Sparse matrix addition

Matrix is defined with a 2-dimensional array that has row and column. An array which has 'm' rows and 'n' columns represent an mXn matrix.Sometimes it happens when a matrix has zero values is more than NON-ZERO values. The matrix which has a greater number of ZERO values in comparison to the non-zero values is known as a sparse matrix.

Algorithm

To add the matrices, we simply traverse through both matrices element by element and insert the smaller element (one with smaller row and col value) into the resultant matrix. If we come across an element with the same row and column value, we simply add their values and insert the added data into the resultant matrix.

Program using C

//SPARSE MATRIX ADDITION
#include<stdio.h>
#include<stdlib.h>
#define MAX 20
void printsparse(int b[MAX][3]);
void readsparse(int b[MAX][3]);
void addsparse(int b1[MAX][3],int b2[MAX][3], int b3[MAX][3]);

main()
{
   
   int b1[MAX][3],b2[MAX][3],b3[MAX][3];
   printf("Enter data for 1st sparse matrix:\n");
   readsparse(b1);
   printf("Enter the data for 2nd matrix:\n");
   readsparse(b2);
   addsparse(b1,b2,b3);
   printsparse(b3);
}

void readsparse(int b[MAX][3])
{
   
   int i,t,m,n;
   printf("\nEnter no of rows and columns:- ");
   scanf("%d%d",&m,&n);
    printf("Enter no. of non of non zero elements:- ");
   scanf("%d",&t);
   b[0][0]=m;
   b[0][1]=n;
   b[0][2]=t;
   printf("Enter row no., column no., value of non zero elements:- ");
   for(i=1;i<=t;i++)
    {
      scanf("%d%d%d",&b[i][0],&b[i][1],&b[i][2]);
    }
}

void addsparse(int b1[MAX][3], int  b2[MAX][3],int b3[MAX][3])
{
   
int t1,t2,i,j,k;
if(b1[0][0]!=b2[0][0]||b1[0][1]!=b2[0][1])
   {
       printf("\n Entered invalid matrix.");
       exit(0);
    }
   t1=b1[0][2];
   t2=b2[0][2];
   i=j=k=1;
   
b3[0][0]=b1[0][0];
b3[0][1]=b1[0][1];
while(i<=t1&&j<=t2)
    {
if(b1[i][0]<b2[j][0])      
{
    b3[k][0]=b1[i][0];
    b3[k][1]=b1[i][1];
    b3[k][2]=b1[i][2];
    k++;
    i++;

}
else if(b2[j][0]<b1[i][0])      
{
    b3[k][0]=b2[j][0];
    b3[k][1]=b2[j][1];
    b3[k][2]=b2[j][2];
    k++;j++;
}
       
else if(b1[i][1]<b2[j][1])      
          {
            b3[k][0]=b1[i][0];
            b3[k][1]=b1[i][1];
            b3[k][2]=b1[i][2];
            k++;
            i++;
          }
else if(b2[j][1]<b1[i][1])      
       {
           b3[k][0]=b2[j][0];
           b3[k][1]=b2[j][1];
           b3[k][2]=b2[j][2];
           k++;
           j++;
       }
   else
       {
           b3[k][0]=b1[i][0];      
           b3[k][1]=b1[i][1];
           b3[k][2]=b1[i][2]+b2[j][2];
           k++;
           i++;
           j++;
       }
    }
   while(i<=t1)     
    {
       b3[k][0]=b1[i][0];
       b3[k][1]=b1[i][1];
       b3[k][2]=b1[i][2];
       i++;
       k++;
    }
   while(j<=t2)        
    {
       b3[k][0]=b2[j][0];
       b3[k][1]=b1[j][1];
       b3[k][2]=b1[j][2];
       j++;
       k++;   
    }
    b3[0][2]=k-1;       
}

void printsparse (int b[MAX][3])
{
   int i,t;
   t=b[0][2];
   printf("\nROW\tCOLUMN\t VALUE");
   for(i=0;i<=t;i++)
    {
       printf("\n%d\t%d\t%d",b[i][0],b[i][1],b[i][2]);
    }
}