Section 5 - Arrays

Problem solving often requires information be viewed as a “list”

List may be one-dimensional or multidimensional

List is implemented by an array construct.

Array is a group of variables

- Same name and data type

- Variables are related in some way

- Most commonly used – multi-dimensional

- One-dimensional array

- Two-dimensional array

Arrays

Arrays allow you to store a number of similar type items but with asingle name.

• Array: variable that can store multiple values of the same type

• Values are stored in adjacent memory locations

• Declared using [] operator:

int tests[5];

This creates an array named tests with 5 elements (storage locations)

Array Terminology

In the definition int tests[5];

• int is the data type of the array elements

• tests is the name of the array

• 5, in [5], is the size declarator. It shows the number of elements in the array.

Array Declaration

element-type array-name [array-size];

Type of all the values in the array

Name of the entire collection of values

Integer expression indicating number of elements in the array

Declaring Array Variables

datatype arrayName[arraySize];

Example:

double myList[10];

C++ requires that the array size used to declare an array must be a constant expression.

For example, the following code is illegal:int size = 4;double myList[size]; // Wrong

But it would be OK, if size is a constant as follow:const int size = 4;double myList[size]; // Correct

Suppose

const int N = 20;

const int M = 40;

const int MaxStringSize = 80;

const int MaxListSize = 1000;

Then the following are all valid array definitions

int A[10]; // array of 10 ints

char B[MaxStringSize]; // array of 80 chars

double C[M*N]; // array of 800 floats

int Values[MaxListSize]; // array of 1000 ints

Array - Memory Layout

• The definition: int tests[5]; // size is 5 elements

allocates the following memory:

first element

second element

third element

fourth element

fifth element

Accessing Array Elements

• Each array element has a subscript, used to access the element.

• Subscripts start at 0

0 1 2 3 4Subscripts

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 integer type

• To be valid, subscript must be a value between 0 and one less than the array size

Accessing Array Elements

• Array elements can be used as regular variables: tests[0] = 79;cout << tests[0];cin >> tests[1];tests[4] = tests[0] + tests[1];

• Arrays must be accessed via individual elements:cout << tests; // not legal

Accessing Array Contents

• Can access element with constant subscript:cout << tests[3] << endl;

• Can use integer expression as subscript:for (i = 0; i < 5; i++)

cout << tests[i] << endl;

Suppose

int A[10]; // array of 10 int A[0], … A[9]

To access individual element must apply a subscript to list name A

A subscript is a bracketed expression also known as the index

First element of list has index 0

A[0]

Second element of list has index 1, and so on

A[1]

Last element has an index one less than the size of the list

A[9]

Incorrect indexing is a common error

A[10] // does not exist

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

• Size of array can be automatically set to number of initializing values using empty brackets ([ ])

Initialization

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 12.0 14.0 -54.5

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];

double myList[4] = {1.9, 2.9, 3.4, 3.5};

This shorthand notation is equivalent to the following statements:

double myList[4];

myList[0] = 1.9;

myList[1] = 2.9;

myList[2] = 3.4;

myList[3] = 3.5;

C++ allows you to omit the array size when declaring and creating an array using an initializer.

For example, the following declaration is valid

double myList[] = {1.9, 2.9, 3.4, 3.5};

C++ automatically figures out how many elements are in the array.

C++ allows you to initialize a part of the array.

For example, the following statement assigns values 1.9, 2.9 to the first two elements of the array.

The other two elements will be set to zero.

Note that if an array is declared, but not initialized, all its elements will contain “unkowns”, like all other local variables.

double myList[4] = {1.9, 2.9};

Access to Array Elements

• Random Access– Access elements is any order

• Sequential Access– Process elements in sequential order starting with the first

Example of Sequential Access

int cube[10];for (int i = 0; i < 10; i++)

cube[i] = i * i * i;

Displaying an Array

// List A of n elements has already been set

for (int i = 0; i < n; ++i) {cout << A[i] << " ";

}cout << endl;

Finding the smallest index of the largest element

double max = myList[0];int indexOfMax = 0;

for (int i = 1; i < ARRAY_SIZE; i++) { if (myList[i] > max) { max = myList[i]; indexOfMax = i; }}

#include <iostream>using namespace std;

int main(){ const int NUMBER_OF_ELEMENTS = 10; double numbers[NUMBER_OF_ELEMENTS]; double sum = 0;

for (int i = 0; i < NUMBER_OF_ELEMENTS; i++) { cout << "Enter a new number: "; cin >> numbers[i]; sum += numbers[i]; }

double average = sum / NUMBER_OF_ELEMENTS;

int count = 0; // The number of elements above average for (int i = 0; i < NUMBER_OF_ELEMENTS; i++) if (numbers[i] > average) count++;

cout << "Average is " << average << endl; cout << "Number of elements above the average " << count << endl;

return 0;}

Example

Multidimensional Arrays

• Allows for complex arrangement of data• Can have many dimensions• Syntax

element-type arrayName [size1] [size2]…[sizen];

Exampledouble table[NROWS] [NCOLS];

Declaring Two- Dimensional Arrays

• Most common multidimensional array• Represents a table

Examplechar ticTacToe[3][3];

• AccessticTacToe[1][2]

Row

Column

Function sumMatrix

float sumMatrix (float table[NROWS][NCOLS]){

float sum = 0.0;

// Add each array element value to sum. for (int r = 0; r < NROWS; r++) for (int c = 0; c < NCOLS; c++) sum += table[r][c];

return sum;}

Example - A classroom seating plan

Example

const int NUM_ROWS = 11;const int SEATS_IN_ROW = 9;

string seatPlan [NUM_ROWS][SEATS_IN_ROW];

. . .

seatPlan[0][8] = “Gerry”;

Initialization

• Each inner pair of braces contains initial values for one row of the array matrix

const int NUM_ROWS = 2;const int NUM_COLS = 3;

float matrix[NUM_ROWS][NUM_COLS] ={{5.0, 4.5, 3.0}, {-16.0, -5.9, 0.0}};

Two-dimensional Array Illustration

[0] [1] [2] [3] [4]

[0]

7

[1] [2] [3] [4]

matrix[2][1] = 7;

int matrix[5][5];

7

int array[][] = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12} };

1

2

3

4

5

6

8

9

10

11

12

[0] [1] [2] [3] [4] [0] [1] [2] [3]

[0] [1] [2] [3] [4]

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

int array[4][3] = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12} };

(a)

Equivalent

int array[4][3]; array[0][0] = 1; array[0][1] = 2; array[0][2] = 3; array[1][0] = 4; array[1][1] = 5; array[1][2] = 6; array[2][0] = 7; array[2][1] = 8; array[2][2] = 9; array[3][0] = 10; array[3][1] = 11; array[3][2] = 12;

(b)

Nested Loops for 2-D Arrays

• Row order– use row subscript as outer loop control variable

• Column order– use column subscript as outer loop control variable

Initializing Arrays with Random Values

The following loop initializes the array with random values between 0 and 99:

for (int row = 0; row < rowSize; row++) { for (int column = 0; column < columnSize; column++) { matrix[row][column] = rand() % 100; }}

Printing Arrays

To print a two-dimensional array, you have to print each element in the array using a loop like the following:

for (int row = 0; row < rowSize; row++) { for (int column = 0; column < columnSize; column++) { cout << matrix[row][column] << " "; } cout << endl;}

Summing Elements by Column

For each column, use a variable named total to store its sum. Add each element in the column to total using a loop like this:

for (int column = 0; column < columnSize; column++) { int total = 0;

for (int row = 0; row < rowSize; row++) total += matrix[row][column];

cout << "Sum for column " << column << " is " << total << endl;}

No Bounds Checking in C++

• C++ does not check if an array subscript is in the range of values for subscripts of the array

• Can access memory using subscripts that is before or after the memory for an array

• Can corrupt other memory locations, crash program, or lock up computer

• Need to be careful!