Group A : Assignment No : 04 (SPPU Syllabus Assignment No: 11)
Problem Statement:
Problem Statement:
Write C++ program for sparse matrix realization and operations on it- Transpose, Fast Transpose and addition of two matrices.
Program Code:
//Author:Prof.Nitin Shivale
//Program:Sparse Matrix and it's Operations like 1.Addition, 2.Transpose(Simple/Fast).
//Group A:Assignment No:4
#include<iostream>
#include<string.h>
using namespace std;
//define structure to store non zero values of sparse matrix.
typedef struct spm
{
int row,col;
int nval;
};
class sparse
{
spm sp1[10],sp2[10],sp3[20],spltr[10],fstr[10];
int mat1[10][10],mat2[10][10]; //data members
int r1,r2,c1,c2,i,j,k;
public:
sparse() //default constructor
{
r1=r2=i=0;
j=k=0;
c1=c2=0;
}
void getmat();
void showmat(); //member function
void addspm();
void simpl_trnspose();
void fast_trnspose();
};
//To accept sparse matrix from user
//sparse matrix is the matrix where most of the elements are zero in it.
void sparse::getmat()
{
//To store first matrix
cout<<"\nHow many rows in mat1:";
cin>>r1;
cout<<"\nHow many cols in mat1:";
cin>>c1;
for(i=0;i<r1;i++)
{
for(j=0;j<c1;j++)
{
cout<<"\nEnter ["<<i<< "]["<<j<<"] value of mat1: ";
cin>>mat1[i][j];
}
}
//To store second matrix
cout<<"\nHow many rows in mat2:";
cin>>r2;
cout<<"\nHow many cols in mat2:";
cin>>c2;
for(i=0;i<r2;i++)
{
for(j=0;j<c2;j++)
{
cout<<"\nEnter ["<<i<< "]["<<j<<"] value of mat2: ";
cin>>mat2[i][j];
}
}
}
//To display values inside both the sparse matrix.
void sparse::showmat()
{
//To display value of first sparse matrix.
cout<<"\n Matrix 1 value are as follows\n";
for(i=0;i<r1;i++)
{
for(j=0;j<c1;j++)
{
cout<<"\t"<<mat1[i][j];
}
cout<<"\n";
}
//To display value of second spaese matrix
cout<<"\n Matrix 2 value are as follows\n";
for(i=0;i<r2;i++)
{
for(j=0;j<c2;j++)
{
cout<<"\t"<<mat2[i][j];
}
cout<<"\n";
}
}
//Addition of both the sparse matrix.
//Addition of non zero element only which is stored in structure object sp1 and sp2.
void sparse::addspm()
{
int n1,n2;
n1=n2=0;
//conversion of sparse matrix to non zero value code as follows.
//conversion of first sparse matrix mat1 into sp1
sp1[0].row=r1;
sp1[0].col=c1;
k=1;
cout<<"\n Sparse matrix1 non_zero value are as follows:\n";
for(i=0;i<r1;i++)
{
for(j=0;j<c1;j++)
{
if(mat1[i][j]!=0)
{
sp1[k].row=i;
sp1[k].col=j;
sp1[k].nval=mat1[i][j];
k=k+1;
}
}
}
sp1[0].nval=k-1;
//display non zero values of sparse matrix mat1 which is inside sp1.
cout<<"\nRow\tCol\tnval";
for(i=0;i<k;i++)
{
cout<<"\n"<<sp1[i].row<<"\t"<<sp1[i].col<<"\t"<<sp1[i].nval;
}
//conversion of second sparse matrix mat2 into sp2
cout<<"\n\nSparse matrix2 non_zero value are as follows:\n";
sp2[0].row=r2;
sp2[0].col=c2;
k=1;
for(i=0;i<r2;i++)
{
for(j=0;j<c2;j++)
{
if(mat2[i][j]!=0)
{
sp2[k].row=i;
sp2[k].col=j;
sp2[k].nval=mat2[i][j];
k=k+1;
}
}
}
sp2[0].nval=k-1;
//display non zero values of sparse matrix mat2 which is inside sp2.
cout<<"\nRow\tCol\tnval";
for(i=0;i<k;i++)
{
cout<<"\n"<<sp2[i].row<<"\t"<<sp2[i].col<<"\t"<<sp2[i].nval;
}
//Addition of non zero values sp1 and sp2 logic are as follows.
//1.Store number of non zero term of mat1 in n1 and number of non zero term of mat2 in n2.
n1=sp1[0].nval;
n2=sp2[0].nval;
i=j=k=1;
cout<<"\n No of term in sp1:"<<n1<<"\tNo of term in sp2:"<<n2;
//2.Store the largest row and colom term of both matrices in sp3 row and col.
if(sp1[0].row>sp2[0].row)
{
sp3[0].row=sp1[0].row;
}
else
{
sp3[0].row=sp2[0].row;
}
if(sp1[0].col>sp2[0].col)
{
sp3[0].col=sp1[0].col;
}
else
{
sp3[0].col=sp2[0].col;
}
//3. Start addition by checking following conditions.
while((i<=n1)&&(j<=n2))//check for both term
{
if(sp1[i].row==sp2[j].row)//check if rows are same in sp1 and sp2.
{
if(sp1[i].col==sp2[j].col)//check if cols are same in sp1 and sp2.
{
sp3[k].row=sp1[i].row;
sp3[k].col=sp1[i].col;
sp3[k].nval=sp1[i].nval+sp2[j].nval; //if yes add both non zero values and store in sp3 with row,col and values detail.
cout<<"\nvalu of add:"<<sp3[k].nval;
i++;
j++; //increment all indexes.
k++;
cout<<"\nval of i:"<<i<<"\tval of j:"<<j<<"\tval of k:"<<k;
}
else if(sp1[i].col<sp2[j].col)//check col of sp1 is less than col of sp2
{
sp3[k].row=sp1[i].row;
sp3[k].col=sp1[i].col;
sp3[k].nval=sp1[i].nval; //if yes store all values of sp1 in sp3
i++;
k++; //increment i and k.
cout<<"\nval of i:"<<i<<"\tval of K:"<<k;
}
else
{
sp3[k].row=sp2[j].row;
sp3[k].col=sp2[j].col; //if no store all values of sp2 in sp3
sp3[k].nval=sp2[j].nval;
j++;
k++; //increment j and k.
cout<<"\nval of j:"<<j<<"\tval of K:"<<k;
}
}
else if(sp1[i].row<sp2[j].row)//check row of sp1 is less than row of sp2
{
sp3[k].row=sp1[i].row;
sp3[k].col=sp1[i].col;
sp3[k].nval=sp1[i].nval; //if yes store all values of sp1 in sp3
i++;
k++;
cout<<"\nval of i:"<<i<<"\tval of K:"<<k;
}
else
{
sp3[k].row=sp2[j].row;
sp3[k].col=sp2[j].col; //if no store all values of sp2 in sp3
sp3[k].nval=sp2[j].nval;
j++;
k++;
cout<<"\nval of j:"<<j<<"\tval of K:"<<k;
}
}//end of while loop
while(i<=n1) //Store remaining terms of sp1 in sp3 if above while (i<=n1&&j<=n2) is not true
{
sp3[k].row=sp1[i].row;
sp3[k].col=sp1[i].col;
sp3[k].nval=sp1[i].nval;
i++;
k++;
cout<<"\nval of outer while i:"<<i<<"\tval of K:"<<k;
}
while(j<=n2)
{
sp3[k].row=sp2[j].row; //Store remaining terms of sp2 in sp3 if above while (i<=n1&&j<=n2) is not true.
sp3[k].col=sp2[j].col;
sp3[k].nval=sp2[j].nval;
j++;
k++;
cout<<"\nval of outer while j:"<<j<<"\tval of K:"<<k;
}
sp3[0].nval=k-1;
//Display the addition result which is inside sp3.
cout<<"\nRow\tCol\tnval";
for(i=0;i<k;i++)
{
cout<<"\n"<<sp3[i].row<<"\t"<<sp3[i].col<<"\t"<<sp3[i].nval;
}
}
//To Transpose the sparse matrix
//Method: simple Transpose O(n*n)
//To chnage the rows into column and their values.
void sparse::simpl_trnspose()
{
//chainging the rows of sp1 to columns in spltr structure.
spltr[0].row=sp3[0].col;
spltr[0].col=sp3[0].row;
spltr[0].nval=sp3[0].nval;
k=1;
for(i=0;i<=spltr[0].row;i++)//To check number of colms
{
for(j=0;j<=spltr[0].nval;j++)//To check value in total no of non zero values
{
if(sp3[j].col==i)// if found swap the rows into colom and colm into rows.
{
spltr[k].row=sp3[j].col;
spltr[k].col=sp3[j].row;
spltr[k].nval=sp3[j].nval;
k++;
}
}
}//Total time required to execute is O(n*n).
cout<<"\n\n Simple Transpose of addition matrix are as follows...";
cout<<"\nRow\tCol\tnval";
for(i=0;i<k-1;i++)
{
cout<<"\n"<<spltr[i].row<<"\t"<<spltr[i].col<<"\t"<<spltr[i].nval;
}
}
void sparse::fast_trnspose()
{
int term[5],pos[5];
//First 0th row interchange row and col value.
fstr[0].row=sp3[0].col;
fstr[0].col=sp3[0].row;
fstr[0].nval=sp3[0].nval;
//initialize the term as zero.
for(i=0;i<=sp3[0].col;i++)
{
term[i]=0;
}
//Now find out how mnay times the col occures in nonzero value.
for(i=1;i<=sp3[0].nval;i++)
{
//term[sp3[i].col]=term[sp3[i].col]+1;
term[sp3[i].col]++;
}
//find out the actual position of each term i:e coloms in row.
pos[0]=1;
for(i=1;i<=sp3[0].col;i++)
{
pos[i]=pos[(i-1)]+term[(i-1)];
}
//fid the position and interchange the value.
for(i=1;i<=sp3[0].nval;i++)
{
j=pos[sp3[i].col];
fstr[j].row=sp3[i].col;
fstr[j].col=sp3[i].row;
fstr[j].nval=sp3[i].nval;
pos[sp3[i].col]=j+1;
}//Totla time required to execute is O(n)+O(n)+O(n)+O(n) i:e O(n)
cout<<"\n\n Fast Transpose of addition matrix are as follows...";
cout<<"\nRow\tCol\tnval";
for(i=0;i<=fstr[0].nval;i++)
{
cout<<"\n"<<fstr[i].row<<"\t"<<fstr[i].col<<"\t"<<fstr[i].nval;
}
}
//Main function logic.
//Program execution starts from here.
int main()
{
int n;
sparse s1; //s1 object of class sparse
s1.getmat();
s1.showmat(); //calling of member functions.
s1.addspm();
s1.simpl_trnspose();
s1.fast_trnspose();
// getch();
cout<<"\nPress one to exit....";
cin>>n;
return 0;
}
/********************** OUTPUT ****************************************
[student@localhost Documents]$ g++ SPMAT.CPP
SPMAT.CPP:10:1: warning: ‘typedef’ was ignored in this declaration [enabled by default]
};
^
[student@localhost Documents]$ ./a.out
How many rows in mat1:3
How many cols in mat1:3
Enter [0][0] value of mat1: 0
Enter [0][1] value of mat1: 0
Enter [0][2] value of mat1: 3
Enter [1][0] value of mat1: 4
Enter [1][1] value of mat1: 0
Enter [1][2] value of mat1: 5
Enter [2][0] value of mat1: 0
Enter [2][1] value of mat1: 0
Enter [2][2] value of mat1: 0
How many rows in mat2:3
How many cols in mat2:3
Enter [0][0] value of mat2: 0
Enter [0][1] value of mat2: 2
Enter [0][2] value of mat2: 0
Enter [1][0] value of mat2: 2
Enter [1][1] value of mat2: 0
Enter [1][2] value of mat2: 4
Enter [2][0] value of mat2: 0
Enter [2][1] value of mat2: 0
Enter [2][2] value of mat2: 2
Matrix 1 value are as follows
0 0 3
4 0 5
0 0 0
Matrix 2 value are as follows
0 2 0
2 0 4
0 0 2
Sparse matrix1 non_zero value are as follows:
Row Col nval
3 3 3
0 2 3
1 0 4
1 2 5
Sparse matrix2 non_zero value are as follows:
Row Col nval
3 3 4
0 1 2
1 0 2
1 2 4
2 2 2
No of term in sp1:3 No of term in sp2:4
val of j:2 val of K:2
val of i:2 val of K:3
valu of add:6
val of i:3 val of j:3 val of k:4
valu of add:9
val of i:4 val of j:4 val of k:5
val of outer while j:5 val of K:6
Row Col nval
3 3 5
0 1 2
0 2 3
1 0 6
1 2 9
2 2 2
Simple Transpose of addition matrix are as follows...
Row Col nval
3 3 5
0 1 6
1 0 2
2 0 3
2 1 9
2 2 2
Fast Transpose of addition matrix are as follows...
Row Col nval
3 3 5
0 1 6
1 0 2
2 0 3
2 1 9
2 2 2
Press one to exit....
*******************************************************************************************/
//Program:Sparse Matrix and it's Operations like 1.Addition, 2.Transpose(Simple/Fast).
//Group A:Assignment No:4
#include<iostream>
#include<string.h>
using namespace std;
//define structure to store non zero values of sparse matrix.
typedef struct spm
{
int row,col;
int nval;
};
class sparse
{
spm sp1[10],sp2[10],sp3[20],spltr[10],fstr[10];
int mat1[10][10],mat2[10][10]; //data members
int r1,r2,c1,c2,i,j,k;
public:
sparse() //default constructor
{
r1=r2=i=0;
j=k=0;
c1=c2=0;
}
void getmat();
void showmat(); //member function
void addspm();
void simpl_trnspose();
void fast_trnspose();
};
//To accept sparse matrix from user
//sparse matrix is the matrix where most of the elements are zero in it.
void sparse::getmat()
{
//To store first matrix
cout<<"\nHow many rows in mat1:";
cin>>r1;
cout<<"\nHow many cols in mat1:";
cin>>c1;
for(i=0;i<r1;i++)
{
for(j=0;j<c1;j++)
{
cout<<"\nEnter ["<<i<< "]["<<j<<"] value of mat1: ";
cin>>mat1[i][j];
}
}
//To store second matrix
cout<<"\nHow many rows in mat2:";
cin>>r2;
cout<<"\nHow many cols in mat2:";
cin>>c2;
for(i=0;i<r2;i++)
{
for(j=0;j<c2;j++)
{
cout<<"\nEnter ["<<i<< "]["<<j<<"] value of mat2: ";
cin>>mat2[i][j];
}
}
}
//To display values inside both the sparse matrix.
void sparse::showmat()
{
//To display value of first sparse matrix.
cout<<"\n Matrix 1 value are as follows\n";
for(i=0;i<r1;i++)
{
for(j=0;j<c1;j++)
{
cout<<"\t"<<mat1[i][j];
}
cout<<"\n";
}
//To display value of second spaese matrix
cout<<"\n Matrix 2 value are as follows\n";
for(i=0;i<r2;i++)
{
for(j=0;j<c2;j++)
{
cout<<"\t"<<mat2[i][j];
}
cout<<"\n";
}
}
//Addition of both the sparse matrix.
//Addition of non zero element only which is stored in structure object sp1 and sp2.
void sparse::addspm()
{
int n1,n2;
n1=n2=0;
//conversion of sparse matrix to non zero value code as follows.
//conversion of first sparse matrix mat1 into sp1
sp1[0].row=r1;
sp1[0].col=c1;
k=1;
cout<<"\n Sparse matrix1 non_zero value are as follows:\n";
for(i=0;i<r1;i++)
{
for(j=0;j<c1;j++)
{
if(mat1[i][j]!=0)
{
sp1[k].row=i;
sp1[k].col=j;
sp1[k].nval=mat1[i][j];
k=k+1;
}
}
}
sp1[0].nval=k-1;
//display non zero values of sparse matrix mat1 which is inside sp1.
cout<<"\nRow\tCol\tnval";
for(i=0;i<k;i++)
{
cout<<"\n"<<sp1[i].row<<"\t"<<sp1[i].col<<"\t"<<sp1[i].nval;
}
//conversion of second sparse matrix mat2 into sp2
cout<<"\n\nSparse matrix2 non_zero value are as follows:\n";
sp2[0].row=r2;
sp2[0].col=c2;
k=1;
for(i=0;i<r2;i++)
{
for(j=0;j<c2;j++)
{
if(mat2[i][j]!=0)
{
sp2[k].row=i;
sp2[k].col=j;
sp2[k].nval=mat2[i][j];
k=k+1;
}
}
}
sp2[0].nval=k-1;
//display non zero values of sparse matrix mat2 which is inside sp2.
cout<<"\nRow\tCol\tnval";
for(i=0;i<k;i++)
{
cout<<"\n"<<sp2[i].row<<"\t"<<sp2[i].col<<"\t"<<sp2[i].nval;
}
//Addition of non zero values sp1 and sp2 logic are as follows.
//1.Store number of non zero term of mat1 in n1 and number of non zero term of mat2 in n2.
n1=sp1[0].nval;
n2=sp2[0].nval;
i=j=k=1;
cout<<"\n No of term in sp1:"<<n1<<"\tNo of term in sp2:"<<n2;
//2.Store the largest row and colom term of both matrices in sp3 row and col.
if(sp1[0].row>sp2[0].row)
{
sp3[0].row=sp1[0].row;
}
else
{
sp3[0].row=sp2[0].row;
}
if(sp1[0].col>sp2[0].col)
{
sp3[0].col=sp1[0].col;
}
else
{
sp3[0].col=sp2[0].col;
}
//3. Start addition by checking following conditions.
while((i<=n1)&&(j<=n2))//check for both term
{
if(sp1[i].row==sp2[j].row)//check if rows are same in sp1 and sp2.
{
if(sp1[i].col==sp2[j].col)//check if cols are same in sp1 and sp2.
{
sp3[k].row=sp1[i].row;
sp3[k].col=sp1[i].col;
sp3[k].nval=sp1[i].nval+sp2[j].nval; //if yes add both non zero values and store in sp3 with row,col and values detail.
cout<<"\nvalu of add:"<<sp3[k].nval;
i++;
j++; //increment all indexes.
k++;
cout<<"\nval of i:"<<i<<"\tval of j:"<<j<<"\tval of k:"<<k;
}
else if(sp1[i].col<sp2[j].col)//check col of sp1 is less than col of sp2
{
sp3[k].row=sp1[i].row;
sp3[k].col=sp1[i].col;
sp3[k].nval=sp1[i].nval; //if yes store all values of sp1 in sp3
i++;
k++; //increment i and k.
cout<<"\nval of i:"<<i<<"\tval of K:"<<k;
}
else
{
sp3[k].row=sp2[j].row;
sp3[k].col=sp2[j].col; //if no store all values of sp2 in sp3
sp3[k].nval=sp2[j].nval;
j++;
k++; //increment j and k.
cout<<"\nval of j:"<<j<<"\tval of K:"<<k;
}
}
else if(sp1[i].row<sp2[j].row)//check row of sp1 is less than row of sp2
{
sp3[k].row=sp1[i].row;
sp3[k].col=sp1[i].col;
sp3[k].nval=sp1[i].nval; //if yes store all values of sp1 in sp3
i++;
k++;
cout<<"\nval of i:"<<i<<"\tval of K:"<<k;
}
else
{
sp3[k].row=sp2[j].row;
sp3[k].col=sp2[j].col; //if no store all values of sp2 in sp3
sp3[k].nval=sp2[j].nval;
j++;
k++;
cout<<"\nval of j:"<<j<<"\tval of K:"<<k;
}
}//end of while loop
while(i<=n1) //Store remaining terms of sp1 in sp3 if above while (i<=n1&&j<=n2) is not true
{
sp3[k].row=sp1[i].row;
sp3[k].col=sp1[i].col;
sp3[k].nval=sp1[i].nval;
i++;
k++;
cout<<"\nval of outer while i:"<<i<<"\tval of K:"<<k;
}
while(j<=n2)
{
sp3[k].row=sp2[j].row; //Store remaining terms of sp2 in sp3 if above while (i<=n1&&j<=n2) is not true.
sp3[k].col=sp2[j].col;
sp3[k].nval=sp2[j].nval;
j++;
k++;
cout<<"\nval of outer while j:"<<j<<"\tval of K:"<<k;
}
sp3[0].nval=k-1;
//Display the addition result which is inside sp3.
cout<<"\nRow\tCol\tnval";
for(i=0;i<k;i++)
{
cout<<"\n"<<sp3[i].row<<"\t"<<sp3[i].col<<"\t"<<sp3[i].nval;
}
}
//To Transpose the sparse matrix
//Method: simple Transpose O(n*n)
//To chnage the rows into column and their values.
void sparse::simpl_trnspose()
{
//chainging the rows of sp1 to columns in spltr structure.
spltr[0].row=sp3[0].col;
spltr[0].col=sp3[0].row;
spltr[0].nval=sp3[0].nval;
k=1;
for(i=0;i<=spltr[0].row;i++)//To check number of colms
{
for(j=0;j<=spltr[0].nval;j++)//To check value in total no of non zero values
{
if(sp3[j].col==i)// if found swap the rows into colom and colm into rows.
{
spltr[k].row=sp3[j].col;
spltr[k].col=sp3[j].row;
spltr[k].nval=sp3[j].nval;
k++;
}
}
}//Total time required to execute is O(n*n).
cout<<"\n\n Simple Transpose of addition matrix are as follows...";
cout<<"\nRow\tCol\tnval";
for(i=0;i<k-1;i++)
{
cout<<"\n"<<spltr[i].row<<"\t"<<spltr[i].col<<"\t"<<spltr[i].nval;
}
}
void sparse::fast_trnspose()
{
int term[5],pos[5];
//First 0th row interchange row and col value.
fstr[0].row=sp3[0].col;
fstr[0].col=sp3[0].row;
fstr[0].nval=sp3[0].nval;
//initialize the term as zero.
for(i=0;i<=sp3[0].col;i++)
{
term[i]=0;
}
//Now find out how mnay times the col occures in nonzero value.
for(i=1;i<=sp3[0].nval;i++)
{
//term[sp3[i].col]=term[sp3[i].col]+1;
term[sp3[i].col]++;
}
//find out the actual position of each term i:e coloms in row.
pos[0]=1;
for(i=1;i<=sp3[0].col;i++)
{
pos[i]=pos[(i-1)]+term[(i-1)];
}
//fid the position and interchange the value.
for(i=1;i<=sp3[0].nval;i++)
{
j=pos[sp3[i].col];
fstr[j].row=sp3[i].col;
fstr[j].col=sp3[i].row;
fstr[j].nval=sp3[i].nval;
pos[sp3[i].col]=j+1;
}//Totla time required to execute is O(n)+O(n)+O(n)+O(n) i:e O(n)
cout<<"\n\n Fast Transpose of addition matrix are as follows...";
cout<<"\nRow\tCol\tnval";
for(i=0;i<=fstr[0].nval;i++)
{
cout<<"\n"<<fstr[i].row<<"\t"<<fstr[i].col<<"\t"<<fstr[i].nval;
}
}
//Main function logic.
//Program execution starts from here.
int main()
{
int n;
sparse s1; //s1 object of class sparse
s1.getmat();
s1.showmat(); //calling of member functions.
s1.addspm();
s1.simpl_trnspose();
s1.fast_trnspose();
// getch();
cout<<"\nPress one to exit....";
cin>>n;
return 0;
}
/********************** OUTPUT ****************************************
[student@localhost Documents]$ g++ SPMAT.CPP
SPMAT.CPP:10:1: warning: ‘typedef’ was ignored in this declaration [enabled by default]
};
^
[student@localhost Documents]$ ./a.out
How many rows in mat1:3
How many cols in mat1:3
Enter [0][0] value of mat1: 0
Enter [0][1] value of mat1: 0
Enter [0][2] value of mat1: 3
Enter [1][0] value of mat1: 4
Enter [1][1] value of mat1: 0
Enter [1][2] value of mat1: 5
Enter [2][0] value of mat1: 0
Enter [2][1] value of mat1: 0
Enter [2][2] value of mat1: 0
How many rows in mat2:3
How many cols in mat2:3
Enter [0][0] value of mat2: 0
Enter [0][1] value of mat2: 2
Enter [0][2] value of mat2: 0
Enter [1][0] value of mat2: 2
Enter [1][1] value of mat2: 0
Enter [1][2] value of mat2: 4
Enter [2][0] value of mat2: 0
Enter [2][1] value of mat2: 0
Enter [2][2] value of mat2: 2
Matrix 1 value are as follows
0 0 3
4 0 5
0 0 0
Matrix 2 value are as follows
0 2 0
2 0 4
0 0 2
Sparse matrix1 non_zero value are as follows:
Row Col nval
3 3 3
0 2 3
1 0 4
1 2 5
Sparse matrix2 non_zero value are as follows:
Row Col nval
3 3 4
0 1 2
1 0 2
1 2 4
2 2 2
No of term in sp1:3 No of term in sp2:4
val of j:2 val of K:2
val of i:2 val of K:3
valu of add:6
val of i:3 val of j:3 val of k:4
valu of add:9
val of i:4 val of j:4 val of k:5
val of outer while j:5 val of K:6
Row Col nval
3 3 5
0 1 2
0 2 3
1 0 6
1 2 9
2 2 2
Simple Transpose of addition matrix are as follows...
Row Col nval
3 3 5
0 1 6
1 0 2
2 0 3
2 1 9
2 2 2
Fast Transpose of addition matrix are as follows...
Row Col nval
3 3 5
0 1 6
1 0 2
2 0 3
2 1 9
2 2 2
Press one to exit....
*******************************************************************************************/
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