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

C++ Programming: From Problem Analysis to

Program Design, Fifth Edition

Chapter 10:

Applications of Arrays and the class

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

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

Searching

• Sequential search algorithm

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

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

Bubble Sort

•

list[0]...list[n - 1]

– List of n elements, indexed 0 to n - 1

Bubble Sort (cont'd.)

• Series of

n - 1

iterations

– Successive elements

list[index]

and

list[index + 1]

of

list

are compared

– If

list[index]

>

list[index + 1]

• Elements

list[index]

and

list[index + 1]

are swapped

• Smaller elements move toward the top

• Larger elements move toward the bottom

Bubble Sort (cont'd.)

Bubble Sort (cont'd.)

Bubble Sort (cont'd.)

Bubble Sort (cont'd.)

Bubble Sort (cont'd.)

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

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

Selection Sort (cont'd.)

Selection Sort (cont'd.)

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

Selection Sort (cont'd.)

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

Insertion Sort

• Sorts the list by moving each element to

its proper place

Insertion Sort (cont'd.)

• Consider the element

list[4]

– First element of unsorted list

–

list[4] < list[3]

• Move

list[4]

to proper location

• At

list[2]

C++ Programming: From Problem Analysis to Program Design, Fifth Edition 23

C++ Programming: From Problem Analysis to Program Design, Fifth Edition 24

Insertion Sort (cont'd.)

• During the sorting phase

– Array containing the list is divided into two

sublists: sorted and unsorted

Insertion Sort (cont'd.)

Insertion Sort (cont'd.)

• List of length

n

– About (

n

2

+

3

n –

4) / 4 key comparisons

– About

n

(

n –

1) / 4 item assignments

• n

= 1000

– 250,000 key comparisons

– 250,000 item assignments

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

Binary Search (cont'd.)

Binary Search (cont'd.)

Binary Search (cont'd.)

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

Performance of Binary Search

(cont'd.)

• List of length

n

– Maximum number comparisons 2log

₂

_n

+ 2

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

vector type (class) (cont'd.)

vector type (class) (cont'd.)

C++ Programming: From Problem Analysis to Program Design, Fifth Edition 37

vector type (class) (cont'd.)

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

Programming Example: Election

Results (cont'd.)

• Desired output:

C++ Programming: From Problem Analysis to Program Design, Fifth Edition 40

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

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

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

Programming Example: Problem

Analysis (cont'd.)

• Data type of a candidate’s 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

Programming Example: Problem

Analysis (cont'd.)

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

Programming Example: Function

getCandidatesName()

Programming Example: Function

sortCandidateName()

Programming Example: Function

initialize()

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

Programming Example: Process

Voting Data

(cont'd.)

• Update the appropriate entry in the array

votesByRegion

by adding the

numberOfVotesForTheCandidate

Programming Example: Function

binSearch()

Programming Example: Function

processVotes()

Programming Example: Function

addRegionsVote()

Programming Example: Function

printHeading()

Programming Example: Function

printResults()

• Initialize

sumVotes

,

largestVotes

, and

winLoc

to 0

• For each row in each array:

• Output the final lines of output

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

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

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

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