Lecture 21:
Arrays
Lecture Contents:





Declaring and referencing arrays
Array subscripts
Using for/while loops for sequential access
Demo programs
Exercises
2
Basic description

Data structure: composite of related data items
stored in memory under the same name.

Typical data structures available in most PL:
– Array: to be discussed today
– Structure: (struct in C like PLs)
– Class: structure with methods (OOP)
– File (I/O processing aside keyboard and screen)
3
Basic description
Array: a collection of data items of the same type.
Reminder:
Simple data type: Data type used to store a single value.
scalar variable stores a single value.
Therefore array may store many data items (scalar values)
of the same type.
4
Array: a collection of data
items of the same type
How to define (declare) an array:

Using a definition statement to specify:
– data type for all array elements
– name of the array, i.e. identifier
– size of the array, number of array elements
See next three slides
5
Array: a collection of data
items of the same type
How to define (declare) an array:
int a[6];
// array named a with size of 6
// a names a collection of 6 integer data items
// where 6 integer values may store
6
Array: a collection of data
items of the same type
How to define (declare) an array:
float b[10];
// array named b with size of 10
// b names a collection of 10 real data items
// where 10 real (float) values may store
7
Array: a collection of data
items of the same type
How to define (declare) an array:
char c[20];
// array named c with size of 20
// c names a collection of 20 char data items
// where 20 symbols (char values) may store
8
Array initialization: to set
value at time of definition
Reminder: scalar variable initialization
int pom = 56;
double quantity = 77.8;
// size matches the list of initializers
int prime1[10]={2,3,5,7,11,13,17,19,23,29};
9
Array initialization: to set
value at time of definition
Reminder: scalar variable initialization
int pom = 56; double quantity = 77.8;
// size matches the list of initializers
int prime1[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
// size omitted
int prime2[ ] = { 2, 3, 5, 7, 11, 13 };
10
Array initialization: to set
value at time of definition
Reminder: scalar variable initialization
int pom = 56;
double quantity = 77.8;
// size matches the list of initializers
int prime1[10] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 };
// size omitted
int prime2[ ] = { 2, 3, 5, 7, 11, 13 };
// size is greater than the list of initializers
int prime3[20] = { 2, 3, 5, 7 };
11
Referencing array elements
The access to an array element:

Using subscript, also named index
– Always integer valued

In What context:
– assignment statements,
– Input/Output (cin, cout) statements
– arguments in function calling statement
12
Referencing array elements
Subscripted /indexed/ variable:
a variable followed by a
subscript
in
brackets,
designating an array element.
13
Referencing array elements
Array subscript:
integer literal
or
integer variable or
integer valued expression
enclosed in brackets after array name,
specifying which element to access.
Examples on Array subscripts:
Given:
int x[10], I=5;
x[4]
integer literal
14
Referencing array elements
Array subscript: an integer literal, integer
variable or integer valued expression
enclosed in brackets after array name,
specifying which element to access.
Examples on Array subscripts:
Given:
int x[10], I=5;
x[I]
integer variable
15
Referencing array elements
Array subscript: an integer literal, integer variable or
integer valued expression enclosed in brackets
after array name, specifying which element to
access.
Examples on Array subscripts:
Given:
int x[10], I=5;
x[I+1]
x[2*I-3]
x[I++]
integer expression – 3 examples
16
Array size & Array indexes



Array size of 10
Valid index values are 0, 1, 2, … , 9
Attention: Highest value is 9, but not 10
int x[10];
x[0],
x[1], … , x[9]
17
Sequential access to array
Using for loops for sequential access
Given:
int x[10], i;
for(i=0; i<=9; i++) x[i] = i * 10;
for(i=9; i>=0; i--)
cout << ‘\n’ << x[i] ;
Statistical computation using arrays: computing mean and
standard deviations.
18
Sequential access to array
Using while loops for sequential access
Given: int x[10], i;
i=0; while (i<=9){ x[i] = i*20; i++; }
i=9;
while (i>=0)
{
cout << ‘\n’ << x[i]; i--;
}
Statistical computation using arrays: computing mean and
standard deviations.
19
More on arrays
Extract from Friedman/Koffman, chapter 9
20
Data Structures
Arrays and Structs
Chapter 9
9.1 The Array Data Type

Array elements have a common name
– The array as a whole is referenced through the
common name


Array elements are of the same type — the
base type
Individual elements of the array are
referenced by sub_scripting the group name
2
22
Arrays

Analogies
– Egg carton
– Apartments
– Cassette carrier

More terminology
– Ability to refer to a particular element
• Indexing or sub_scripting
– Ability to look inside an element
• Accessing value
3
23
Arrays

Language restrictions
– Subscripts are denoted as expressions
within brackets: [ ]
– Base type can be
• any fundamental type, or
• library-defined type, or
• programmer-defined type
4
24
Arrays
– The index type is always integer and the
index range must be
0 ... n-1
• where n is a programmer-defined constant
expression.
– Parameter passing style
• Always call by reference (no indication
necessary)
5
25
Array Declaration
BaseType Id [ SizeExp ] ;
Type of
values in
list
Name
of list
Bracketed
constant
expression
indicating
number of
elements in
list
6
26
Sample Declarations

Suppose
const
const
const
const
int
int
int
int
N = 20;
M = 40;
MaxStringSize = 80;
MaxListSize = 1000;
7
27
Sample Declarations

Then the following are all correct array
declarations.
int A[10];
char B[MaxStringSize];
float C[M*N];
int Values[MaxListSize];
Rational D[N-15];
8
28
Subscripting

Suppose
int A[10];

// array of 10 ints
To access an individual element we must
apply a subscript to array name A
– A subscript is a bracketed expression
• The expression in the brackets is known as the index
– First element of A has index 0
A[0]
9
29
Subscripting
– Second element of A has index 1, and so on
A[1]
– Last element has an index one less than the size
of the array
A[9]

Incorrect indexing is a common error
10
30
Array Elements

Suppose
int A[10];
// array of 10
uninitialized ints

To access an individual element we must
apply a subscript to array name A
A
----------A[0] A[1] A[2] A[3] A[4] A[5] A[6] A[7] A[8] A[9]
11
31
Array Element Manipulation

Given the following:
int i = 7, j = 2, k = 4;
A[0] = 1;
A[i] = 5;
A[j] = A[i] + 3;
A[j+1] = A[i] + A[0];
A[A[j]] = 12;
12
32
Array Element Manipulation
A
1
-8
6
3
--5
12
-A[0] A[1] A[2] A[3] A[4] A[5] A[6] A[7] A[8] A[9]
cin >> A[k]; // where the next input value is 3
13
33
Inputting Into An Array
int A[MaxListSize];
int n = 0;
int CurrentInput;
while (n < MaxListSize)
{
cin >> CurrentInput;
A[n] = CurrentInput;
++n;
}
14
34
Displaying An Array
// List A of n elements has
// already been set
for (int i = 0; i < n; ++i)
{
cout << A[i] << " ";
}
cout << endl;
15
35
Remember

Arrays are always passed by reference
– Artifact of C



Can use const if array elements are not to be
modified
You do not need to include the array size within
the brackets when defining an array parameter
Initialize array with 0 or some other known value
16
36
9.2 Sequential Access to
Array Elements

Random Access
– Access elements in random order

Sequential Access
– Process elements in sequential order starting
with the first
– ShowDiff.cpp a program that looks at values
and calculates a difference between the element
and the average
17
37
ShowDiff.cpp
#include <iostream>
#include <iomanip>
using namespace std;
int main()
{
const int MAX_ITEMS = 8;
float x[MAX_ITEMS], average, sum;
// Enter the data.
cout << "Enter " << MAX_ITEMS << " numbers: ";
for (int i = 0; i < MAX_ITEMS; i++) cin >> x[i];
// Compute the average value.
sum = 0.0;
for (int i = 0; i < MAX_ITEMS; i++) sum += x[i];
average = sum / MAX_ITEMS;
18
cout << "The average value is " << average << endl; 38
ShowDiff.cpp
// Display the difference between each item
// and the average.
cout << "Table of differences between x[i]
and the average." << endl;
cout << setw (4) << "i" << setw (8) << "x[i]"
<< setw (14) << "difference" << endl;
for (int i = 0; i < MAX_ITEMS; i++)
cout << setw (4) << i << setw (8) << x[i]
<< setw (14) << (x[i] - average) << endl;
return 0;
}
39
ShowDiff.cpp
Program Output
Enter 8 numbers: 16 12 6 8 2.5 12 14 -54.5
The average value is 2.0
Table of differences between x[i] and the average
I
x[I]
difference
0
16.0
14.0
1
12.0
10.0
2
6.0
4.0
3
8.0
6.0
etc etc
22
40
9.3 Array Arguments



Use <, ==, >, +, - to test and modify array
elements
At times it might benefit you to pass an
entire array to a function
Can pass array elements to functions
– actual function call
exchange (s[3], s[5]);

Examples follow
41
Exchange.cpp
// FILE: Exchange.cpp
// Exchanges two type float values
void exchange (float& a1, float& a2)
{
float temp;
temp = a1;
a1 = a2;
a2 = temp;
}
42
Arrays as Function Arguments

Remember arrays are pass by reference
– Passing the array address

Remember these points when passing arrays to
functions
– The formal array argument in a function is not itself an
array but rather is a name that represents an actual array
argument. Therefore in the function definition, you
need only inform the compiler with [] that the actual
argument will be an array
43
Arrays as Function Arguments

Remember these points when passing arrays
to functions
– Formal array arguments that are not to be
altered by a function should be specified using
the reserved word const. When this
specification is used, any attempt to alter the
contents will cause the compiler generate an
error message

SameArray.cpp example
44
Problem

To check two arrays for identity
45
SameArray.cpp
// FILE: SameArray.cpp
// COMPARES TWO FLOAT ARRAYS FOR EQUALITY BY
// COMPARING CORRESPONDING ELEMENTS
bool sameArray (float a[], float b[], const int size);
void main()
{
float ar1[20], float ar2[20];
// assgn values to ar1 and ar2
bool flag; flag = sameArray(ar1, ar2, 20);
if (flag) cout << “Two identical arrays”;
else cout << “Two non identical arrays”;
}
27
46
SameArray.cpp
// FILE: SameArray.cpp
// COMPARES TWO FLOAT ARRAYS FOR EQUALITY BY
// COMPARING CORRESPONDING ELEMENTS
//
//
//
//
//
Pre: a[i] and b[i] (0 <= i <= size-1) are
assigned values.
Post: Returns true if a[i] == b[i] for all I
in range 0 through size - 1; otherwise,
returns false.
27
47
SameArray.cpp
bool sameArray (float a[], float b[], const int size)
{
int i;
i = 0;
while ((i < size-1) && (a[i] == b[i]))
i++;
return (a[i] == b[i]);
}
48
Problem


To add two arrays (to add their
corresponding elements)
Result saved to third array, same size
49
AddArray.cpp
// to add two arrays
// Post: c[i] = a[i] + b[i] (0 <= i <= size-1)
void addArray (int size, const float a[],
const float b[], float c[]);
void main()
{
float x[40], y[40], z[40];
// assgn values to arrays x, y
addArray( 40, x, y, z);
// display array z
}
50
AddArray.cpp
// Array elements with subscripts ranging from
// 0 to size-1 are summed element by element.
// Pre: a[i] and b[i] are defined
// (0 <= i <= size-1
// Post: c[i] = a[i] + b[i] (0 <= i <= size-1)
void addArray (int size, const float a[],
const float b[], float c[])
{
// Add corresponding elements of a and b and store in c.
for (int i = 0; i < size; i++)
c[i] = a[i] + b[i];
} // end addArray
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9.4 Reading Part of an Array


Sometimes it is difficult to know how many
elements will be in an array
Scores example
– 150 students
– 200 students


Always allocate enough space at compile
time
Remember to start with index [0]
52
ReadScoresFile.cpp
POSTPONE TO LECTURE ON FILES
Skip 6 coming slides
// File: ReadScoresFile.cpp
// Reads an array of exam scores for a lecture
// section of up to max_size students.
#include <iostream>
#include <fstream>
using namespace std;
#define inFile "Scores.txt"
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ReadScoresFile.cpp
void readScoresFile (ifstream& ins,int scores[],
const int MAX_SIZE, int& sectionSize);
int main()
{
int scores[100];
int size;
ifstream ins;
ins.open(inFile);
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ReadScoresFile.cpp
if (ins.fail())
{
cout << "Error" << endl;
return 1;
}
readScoresFile(ins, scores, 5, size);
for (int i = 0; i < size; i++)
cout << scores[i] << " " ;
cout << endl;
return 0;
}
55
ReadScoresFile.cpp
//
//
//
//
File: ReadScoresFile.cpp
Reads an array of exam scores for a lecture
section of up to MAX_SIZE students from a
file.
//
//
//
//
//
Pre: None
Post: The data values are read from a file
and stored in array scores.
The number of values read is stored in
sectionSize.(0 <= sectionSize < MAX_SIZE).
57
ReadScoresFile.cpp
void readScoresFile (ifstream& ins, int scores[],
const int MAX_SIZE, int& sectionSize)
{
// Local data ...
int tempScore;
// Read each array element until done.
sectionSize = 0;
ins >> tempScore;
while (!ins.eof() && (sectionSize < MAX_SIZE))
{
scores[sectionSize] = tempScore;
57
ReadScoresFile.cpp
}
sectionSize++;
ins >> tempScore;
// end while
// End of file reached or array is filled.
if (!ins.eof())
{
cout << "Array is filled!" << endl;
cout << tempScore << " not stored" << endl;
}
}
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36
Strings and Arrays of
Characters

String object uses an array whose elements
are type char

First position of a string object is 0
– example string find function ret of position 0


Can use the find function to locate or search
an array
We will study some various search functions
59
12.4 Recursive Functions with
Array Arguments
// File: findSumTest.cpp
// Program and recursive function to sum an
// array's elements
#include <iostream>
using namespace std;
// Function prototype
int findSum(int[], int);
int binSearch(int[], int, int, int);
60
FindSumTest.cpp
int main()
{
const int SIZE = 10;
int x[SIZE];
int sum1;
int sum2;
// Fill array x
for (int i = 0; i < SIZE; i++)
x[i] = i + 1;
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FindSumTest.cpp
// Calulate sum two ways
sum1 = findSum(x, SIZE);
sum2 = (SIZE * (SIZE + 1)) / 2;
cout << "Recursive sum is " << sum1 << endl;
cout << "Calculated sum is " << sum2 << endl;
cout << binSearch(x, 10, 10, SIZE-1) << endl;
return 0;
}
62
FindSumTest.cpp
// Finds the sum of integers in an n-element
// array
int findSum(int x[], int n)
{
if (n == 1)
return x[0];
else
return x[n-1] + findSum(x, n-1);
}
63
9.9 Common Programming
Errors



Watch non int subscripts (ASCII value)
Enumerated types can be used
Out of range errors
– C++ no range error checking




Lack of subscript to gain access
Subscript reference to non-array variable
Type mixing when using with functions
Initialization of arrays
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64
Exercise 21.1-21.5
Build programs using arrays
Arrays as actual arguments and formal parameters:





function to add two same size arrays (values
associated to all array elements);
function to evaluate the first 20 elements of Fibonacci
series;
sum (product) of the elements of an initialized array;
average value of the sum of array elements entered as
input values;
count the number of digit characters in the input
stream.
65
Before lecture end
Lecture:
Arrays
More to read:
Friedman/Koffman, Chapter 09
66
Chapter 9:
Data Structures: Arrays and Structs
Problem Solving,
Abstraction, and Design using C++ 5e
by Frank L. Friedman and Elliot B. Koffman
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
9.1 The Array Data Type
• Array elements have a common name
– The array as a whole is referenced through the
common name
• Array elements are of the same type — the
base type
• Individual elements of the array are referenced
by sub-scripting the group name
– element’s relative position used, beginning with 0
• Array stored in consecutive memory locations
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
68
Additional Array Details
• Subscripts are denoted as expressions
within brackets: [ ]
• Base type can be any fundamental, librarydefined, or programmer -defined type
• The index type is integer and the index
range must be 0 ... n-1, for array of size n
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
69
Array Declaration
element-type array-name [array-size];
Type of all
the values
in the array
Name of the
entire
collection of
values
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Integer
expression
indicating
number of
elements in
the array
70
Example 1
element-type array-name [array-size] = {initialization-list};
float x[8] = {16.0, 12.0, 6.0, 8.0, 2.5, 12.0, 14.0, -54.5};
16.0
12.0
6.0
8.0
2.5
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
12.0
14.0
-54.5
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Example 1 (con’t)
cout << x[0];
x[3] = 25.0;
sum = x[0] + x[1];
sum += x[2];
x[3] += 1.0;
x[2] = x[0] + x[1];
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Example 2
const int NUM_EMP = 10;
bool onVacation[NUM_EMP];
int vacationDays[NUM_EMP];
enum day {sunday, monday, tuesday, wednesday,
thursday, friday, saturday};
day dayOff[NUM_EMP];
float plantHours[7];
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
73
Figure 9.3
Arrays onVacation, vacationDays, and
dayOff
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Array Initialization
• List of initial values enclosed in braces ({ })
following assignment operator (=)
• Values from initialization list are assigned in order
to array elements
• Length of initialization list cannot exceed size of
the array
• If too few values, value assigned is system
dependent
• Size of array can be automatically set to number
of initializing values using empty brackets ([ ])
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
75
Array Subscripts
• Enclosed in brackets ([ ])
• Indicates which element is referenced by
position
• Array subscript value is different than
array element value
• Subscript can be an expression of any
integral type
• To be valid, subscript must be a value
between 0 and one less than the array size
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
76
9.2 Sequential Access to Array
Elements
• Random Access
– Access elements is any order
• Sequential Access
– Process elements in sequential order starting
with the first
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77
Example of Sequential Access
int cube[10];
for (int i = 0; i < 10; i++)
cube[i] = i * i * i;
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78
Strings and Arrays of Characters
• string object uses an array of char
• Can reference individual character of a
string object in different ways
– name[ i ]
– name.at( i )
• Other member functions of string class
– message.length( i )
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
79
9.3 Array Arguments
• Use <, ==, >, +, -, etc. to test and modify
array elements individually
• Can pass array elements to functions
exchange (s[3], s[5]);
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
80
Listing 9.3
Function to exchange the contents of
two floating-point memory locations
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81
Passing an Array Argument
• Arrays are always passed by reference
• Pass entire array to a function by writing
just its name (no subscripts or brackets) in
the argument list of the function call
• In function definition and prototype, user
empty brackets ([ ]) to identify array
• Use keyword const to indicate that array
argument cannot be changed by function
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
82
Example 1
const int MAX_SIZE = 5;
float x[MAX_SIZE ];
float y[MAX_SIZE ];
...
if (sameArray(x, y, MAX_SIZE))
cout << “Arrays are identical.” << endl;
else
cout << “Arrays are different.” << endl;
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83
Listing 9.4
Function sameArray
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84
Example 2
const int MAX_SIZE = 5;
float x[MAX_SIZE ] = {1.8, 2.2, 3.4, 5.1, 6.7};
float y[MAX_SIZE ] = {2.0, 4.5, 1.3, 4.0, 5.5};
float z[MAX_SIZE];
...
addArray(MAX_SIZE, x, y, z);
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85
Listing 9.5
Function addArray
// File: addArray.cpp
// Stores the sum of a[i] and b[i] in c[i]
// Sums pairs of array elements with subscripts ranging from 0
//
to size – 1
// Pre: a[i] and b[i] are defined (0 <= i <= size-1)
// Post: c[i] = a[i] + b[i] (0 <= i <= size-1)
void addArray
(int size,
// IN: the size of the arrays
const float a[],
// IN: the first array
const float b[],
// IN: the second array
float c[])
// OUT: result array
{
// Add corresponding elements of a and b and store in c
for (int i = 0; i < size; i++)
c[i] = a[i] + c[i];
}
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
86
9.4 Reading Part of an Array
• Sometimes it is difficult to know how many
elements will be in an array
– 150 students in one section
– 200 students in another section
• Always allocate enough space for largest
possible amount needed
• Remember to start reading with index [0]
• Must keep track of how many elements used
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
87
Listing 9.7
Function readScoresFile
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88
Listing 9.7
Function readScoresFile (continued)
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89
9.10 Common Programming
Errors
• Arrays
–
–
–
–
Out-of-range subscript references
Unsubscripted array references
Subscripted references to nonarray variables
Mixing types in passing arrays to functions
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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Thank You
For
Your Attention!
91