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.

Sparse Matrix Representations

A sparse matrix can be represented in two way:

1. Triplet Representation
2. Linked Representation

Triplet Representation

In Triplet Representation of a sparse matrix, we consider only non-zero values along with their row and column index values. The 0th row of the matrix stores the total number of rows, total number of columns, and total non-zero values.

In the above example of the matrix, there are only five non-zero elements, those are 3, 8, 1, 3, 7, and matrix size is 4 X 4. We represent this matrix in triplet representation (row, column, value), as shown in the above image.

Program using C

//SPARSE MATRIX TRIPLET REPRESENTATION #include<stdio.h> int main() { int s[50][50],t[50][3],nonzero,nrow,ncol,i,j,k; printf("Enter the number of rows:- "); scanf("%d",&nrow); printf("Enter the number of column:- "); scanf("%d",&ncol); printf("Enter the sparse matrix:- "); for( i = 0 ; i < nrow; i++) { for ( j = 0; j < ncol; j++) { scanf("%d",&s[i][j]); if (s[i][j] != 0) { nonzero++; } } } t[0][0] = nrow; t[0][1] = ncol; t[0][2] = nonzero; k=1; for ( i = 0; i < nrow; i++) { for ( j = 0; j < ncol; j++) { if(s[i][j] != 0) { t[k][0] = i; t[k][1] = j; t[k][2] = s[i][j]; k++; } } } printf("The triplet representation is :- "); for ( i = 0; i < nrow; i++) { for ( j = 0; j < ncol; j++) { printf("%d\t",t[i][j]); } printf("\n"); } }