Two - Dimensional Arrays

There could be situations where a table of values will have to be stored. 
 Consider a student table with marks in 3 subjects.
Student Mathematics Physics Chemistry
Student # 1 89 77 84
Student # 2 98 89 80
Student # 3 75 70 80
Student # 4 60 75 80
Student # 5 84 80 75

• The above table contains a total of 15 values.

• We can think this table as a matrix consisting of 5 rows & 3 columns.

• Each row represents marks of student # 1 in all (different) subjects.

• Each column represents the subject wise marks of all students.

• In mathematics we represent a particular value in a matrix by using two subscripts such as Vij. Here V denotes the entire matrix Vij refers to the value in “ i ”th row and “ j ”th column.

Example :

In the above table V23 refers to the value “80”.

C allows us to define such tables of items by using two-dimensional arrays.

Definition :

A list of items can be given one variable name using two subscripts and such a variable is called a two – subscripted variable or a two – dimensional array.

Two – Dimensional arrays can be declared as.

  Syntax :
<datatype> <variable-name>[row-size][column-size];

The above table can be defined in “C” as

The above table can be defined in “C” as

Representation of a two Dimensional array in memory :

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Initializing Two- Dimensional Arrays :

• Like the one-dimensional arrays, two-dimensional arrays may be initialized by following their declaration with a list of initial values enclosed in braces.

int table[2] [3] = {0,0,0,1,1,1};

• This initializes the elements of first row to zero and the second row to one.

• This initialization is done row by row.

• The above statement can be equivalently written as

int table[2][3] ={{0,0,0},{1,1,1}};

• we can also initialize a two-dimensional array in the form of a matrix as shown.

int table[2][3] = {
{0,0,0},
{1,1,1}
};

• Commas are required after each brace that closes of a row, except in case of last row.

• If the values are missing in an initialize, they are automatically set to zero.

Ex: int table [2] [3] = {
    {1,1},   1 1 0
    {2}   2 0 0
};

Program : Write a program to display the elements of a two dimensional array.
 # include<stdio.h> 
 # include<conio.h> 
 main( ) { 
         int  i,j; 
         int  a[3][3] = { { 1,2,3}, {4,5,6}, {7,8,9}}; 
         printf(“elements of an array \n \n”); 
         for( i=0; i<3; i++)  { 
              for ( j=0; j<3; j++){ 
                       printf (“%d\t”, a[ i ][ j ]); 
              }  printf(“\n”); 
           } 
getch(); 
 }
Output :

Elements of an Array
1   2   3
4   5   6
7   8   9

Program : To perform addition and subtraction of two matrices. 
# include<stdio.h>
  # include<conio.h>
  main( ) 
   { 
  int i,j,r1,c1, a[10][10], b[10][10]; 
  clrscr( ); 
  printf(“Enter Order of Matrix A & B up to 10 x 10:”);
  scanf(“%d  %d”, &r1, &c1); 
  printf(“Enter Elements of Matrix of A: \n”); 
  for( i=0; i<r1; i++) 
  { 
       for( j=0; j<c1; j++) 
       scanf(“ %d ”, &a[ i ][ j ]); 
  } 
  printf(“Enter Elements of Matrix of B: \ n”); 
  for( i=0; i<r1; i++) 
    { 
      for( j=0; j<c1; j++) 
     scanf(“ %d ”, &b[ i ][ j ]); 
    } 
  printf(“\n Matrix Addition \n”); 
  for( i=0; i<r1; i++) 
    { 
      for( j=0; j<c1; j++) 
       printf(“%d\t”, a[ i ][ j ] + b[ i ][ j ]); 
       printf (“ \n”);
    } 
  printf(“n Matrix Subtraction \n”); 
  for( i=0; i<r1; i++) 
    { 
      for( j=0; j<c1; j++) 
      printf(“%d\t”, a[ i ][ j ] – b[ i ][ j ]); 
      printf(“\n”); 
    } 
  getch( ); 
    }
Output :

Enter order of Matrix A & B up to 10 x 10: 3   3
Enter Elements of Matrix of A :
4   5   8   2   9   8   2   9   4
Enter Elements of Matrix of B :
1   3   5   0   5   4   6   7   2
Matrix Addition

5   8   13
2   14   12
8   16   6
Matrix Subtraction

3   2   3
2   4   4
-4   2   2