
• Inserting and removing elements causes shifting
• vector type implements a list
• vector container
• vector
• vector object
• object

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vector type (class) (cont'd.)
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vector type (class) (cont'd.)
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vector type (class) (cont'd.)
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vector type (class) (cont'd.)
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Programming Example Election Results

• Presidential election for the student council of
  your local university
• Write a program to analyze the data and report
  the winner
• Four major divisions labeled as Region 1, Region
  2, Region 3, and Region 4
• Each division has several department
• Each department manages its own voting process
  and directly reports the results to the election
  committee

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Programming Example Election Results (cont'd.)

• Voting is reported in the following form

• Desired output

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Programming Example Election Results (cont'd.)

• Assume that six candidates are running
• Program can be modified to accommodate any number
  of candidates
• Data is provided in two files
• candData.txt consists of the names of candidates
• voteData.txt each line consists of voting results
• One entry per line

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Programming Example Input and Output

• Input Two files, one containing the candidates
  names and the other containing the voting data
• Output election results in a tabular form and
  the winner

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Programming Example Problem Analysis

• Program must organize the voting data by region
• Program must calculate total number of votes
  received by each candidate as well as the total
  votes cast in the election
• Names of the candidates must appear in
  alphabetical order

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Programming Example Problem Analysis (cont'd.)

• Data type of a candidates name and number of
  votes are different
• Separate arrays
• Use a two-dimensional array to hold the next four
  columns of the output
• One-dimensional array to hold the total votes
  received by each candidate

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Programming Example Problem Analysis (cont'd.)
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Programming Example Algorithm Design

• Read the candidates names into the array
  candidatesName
• Sort the array candidatesName
• Initialize the arrays votesByRegion and
  totalVotes
• Process the voting data
• Calculate the total votes received by each
  candidate
• Output the results

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Programming Example Function getCandidatesName()
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Programming Example Function sortCandidateName()
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Programming Example Function initialize()
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Programming Example Process Voting Data

• Get a candidateName, regionNumber, and
  numberOfVotesForTheCandidate
• Find the row number in the array candidatesName
  that corresponds to this candidate
• This gives the corresponding row number in the
  array votesByRegion for this candidate
• Find the column in the array votesByRegion that
  corresponds to the regionNumber

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Programming Example Process Voting Data (cont'd.)

• Update the appropriate entry in the array
  votesByRegion by adding the numberOfVotesForTheCan
  didate

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Programming Example Function binSearch()
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Programming Example Function processVotes()
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Programming Example Function addRegionsVote()
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Programming Example Function printHeading()
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Programming Example Function printResults()

• Initialize sumVotes, largestVotes, and winLoc to
  0
• For each row in each array
• Output the final lines of output

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Programming Example Main Algorithm

• Declare the variables
• Open the input file candData.txt
• If the input file does not exist, exit the
  program
• Read the data from the file candData.txt into the
  array candidatesName
• Sort the array candidatesName
• Close the file candData.txt and clear the input
  stream

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Programming Example Main Algorithm (cont'd.)

• Open the input file voteData.txt
• If the input file does not exist, exit the
  program
• Initialize the arrays votesByRegion and
  totalVotes
• Process the voting data and store the results in
  the array votesByRegion

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Programming Example Main Algorithm (cont'd.)

• Calculate the number of total votes received by
  each candidate and store the results in the array
  totalVotes
• Print the heading
• Print the results

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Summary

• List
• Set of elements of the same type
• Sorting algorithms
• Bubble sort
• Selection sort
• Insertion sort
• Binary search
• Compare performance to sequential search
• vector type