C Program to Check Matrix is a Sparse Matrix

Any matrix is called as Sparse Matrix if it contains more number of zeros. The mathematical formula behind this is: T >= (m * n )/2 where T is total number of zeros. In this article, we will show you, How to write a C Program to check Matrix is a Sparse Matrix or Not with example.

C Program to Check Matrix is a Sparse Matrix Example

This program allows the user to enter the number of rows and columns of a Matrix. Next, we are going to check whether the given matrix is a sparse matrix or not using For Loop.

/* C Program to check Matrix is a Sparse Matrix or Not */
 
#include<stdio.h>
 
int main()
{
 	int i, j, rows, columns, a[10][10], Total = 0;
  
 	printf("\n Please Enter Number of rows and columns  :  ");
 	scanf("%d %d", &i, &j);
 
 	printf("\n Please Enter the Matrix Elements \n");
 	for(rows = 0; rows < i; rows++)
  	{
   		for(columns = 0;columns < j;columns++)
    	{
      		scanf("%d", &a[rows][columns]);
    	}
  	}
     
 	for(rows = 0; rows < i; rows++)
  	{
   		for(columns = 0; columns < j; columns++)
    	{
    		if(a[rows][columns] == 0)
    		{
    			Total++;    		
			}
   	 	}
  	}
  	if(Total > (rows * columns)/2)
  	{
  		printf("\n The Matrix that you entered is a Sparse Matrix ");
	}
	else
	{
		printf("\n The Matrix that you entered is Not a Sparse Matrix ");
	}
  	
 	return 0;
}

OUTPUT

ANALYSIS
In this Program, We declared single Two dimensional arrays Multiplication of size of 10 * 10.

Below statements asks the User to enter the Matrix size (Number of rows and columns. For instance 2 Rows, 2 Columns = a[2][2] )

printf("\n Please Enter Number of rows and columns  :  ");
scanf("%d %d", &i, &j);

Next, we used for loop to iterate each and every cell present in a[2][2] matrix. Conditions inside for loop ((rows < i) and (columns < j)) will ensure the compiler, not to exceed the matrix limit. Otherwise the matrix will overflow

scanf statement inside the for loop will store the user entered values in every individual array element such as a[0][0], a[0][1], …..

for(rows = 0; rows < i; rows++).
{
  for(columns = 0; columns < j; columns++)
   {
     scanf("%d", &a[rows][columns]);
   }
}

Next, we are trying to check whether each and every element in a matrix is equal to transposed matrix or not

for(rows = 0; rows < i; rows++)
{
	for(columns = 0; columns < j; columns++)
    	{
    		if(a[rows][columns] == 0)
    		{
    			Total++;    		
		}
 	}
}

User inserted values are: a[3][3] = {{10, 20, 0}, { 0, 0, 0},{0, 0, 70}}

Row First Iteration: for(rows = 0; rows < 3; 0++)
The condition (0 < 3) is True.

Column First Iteration: for(columns = 0; 0 < 3; 0++)
The condition (columns < 3) is True.
if(a[rows][columns] == 0) => if(a[0][0] == 0)
This condition is False. So, it will exit from If statement

Column Second Iteration: for(columns = 1; 1 < 3; 1++)
The condition (columns < 3) is True.
if(a[0][1] == 0)
This condition is False.

Column Third Iteration: for(columns = 2; 2 < 3; 1++)
The condition (columns < 3) is True.
if(a[0][2] == 0)
This condition is True. So, Total will be incremented to 1.

Do the same for the remaining iterations.

Next, we are using If Statement to check whether Total Number of Zeros is greater than or equal to (rows * columns) /2

Let me try the program with other values

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