A sparse matrix is one where there are many zero elements. For example, a matrix

Question

A sparse matrix is one where there are many zero elements. For example, a matrix A is as

follows:

A = 3 0 4 0 5

0 0 2 0 1

1 0 0 0 2

0 0 0 0 0

Matrix A has 4 rows and 5 columns. Of the 20 places in the matrix, 13 of them are zero. We

represent this matrix as a sorted list of <row, column, value> triples as shown below. The matrix

operations become operations on lists.

row column value

1 1 3

1 3 4

1 5 5

2 3 2

2 5 1

3 1 1

3 5 2

Processing Notes

(i) The list of values should be kept ordered by column within rows.

(ii) The test plan for an array-based implementation should have been based on the shape of

the matrices. A test plan for a list implementation should include cases dealing with the

length of the list (empty, only one item, etc.).

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(i) Source Code (Assignment1PartB.CPP)

(ii) A DataOutPartB.txt file that your program created

(iii) The screen of your test (Assignment1PartBTest.JPG)

Explanation / Answer

#include <iostream>

using namespace std;

int main()

{

int **a,**sp;

// a matirx

// sp sparse matrix

// n -- rows in matrix

// m -- column in matrix

//count -- counting non zero value in matrix

//s -- no of entry in spare matrix

int n,m,i,j,count=0,s=0;

cout <<"Enter the no of rows in matrix ";

cin>>n;

cout <<"Enter the no of column in matrix ";

cin>>m;

//memory allocated for elements of rows.

a = new int *[n];

//memory allocated for elements of each column

for(i = 0 ; i < n ; i++ )

a[i] = new int[m];

for(i = 0 ; i < n ; i++ )

for(j = 0 ; j < m ; j++ )

{

cout<<"Enter a["<< i <<"]["<<j<<"]value : " ;

cin>>a[i][j];

if(a[i][j]!=0)

count++;

}

cout<<" ENTERED MATRIX IS ";

for(i = 0 ; i < n ; i++ )

{

for(j = 0 ; j < m ; j++ )

cout<<a[i][j]<<" ";

cout<<" ";

}

if(count!=0)

{

cout<<" No of item in Sparse matrix : "<<count<<" ";

//memory allocated for sparse matrix.

sp = new int *[count];

//memory allocated for elements of each column

for(i = 0 ; i < count ; i++ )

sp[i] = new int[3];

//SPARSE MATRIX

for(i = 0 ; i < n ; i++ )

{

for(j = 0 ; j < m ; j++ )

{

if(a[i][j]!=0)

{

sp[s][0]=i;

sp[s][1]=j;

sp[s][2]=a[i][j];

s++;

}

}

}

//Display

cout<<" SPARSE MATRIX IS ";

cout<<" ROW COLUMN VALUE ";

for(i = 0 ; i < s ; i++ )

{

for(j = 0 ; j < 3 ; j++ )

cout<<sp[i][j]<<" ";

cout<<" ";

}

}

else

cout<<" Sparse Matrix is Empty ";

//free the allocated memory for matrix

for( int i = 0 ; i < n ; i++ )

delete [] a[i] ;

delete [] a;

system("pause");

return 0;

}

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