Lecture Notes

TWO-DIMENSIONAL ARRAY

A common use of two-dimensional array is to represent tables of values consisting of information arranged in rows and columns. The figure below shows the two-dimensional array named a. The array contains four rows and three columns, so it is said to be a 4-by-3 ( 4x3) array. The array has a total of 12 elements. In general, an array with m rows and n columns is called an m-by-n array. Two-dimensional array requires two subscripts to identify a particular element: the first (by convention) identifies the element's row, and the second (by convention) identifies the element's columns.

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

Every element in an array idenfied by an element name fo the form a[i][j]; a is the name of the array, and i and j are the subscripts that uniquely identify each element in a.

DECLARING A TWO-DIMENSIONAL ARRAY

Syntax Data type Array-name[ROW-SIZE][COLUMN-SIZE];

Data type - the data type of the array items (integer, float, double, char, long ....)
Array-name - the name of the array. Use the rule naming a variable to name an array.
ROW-SIZE - the number of rows.
COLUMN-SIZE - the number of columns.

Example

Declare a 3 x 2 array of integer named test that holds 6 integer numbers.
const int ROWS = 3;
const int COLS = 2;
int test[ROWS][COLS];
or
int test[3][2];

Note: Declare an array without specifying its array size will cause a syntax error.

Example: int test [ ][ ]; //Illegal array declaration

INITIALIZING A TWO-DIMENSIONAL ARRAY

A two-dimensionla array is initialized row by row.

Syntax Data type Array-name[ROW-SIZE][COLUMN-SIZE] = { {values of row1},{ values of row2}, ........};

or Data type Array-name[ ][ ] = { {values of row1},{ values of row2}, ........};

Example

1 0	20	30	40
35	25	15	5
100	10	68	75

//Declare and initialize a two-dimensional array named grades on the //left

int grades[3][4] = { {10,20,30,40}, {35,25,15,5},{100,10,68,75}};
or
int grades[ ][ ] = { {10,20,30,40}, {35,25,15,5},{100,10,68,75}};

INPUT/OUTPUT A TWO-DIMENSIONAL ARRAY

You use two nested for loop to input values for all elements in an array or to display the values of the array's elements. The input is done row by row.

Example	Output
const int ROWSIZE = 4; const int COLSIZE=3; void main( ) { int grades[ROWSIZE][COLSIZE]; cout<<"Enter input:\n"; for ( int i=0 ; i < ROWSIZE ; i++) for (int j = 0; j<COLSIZE;j++) cin >> grades[i][j]; cout<<"The values of the grades array's elements\n"; for ( i=0 ; i < ROWSIZE ; i++) { for ( j = 0; j<COLSIZE;j++) cout << grade[i][j]<< " "; cout<<endl; } }	Enter input: 10 20 30 40 35 25 15 5 100 10 68 75 The values of the grades array's elements 10 20 30 40 35 25 15 5 100 10 68 75

ACCESSING A TWO-DIMENSIONAL ARRAY ELEMENTS

You can use a nested loop to assign values to all elements in an array.

Example	Comments
const int ROWSIZE = 2; const int COLSIZE = 2; void main( ) { int test[ROWSIZE][COLSIZE]; for ( int i=0 ; i < ROWSIZE ; i++) for (int j = 0; j<COLSIZE;j++) { test[i] = 10; } }	In this example, you use a nestedfor loop to assign a value of 10 to each element of the array test. test[0][0]contains 10. test[0][1] contains 10. test[1][0] contains 10. test[1][1] contains 10.

To access an individual two-dimensional array element, you identify it with an element name of the form a[i][j]; a is the name of the array, i is the row number and j is the column number. Remember the index starts at 0.

Example

const int ROWSIZE = 3;
const int COLSIZE = 3;
void main( )
{int num[ROWSIZE][COLSIZE]={ {1,5,2}, { 12,10,30}, {4,8,25}};
int test[ROWSIZE][COLSIZE];
//Copy values from num array to test array
for ( int i=0; i < ROWSIZE ; i++)
for(int j=0; j<COLSIZE;j++)
test[i][j] == num[i][j];
// Add 5 to the element num[2][1]
num[2][1] = num[2][1] + 5 ; //num[2][1]= 8 + 5 = 13
// Compare num[2][0] and num[1][1]
if ( num[2][0] > num[1][1] )
cout << " num[2][0] is greater than num[1][1]"<<endl;
//Display test[2][2] and test[3][1]
cout<<test[2][2]<< ' '<<test[3][1]<<endl;}

C++ does not perform range checking. As a C++ programmer, you are responsible for the index values used to access array elements are within the legal range. If you overrun the bounds of an array, the value stores at that memory location is read or overwritten. This can cause the program to abort or produce an unexpected result.

Example

const int ROWSIZE = 3;
const int COLSIZE = 3;
int num[ROWSIZE][COLSIZE]={ {1,5,2}, { 12,10,30}, {4,8,25}};
num[3][2] = 12; //Overrun an array element. The array num has only three rows: row 0, row 1 and row 2, not row 3.

PASSING A TWO-DIMENSIONAL ARRAY TO A FUNCTION

Function declaration Return data type function-name( data type [ ][ ] );

In the function declaration, you do not specify the size of the array; rather than, you use an empty square bracket to indicate an array without the size specified.

Function definition Return data type function-name( data type array-name[ ]{COLSZIZE] ,ROWSIZE,COLSIZE)
{ Function body;
}

In the function definition, you do need to specify the array name[ ][COLSIZE], number of rows, and number of columns.

Function calling function-name(array-name)

Passing array name in calling a function. When you pass an array to a function, you actually pass the memory address of the first byte of the array. Any changes made to the array in the function will be reflected to the original array from the calling function.
In the example below, the program will pass a two-dimensional array of integer to a function. The function will add a value of 5 to each item in the array. After returning from calling a function, the program displays the value of each item in the array passing to the function.

Example

#include<iostream.h>
#include<iomanip.h>
const int ROWSIZE = 3;
const int COLSIZE = 3;
void addFive(int [ ][ ],int, int);
void main( )
{int num[ROWSIZE][COLSIZE]={ {1,5,2}, { 4 ,6 ,8}, { 9, 3, 7}};
addFive(num, ROWSIZE,COLSIZE); // passing array name
for (int i =0; i < ROWSIZE ; i++ )
{ for(int j = 0; j < COLSIZE; j++)
cout << setw(4) << num[ i ][ j ];
cout<<endl;
}
}
void addFive( int x[ ][COLSIZE], int rows, int cols) //.
{ for (int i =0; i < rows ; i++ )
for(int j = 0; j < cols; j++)
x[ i ][j] = x[ i ][ j ] + 5;
}

Output

6 10 7
9 11 13
14 8 12

The next example, you pass an item of the array to a function.

Example

#include<iostream.h>
#include<iomanip.h>
const int ROWSIZE = 3;
const int COLSIZE = 3;
void addFive(int);
void main( )
{int num[ROWSIZE][COLSIZE]={ {1,5,2}, { 4 ,6 ,8}, { 9, 3, 7}};
addFive(num[2][1]); //pass a value of 3 to the function
addFive(num[1][0]); //pass a value of 4 to the function
cout<<"Display the items in the array num"<<endl;
for (int i =0; i < ROWSIZE ; i++ )
{ for(int j = 0; j < COLSIZE; j++)
cout << setw(2) << num[ i ][ j ];
cout<<endl;
}
}
void addFive( int value)
{
value = value + 5;
cout<< value <<endl;
}

Output

8
9
Display the items in the array num
1 5 2
4 6 8
9 3 7

COPYING TWO-DIMENSIONAL ARRAY
To copy values from one array to another array, you must use two nested for loop.

Example

int num[ROWSIZE][COLSIZE]={ {1,5,2}, { 12,10,30}, {4,8,25}};
int test[ROWSIZE][COLSIZE];
//Copy values from num array to test array
for ( int i=0; i < ROWSIZE ; i++)
for(int j=0; j<COLSIZE;j++)
test[i][j] == num[i][j];