CS 192

Lecture 10

Winter 2003

December 22-23, 2003

Dr. Shafay Shamail

Arrays• An array is a collection of data elements of same type

in contiguous memory e.g. list of names, list of scores• Easier way to compare and use data than having

separate variables for data elements• data_type identifier[size]• int arr[3]

– declares a one-dimensional array named arr with space for 3 integer variables

• Variables contiguous in memory; lowest address has first value, next address has second variable value, and so on

Arrays

• An individual variable within an array is called an element of the array

• The elements of an array are not named, and are accessed by the array’s name and their position in the array (indexing or subcripting)

• Index of first element is zero, index of last element is size-1 e.g. int arr[3] has variables arr[0], arr[1] and arr[2]

• size has to be a positive constant (not variable) i.e. can’t do: int x = 3; int arr[x]; but can do: int arr[3 * 2];

• Number of bytes reserved with int arr[3]; ?

Arrays• An array is an indexed data structure • An array stores a collection of variables• All variables stored in an array are of the same data type• An individual variable within an array is called an

element of the array• An element of an array is accessed using the array name

and an index• The name of the array is the address of the first element.

The index is the offset

Declaring an array

data_type array_name[size];– allocates memory for size variables

– index of first element is 0

– index of last element is size-1

– size must be a constant

Declaring an Array• Example: int list[10];

– allocates memory for 10 integer variables– index of first element is 0– index of last element is 9– C++ does not perform any bounds checking on arrays

list[0]

list[1]

list[9]

Arrays Arrays offer convenient means of grouping

together several related variables

One- dimensional arrays

type var_name[size]

int sample[10];

double d[30];

char ch[100];

Initializing Arrays

• Arrays can be initialized at the time they are declared.

Examples:double taxrate[3] = {0.15, 0.25, 0.3};

char word[] = “hello”; //word has size 6

char list[5] = {‘h’,’e’,’l’,’l’,’o’};

//list of characters, not a string

double vector[100] = {0.0}; //assigns zero to all 100 elements

Initializing Arrays• float f[5]={0.0, 1.0, 2.0, 3.0, 4.0};

// initializes f[0] to 0.0, f[1] to 1.0…f[4] to 4.0• Or• float f[5]; f[0]=0.0; f[1]=1.0; …

• int a[10]={2}; //rest initialized to zero cout << a[0]<< endl << a[5] << endl;

• If no size given, allocates as much as the no. of initializers e.g. int a[] = {5, 2, -9}; // and

int a[3] = {5, 2, -9}; // are equivalent

• Can’t do: int hand[2]; hand[2]={5, 9};• Can’t do: short y[2]={1,2,3,4};

• Don’t confuse:short b[4] and b[4]

Initializing Arrays• for loops used to initialize arrays

#include <iostream.h>

int main() { int t, sample[10]; // this reserves 10 integer

elements // load the array for(t=0; t<10; ++t)

sample[t]=t; // display the array for(t=0; t<10; ++t)

cout << sample[t] << ' ';

return 0; }

Initializing Arraysint a[5];

• Now an indexed variable like a[1] can be used anywhere that a variable of type int can be used

int a[5];cin >> a[4] >> a[2];cout << a[2] << “ “ << a[4] << endl;

cin >> a[3] >> a[0];int max; max = a[3] + a[0]; cout << max << endl;

int next; cin >> next;a[1]= next; cout << a[1] << endl;a[3]= 42; cout << a[3] << endl;

int student = 2;a[student] = 99;cout << a[student] << “ “ << a[2] << endl;

• Also: a[get_index())] = 3; if get_index() returns an int

//Reads in 5 scores, displays max_score and shows //how much each score differs from max_score

int main() {

const int SIZE = 5; int i, score[SIZE], max_score;

cout << “Enter “ << SIZE << “ scores: \n”; cin >> score[0]; max_score = score[0];

for (i=1; i<SIZE; i++) { cin >> score[i]; if (score[i] > max_score)

max_score=score[i]; }

cout << “The highest score is: “ << max_score << endl << “Scores & their difference from highest: \n”;

for (i=0; i<SIZE; i++) { cout << score[i] << “ off by “ << (max_score – score[i]) << endl; } return 0; }

Initializing Arrays• Useful to give a constant name to the size of array

/*const type modifier*/

const int NUM_EMPLOYEES = 10; int salaries[NUM_EMPLOYEES];

for (int i=0; i < NUM_EMPLOYEES; i++)cin >> salaries[i];

• Advantage? Why not use a variable name?• Another way:

# define NUM_EMPLOYEES 10

• And yes, sizeof(salaries); gives what?

Arrays • Total size of an array in bytes?

• Total bytes =

number of bytes in type * number of elements

• e.g. int sample[10];• Has size in bytes = 10 * sizeof(int)

Initializing Arrays• What is wrong with the following?

int num=10;

int iarray[num];

int size;

cin >> size;

int myarray[size];

double darray[5]={3.2, 4.5, 6.7, 324.0, 45.8, 23.1, 34.9}

Assigning One Array to Another

int a[10], b[10];

// ...

a = b; // error -- illegal

/*So how do we make the contents of one array same as the other?*/

Assigning One Array to Another• int a[5], b[5]; // ... a = b; // error – illegal

• Cannot assign one array to another; each element must be copied individually

const int ARRAY_SIZE = 5; int a[] = {10, 11, 12, 13, 14};

int main() { int b[ARRAY_SIZE]; for (int i=0; i < ARRAY_SIZE; ++i) b[i] = a[i]; return 0; }

Assigning Values to an Array•Example

int list[10];int count;

cin >> count;

for(int i=0; i<count; i++)cin >> list[i];

What if count >9?

Summarize Arrays • In C++ all arrays are stored in contiguous memory

locations

• An individual element is accessed by use of an index.

• An index describes the position of an element within an array.

• In C++ all arrays have zero as the index of their first element.

Arrays: Min Max int main()

{

const int SIZE = 10;

int i, min_value, max_value;

int list[SIZE];

for(i=0; i<SIZE; i++)

{

list[i] = rand();

cout<<list[i]<<" ";

}

Arrays // find minimum value

min_value = list[0];

for(i=0; i<SIZE; i++)

{

if (min_value>list[i])

{

min_value = list[i];

}

}

cout << "minimum value: " << min_value << ‘\n’;

Arrays // find maximum value

max_value = list[0];

for(i=0; i<SIZE; i++)

{

if (max_value<list[i])

{

max_value = list[i];

}

}

cout << "maximum value: " << max_value << '\n';

return 0;

} // end of main function

Arrays - No Bounds Checking // An incorrect program. Do Not Execute!

int main()

{ int crash[10], i;

for(i=0; i<100; i++)

crash[i]=i;

return 1;

}

• What is wrong with the following?

char name[5]=”class";

int myarray[];

Arrays

int a[10] = {1,2,3,4,0,3,4,6,7,8};int x=3; y=1;

cout<< a[x+2*y] <<“\n”;

cout<<“Answer= “<<a[a[a[4]]]<<“\n”;

Output?

Sorting an Array• Lots of applications require sorting

• Algorithm for sorting

Sorting an Array

int main(void){

const int SIZE = 10;double darray[SIZE] = {34, 5.6, 0.9, 345.7, 54.1, 23.5, 2.5, 6.78, 12.4, 13.9};int i, j;

for (i=0; i<SIZE-1; i++){

for (j=i+1; j< SIZE; j++){

if (darray[i]>darray[j]){

double temp;temp = darray[i];darray[i] = darray[j];darray[j] = temp;

}}

} //inplace sorting ?return 0;

}

Sorting an Array// Using the bubble sort to order an array.

int main()

{

const int SIZE = 10; int nums[SIZE];

int a, b, t;

// give the array some random initial values

for(t=0; t<SIZE; t++)

nums[t] = rand();

Sorting an Array// This is the bubble sort.

for(a=1; a<SIZE; a++)

{

for(b=SIZE-1; b>=a; b--)

{

if (nums[b-1] > nums[b])

{ // if out of order exchange elements

t = nums[b-1];

nums[b-1] = nums[b];

nums[b] = t;

}

}

} // This is the end of the bubble sort.

} // end of main program

Searching Another Example -

• Sequential Search

• Binary Search

Two Dimensional Arrays

• C++ supports multi-dimensional array– data_type array_name[ROW_SIZE][COLUMN_SIZE]– int matrix[3][4];

row[0]

row[1]

row[2]

row1 row2 row3

in memory

Two-D ArraysRow Major, Col Major

• Row Major Storage row[0]

row[1]

row[2]

row3row2row1

in memory

• Col Major Storage

c[0] c[1] c[2] c[3]

c3c2c1

in memory

c3

Accessing Array Elements

• int matrix[3][4];– matrix has 12 integer elements– matrix[0][0] element in first row, first column– matrix[2][3] element in last row, last column

int main()

{

const int ROWS = 3;

const int COLS = 4;

int i, j, num[ROWS][COLS];

for(i=0; i<ROWS; ++i)

{

for(j=0; j<COLS; ++j)

{

num[i][j] = (i*COLS)+j+1;

cout << num[i][j] << “\t“;

}

cout << “\n”;

}

return 0;

} // output?

Two Dimensional Arrays

Output:1 2 3 45 6 7 89 10 11 12

int main()

{ const int ROWS = 3;

const int COLS = 4;

int i, j, num[ROWS][COLS];

for(i=0; i<ROWS; ++i)

{

for(j=0; j<COLS; ++j)

{

num[i][j] = (i*COLS)+j+1;

cout << num[i][j] << “ “;

}

cout << “\n”;

}

return 0;

} // output?

Two Dimensional ArraysWhat happens if I change [3][4] to [2][6]?

Output:1 2 3 4 5 67 8 9 10 11 12

Two dimensional arrays

int E[][2]={1,2,

3,4};

• Matrix Multiplication

• type name[size1][size2] . . . [sizeN];

• int multidim[4][10][3];

• when multidimensional arrays are used, large amounts of memory are consumed.

Multidimentional Arrays

int sqrs[10][2] = { 1, 1, 2, 4, 3, 9, 4, 16, 5, 25, 6, 36, 7, 49, 8, 64, 9, 81, 10, 100};

Multidimensional Array Initialization

int main(void){

const int ALPHABETS = 26;char code[ALPHABETS][2] = {

{'a', 'f'}, {'b', 'w'}, {'c', 'x'},{'d', 'v'}, {'e', 's'}, {'f', 'r'},{'g', 'q'}, {'h', 'c'}, {'i', 'g'},{'j', 'h'}, {'k', 'e'}, {'l', 'u'},{'m', 'b'}, {'n', 'j'}, {'o', 'd'},{'p', 'k'}, {'q', 't'}, {'r', 'l'},{'s', 'm'}, {'t', 'n'}, {'u', 'a'},{'v', 'o'}, {'w', 'p'}, {'x', 'z'},{'y', 'i'}, {'z', 'y'}

};

Multidimensional Arrays

int i; char alpha;

cout << "Enter an alphabet: "; cin >> alpha;

for(i=0; i< ALPHABETS; i++) {

if(code[i][0]==alpha) {

cout << "The code of " << alpha << " is ";

cout << code[i][1]<<endl; break;

} } return 0;

} // end of main program

Multidimensional Arrays

Reference

Dietel & Dietel

Case Study:Computing Mean, Median and Mode Using Arrays

• Mean– Average

• Median– Number in middle of sorted list– 1, 2, 3, 4, 5 (3 is median)

• Mode– Number that occurs most often– 1, 1, 1, 2, 3, 3, 4, 5 (1 is mode)

1 // Fig. 4.17: fig04_17.cpp2 // This program introduces the topic of survey data analysis.3 // It computes the mean, median, and mode of the data.4 #include <iostream>56 using std::cout;7 using std::endl;8 using std::ios;910 #include <iomanip>1112 using std::setw;13 using std::setiosflags;14 using std::setprecision;1516 void mean( const int [], int );17 void median( int [], int );18 void mode( int [], int [], int );19 void bubbleSort( int[], int );20 void printArray( const int[], int );2122 int main()23 {24 const int responseSize = 99;25 int frequency[ 10 ] = { 0 },26 response[ responseSize ] = 27 { 6, 7, 8, 9, 8, 7, 8, 9, 8, 9,28 7, 8, 9, 5, 9, 8, 7, 8, 7, 8,29 6, 7, 8, 9, 3, 9, 8, 7, 8, 7,30 7, 8, 9, 8, 9, 8, 9, 7, 8, 9,31 6, 7, 8, 7, 8, 7, 9, 8, 9, 2,32 7, 8, 9, 8, 9, 8, 9, 7, 5, 3,33 5, 6, 7, 2, 5, 3, 9, 4, 6, 4,

34 7, 8, 9, 6, 8, 7, 8, 9, 7, 8,35 7, 4, 4, 2, 5, 3, 8, 7, 5, 6,36 4, 5, 6, 1, 6, 5, 7, 8, 7 };3738 mean( response, responseSize );39 median( response, responseSize );40 mode( frequency, response, responseSize );4142 return 0;43 }4445 void mean( const int answer[], int arraySize )46 {47 int total = 0;4849 cout << "********\n Mean\n********\n";5051 for ( int j = 0; j < arraySize; j++ )52 total += answer[ j ];5354 cout << "The mean is the average value of the data\n"55 << "items. The mean is equal to the total of\n"56 << "all the data items divided by the number\n"57 << "of data items (" << arraySize 58 << "). The mean value for\nthis run is: " 59 << total << " / " << arraySize << " = "60 << setiosflags( ios::fixed | ios::showpoint )61 << setprecision( 4 )62 << static_cast< double >( total ) / arraySize << "\n\n";63 }6465 void median( int answer[], int size )66 {67 cout << "\n********\n Median\n********\n"

68 << "The unsorted array of responses is";

69

70 printArray( answer, size );

71 bubbleSort( answer, size );

72 cout << "\n\nThe sorted array is";

73 printArray( answer, size );

74 cout << "\n\nThe median is element " << size / 2

75 << " of\nthe sorted " << size

76 << " element array.\nFor this run the median is "

77 << answer[ size / 2 ] << "\n\n";

78 }

79

80 void mode( int freq[], int answer[], int size )

81 {

82 int rating, largest = 0, modeValue = 0;

83

84 cout << "\n********\n Mode\n********\n";

85

86 for ( rating = 1; rating <= 9; rating++ )

87 freq[ rating ] = 0;

88

89 for ( int j = 0; j < size; j++ )

90 ++freq[ answer[ j ] ];

91

92 cout << "Response"<< setw( 11 ) << "Frequency"

93 << setw( 19 ) << "Histogram\n\n" << setw( 55 )

94 << "1 1 2 2\n" << setw( 56 )

95 << "5 0 5 0 5\n\n";

Notice how the subscript in frequency[] is the value of an element in response[] (answer[]).

96

97 for ( rating = 1; rating <= 9; rating++ ) {

98 cout << setw( 8 ) << rating << setw( 11 )

99 << freq[ rating ] << " ";

100

101 if ( freq[ rating ] > largest ) {

102 largest = freq[ rating ];

103 modeValue = rating;

104 }

105

106 for ( int h = 1; h <= freq[ rating ]; h++ )

107 cout << '*';

108

109 cout << '\n';

110 }

111

112 cout << "The mode is the most frequent value.\n"

113 << "For this run the mode is " << modeValue

114 << " which occurred " << largest << " times." << endl;

115}

116

117void bubbleSort( int a[], int size )

118{

119 int hold;

120

Print stars depending on value of frequency[]

121 for ( int pass = 1; pass < size; pass++ )

122

123 for ( int j = 0; j < size - 1; j++ )

124

125 if ( a[ j ] > a[ j + 1 ] ) {

126 hold = a[ j ];

127 a[ j ] = a[ j + 1 ];

128 a[ j + 1 ] = hold;

129 }

130}

131

132void printArray( const int a[], int size )

133{

134 for ( int j = 0; j < size; j++ ) {

135

136 if ( j % 20 == 0 )

137 cout << endl;

138

139 cout << setw( 2 ) << a[ j ];

140 }

141}

Bubble sort: if elements out of order, swap them.

4. Program Output

******** Mean********The mean is the average value of the dataitems. The mean is equal to the total ofall the data items divided by the numberof data items (99). The mean value forthis run is: 681 / 99 = 6.8788  ******** Median********The unsorted array of responses is 6 7 8 9 8 7 8 9 8 9 7 8 9 5 9 8 7 8 7 8 6 7 8 9 3 9 8 7 8 7 7 8 9 8 9 8 9 7 8 9 6 7 8 7 8 7 9 8 9 2 7 8 9 8 9 8 9 7 5 3 5 6 7 2 5 3 9 4 6 4 7 8 9 6 8 7 8 9 7 8 7 4 4 2 5 3 8 7 5 6 4 5 6 1 6 5 7 8 7 The sorted array is 1 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 The median is element 49 ofthe sorted 99 element array.For this run the median is 7

Program Output

******** Mode********Response Frequency Histogram  1 1 2 2 5 0 5 0 5  1 1 * 2 3 *** 3 4 **** 4 5 ***** 5 8 ******** 6 9 ********* 7 23 *********************** 8 27 *************************** 9 19 *******************The mode is the most frequent value.For this run the mode is 8 which occurred 27 times.