Given two sparse matrices (Sparse Matrix and its representations | Set 1 (Using Arrays and Linked Lists)), perform operations such as add, multiply or transpose of the matrices in their sparse form itself. The result should consist of three sparse matrices, one obtained by adding the two input matrices, one by multiplying the two matrices and one obtained by transpose of the first matrix.
Example: Note that other entries of matrices will be zero as matrices are sparse.
Input : Matrix 1: (4x4) Row Column Value 1 2 10 1 4 12 3 3 5 4 1 15 4 2 12 Matrix 2: (4X4) Row Column Value 1 3 8 2 4 23 3 3 9 4 1 20 4 2 25 Output : Result of Addition: (4x4) Row Column Value 1 2 10 1 3 8 1 4 12 2 4 23 3 3 14 4 1 35 4 2 37 Result of Multiplication: (4x4) Row Column Value 1 1 240 1 2 300 1 4 230 3 3 45 4 3 120 4 4 276 Result of transpose on the first matrix: (4x4) Row Column Value 1 4 15 2 1 10 2 4 12 3 3 5 4 1 12
The sparse matrix used anywhere in the program is sorted according to its row values. Two elements with the same row values are further sorted according to their column values.
Now 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.
To Transpose a matrix, we can simply change every column value to the row value and vice-versa, however, in this case, the resultant matrix won’t be sorted as we require. Hence, we initially determine the number of elements less than the current element’s column being inserted in order to get the exact index of the resultant matrix where the current element should be placed. This is done by maintaining an array index[] whose ith value indicates the number of elements in the matrix less than the column i.
To Multiply the matrices, we first calculate transpose of the second matrix to simplify our comparisons and maintain the sorted order. So, the resultant matrix is obtained by traversing through the entire length of both matrices and summing the appropriate multiplied values.
Any row value equal to x in the first matrix and row value equal to y in the second matrix (transposed one) will contribute towards result[x][y]. This is obtained by multiplying all such elements having col value in both matrices and adding only those with the row as x in first matrix and row as y in the second transposed matrix to get the result[x][y].
For example: Consider 2 matrices:
Row Col Val Row Col Val 1 2 10 1 1 2 1 3 12 1 2 5 2 1 1 2 2 1 2 3 2 3 1 8
The resulting matrix after multiplication will be obtained as follows:
Transpose of second matrix: Row Col Val Row Col Val 1 2 10 1 1 2 1 3 12 1 3 8 2 1 1 2 1 5 2 3 2 2 2 1 Summation of multiplied values: result[1][1] = A[1][3]*B[1][3] = 12*8 = 96 result[1][2] = A[1][2]*B[2][2] = 10*1 = 10 result[2][1] = A[2][1]*B[1][1] + A[2][3]*B[1][3] = 2*1 + 2*8 = 18 result[2][2] = A[2][1]*B[2][1] = 1*5 = 5 Any other element cannot be obtained by any combination of row in Matrix A and Row in Matrix B. Hence the final resultant matrix will be: Row Col Val 1 1 96 1 2 10 2 1 18 2 2 5
Following is the implementation of above approach:
// C++ code to perform add, multiply // and transpose on sparse matrices #include <iostream> using namespace std;
class sparse_matrix
{ // Maximum number of elements in matrix
const static int MAX = 100;
// Double-pointer initialized by
// the constructor to store
// the triple-represented form
int **data;
// dimensions of matrix
int row, col;
// total number of elements in matrix
int len;
public :
sparse_matrix( int r, int c)
{
// initialize row
row = r;
// initialize col
col = c;
// initialize length to 0
len = 0;
//Array of Pointer to make a matrix
data = new int *[MAX];
// Array representation
// of sparse matrix
//[,0] represents row
//[,1] represents col
//[,2] represents value
for ( int i = 0; i < MAX; i++)
data[i] = new int [3];
}
// insert elements into sparse matrix
void insert( int r, int c, int val)
{
// invalid entry
if (r > row || c > col)
{
cout << "Wrong entry" ;
}
else
{
// insert row value
data[len][0] = r;
// insert col value
data[len][1] = c;
// insert element's value
data[len][2] = val;
// increment number of data in matrix
len++;
}
}
void add(sparse_matrix b)
{
// if matrices don't have same dimensions
if (row != b.row || col != b.col)
{
cout << "Matrices can't be added" ;
}
else
{
int apos = 0, bpos = 0;
sparse_matrix result(row, col);
while (apos < len && bpos < b.len)
{
// if b's row and col is smaller
if (data[apos][0] > b.data[bpos][0] ||
(data[apos][0] == b.data[bpos][0] &&
data[apos][1] > b.data[bpos][1]))
{
// insert smaller value into result
result.insert(b.data[bpos][0],
b.data[bpos][1],
b.data[bpos][2]);
bpos++;
}
// if a's row and col is smaller
else if (data[apos][0] < b.data[bpos][0] ||
(data[apos][0] == b.data[bpos][0] &&
data[apos][1] < b.data[bpos][1]))
{
// insert smaller value into result
result.insert(data[apos][0],
data[apos][1],
data[apos][2]);
apos++;
}
else
{
// add the values as row and col is same
int addedval = data[apos][2] +
b.data[bpos][2];
if (addedval != 0)
result.insert(data[apos][0],
data[apos][1],
addedval);
// then insert
apos++;
bpos++;
}
}
// insert remaining elements
while (apos < len)
result.insert(data[apos][0],
data[apos][1],
data[apos++][2]);
while (bpos < b.len)
result.insert(b.data[bpos][0],
b.data[bpos][1],
b.data[bpos++][2]);
// print result
result.print();
}
}
sparse_matrix transpose()
{
// new matrix with inversed row X col
sparse_matrix result(col, row);
// same number of elements
result.len = len;
// to count number of elements in each column
int *count = new int [col + 1];
// initialize all to 0
for ( int i = 1; i <= col; i++)
count[i] = 0;
for ( int i = 0; i < len; i++)
count[data[i][1]]++;
int *index = new int [col + 1];
// to count number of elements having
// col smaller than particular i
// as there is no col with value < 0
index[0] = 0;
// initialize rest of the indices
for ( int i = 1; i <= col; i++)
index[i] = index[i - 1] + count[i - 1];
for ( int i = 0; i < len; i++)
{
// insert a data at rpos and
// increment its value
int rpos = index[data[i][1]]++;
// transpose row=col
result.data[rpos][0] = data[i][1];
// transpose col=row
result.data[rpos][1] = data[i][0];
// same value
result.data[rpos][2] = data[i][2];
}
// the above method ensures
// sorting of transpose matrix
// according to row-col value
return result;
}
void multiply(sparse_matrix b)
{
if (col != b.row)
{
// Invalid multiplication
cout << "Can't multiply, Invalid dimensions" ;
return ;
}
// transpose b to compare row
// and col values and to add them at the end
b = b.transpose();
int apos, bpos;
// result matrix of dimension row X b.col
// however b has been transposed,
// hence row X b.row
sparse_matrix result(row, b.row);
// iterate over all elements of A
for (apos = 0; apos < len;)
{
// current row of result matrix
int r = data[apos][0];
// iterate over all elements of B
for (bpos = 0; bpos < b.len;)
{
// current column of result matrix
// data[,0] used as b is transposed
int c = b.data[bpos][0];
// temporary pointers created to add all
// multiplied values to obtain current
// element of result matrix
int tempa = apos;
int tempb = bpos;
int sum = 0;
// iterate over all elements with
// same row and col value
// to calculate result[r]
while (tempa < len && data[tempa][0] == r &&
tempb < b.len && b.data[tempb][0] == c)
{
if (data[tempa][1] < b.data[tempb][1])
// skip a
tempa++;
else if (data[tempa][1] > b.data[tempb][1])
// skip b
tempb++;
else
// same col, so multiply and increment
sum += data[tempa++][2] *
b.data[tempb++][2];
}
// insert sum obtained in result[r]
// if its not equal to 0
if (sum != 0)
result.insert(r, c, sum);
while (bpos < b.len &&
b.data[bpos][0] == c)
// jump to next column
bpos++;
}
while (apos < len && data[apos][0] == r)
// jump to next row
apos++;
}
result.print();
}
// printing matrix
void print()
{
cout << "\nDimension: " << row << "x" << col;
cout << "\nSparse Matrix: \nRow\tColumn\tValue\n" ;
for ( int i = 0; i < len; i++)
{
cout << data[i][0] << "\t " << data[i][1]
<< "\t " << data[i][2] << endl;
}
}
}; // Driver Code int main()
{ // create two sparse matrices and insert values
sparse_matrix a(4, 4);
sparse_matrix b(4, 4);
a.insert(1, 2, 10);
a.insert(1, 4, 12);
a.insert(3, 3, 5);
a.insert(4, 1, 15);
a.insert(4, 2, 12);
b.insert(1, 3, 8);
b.insert(2, 4, 23);
b.insert(3, 3, 9);
b.insert(4, 1, 20);
b.insert(4, 2, 25);
// Output result
cout << "Addition: " ;
a.add(b);
cout << "\nMultiplication: " ;
a.multiply(b);
cout << "\nTranspose: " ;
sparse_matrix atranspose = a.transpose();
atranspose.print();
} // This code is contributed // by Bharath Vignesh J K |
// Java code to perform add, // multiply and transpose on sparse matrices public class sparse_matrix {
// Maximum number of elements in matrix
int MAX = 100 ;
// Array representation
// of sparse matrix
//[][0] represents row
//[][1] represents col
//[][2] represents value
int data[][] = new int [MAX][ 3 ];
// dimensions of matrix
int row, col;
// total number of elements in matrix
int len;
public sparse_matrix( int r, int c)
{
// initialize row
row = r;
// initialize col
col = c;
// initialize length to 0
len = 0 ;
}
// insert elements into sparse matrix
public void insert( int r, int c, int val)
{
// invalid entry
if (r > row || c > col) {
System.out.println( "Wrong entry" );
}
else {
// insert row value
data[len][ 0 ] = r;
// insert col value
data[len][ 1 ] = c;
// insert element's value
data[len][ 2 ] = val;
// increment number of data in matrix
len++;
}
}
public void add(sparse_matrix b)
{
// if matrices don't have same dimensions
if (row != b.row || col != b.col) {
System.out.println( "Matrices can't be added" );
}
else {
int apos = 0 , bpos = 0 ;
sparse_matrix result = new sparse_matrix(row, col);
while (apos < len && bpos < b.len) {
// if b's row and col is smaller
if (data[apos][ 0 ] > b.data[bpos][ 0 ] ||
(data[apos][ 0 ] == b.data[bpos][ 0 ] &&
data[apos][ 1 ] > b.data[bpos][ 1 ]))
{
// insert smaller value into result
result.insert(b.data[bpos][ 0 ],
b.data[bpos][ 1 ],
b.data[bpos][ 2 ]);
bpos++;
}
// if a's row and col is smaller
else if (data[apos][ 0 ] < b.data[bpos][ 0 ] ||
(data[apos][ 0 ] == b.data[bpos][ 0 ] &&
data[apos][ 1 ] < b.data[bpos][ 1 ]))
{
// insert smaller value into result
result.insert(data[apos][ 0 ],
data[apos][ 1 ],
data[apos][ 2 ]);
apos++;
}
else {
// add the values as row and col is same
int addedval = data[apos][ 2 ] + b.data[bpos][ 2 ];
if (addedval != 0 )
result.insert(data[apos][ 0 ],
data[apos][ 1 ],
addedval);
// then insert
apos++;
bpos++;
}
}
// insert remaining elements
while (apos < len)
result.insert(data[apos][ 0 ],
data[apos][ 1 ],
data[apos++][ 2 ]);
while (bpos < b.len)
result.insert(b.data[bpos][ 0 ],
b.data[bpos][ 1 ],
b.data[bpos++][ 2 ]);
// print result
result.print();
}
}
public sparse_matrix transpose()
{
// new matrix with inversed row X col
sparse_matrix result = new sparse_matrix(col, row);
// same number of elements
result.len = len;
// to count number of elements in each column
int count[] = new int [col + 1 ];
// initialize all to 0
for ( int i = 1 ; i <= col; i++)
count[i] = 0 ;
for ( int i = 0 ; i < len; i++)
count[data[i][ 1 ]]++;
int [] index = new int [col + 1 ];
// to count number of elements having col smaller
// than particular i
// as there is no col with value < 1
index[ 1 ] = 0 ;
// initialize rest of the indices
for ( int i = 2 ; i <= col; i++)
index[i] = index[i - 1 ] + count[i - 1 ];
for ( int i = 0 ; i < len; i++) {
// insert a data at rpos and increment its value
int rpos = index[data[i][ 1 ]]++;
// transpose row=col
result.data[rpos][ 0 ] = data[i][ 1 ];
// transpose col=row
result.data[rpos][ 1 ] = data[i][ 0 ];
// same value
result.data[rpos][ 2 ] = data[i][ 2 ];
}
// the above method ensures
// sorting of transpose matrix
// according to row-col value
return result;
}
public void multiply(sparse_matrix b)
{
if (col != b.row) {
// Invalid multiplication
System.out.println( "Can't multiply, "
+ "Invalid dimensions" );
return ;
}
// transpose b to compare row
// and col values and to add them at the end
b = b.transpose();
int apos, bpos;
// result matrix of dimension row X b.col
// however b has been transposed, hence row X b.row
sparse_matrix result = new sparse_matrix(row, b.row);
// iterate over all elements of A
for (apos = 0 ; apos < len;) {
// current row of result matrix
int r = data[apos][ 0 ];
// iterate over all elements of B
for (bpos = 0 ; bpos < b.len;) {
// current column of result matrix
// data[][0] used as b is transposed
int c = b.data[bpos][ 0 ];
// temporary pointers created to add all
// multiplied values to obtain current
// element of result matrix
int tempa = apos;
int tempb = bpos;
int sum = 0 ;
// iterate over all elements with
// same row and col value
// to calculate result[r]
while (tempa < len && data[tempa][ 0 ] == r
&& tempb < b.len && b.data[tempb][ 0 ] == c) {
if (data[tempa][ 1 ] < b.data[tempb][ 1 ])
// skip a
tempa++;
else if (data[tempa][ 1 ] > b.data[tempb][ 1 ])
// skip b
tempb++;
else
// same col, so multiply and increment
sum += data[tempa++][ 2 ] * b.data[tempb++][ 2 ];
}
// insert sum obtained in result[r]
// if its not equal to 0
if (sum != 0 )
result.insert(r, c, sum);
while (bpos < b.len && b.data[bpos][ 0 ] == c)
// jump to next column
bpos++;
}
while (apos < len && data[apos][ 0 ] == r)
// jump to next row
apos++;
}
result.print();
}
// printing matrix
public void print()
{
System.out.println( "Dimension: " + row + "x" + col);
System.out.println( "Sparse Matrix: \nRow Column Value" );
for ( int i = 0 ; i < len; i++) {
System.out.println(data[i][ 0 ] + " "
+ data[i][ 1 ] + " " + data[i][ 2 ]);
}
}
public static void main(String args[])
{
// create two sparse matrices and insert values
sparse_matrix a = new sparse_matrix( 4 , 4 );
sparse_matrix b = new sparse_matrix( 4 , 4 );
a.insert( 1 , 2 , 10 );
a.insert( 1 , 4 , 12 );
a.insert( 3 , 3 , 5 );
a.insert( 4 , 1 , 15 );
a.insert( 4 , 2 , 12 );
b.insert( 1 , 3 , 8 );
b.insert( 2 , 4 , 23 );
b.insert( 3 , 3 , 9 );
b.insert( 4 , 1 , 20 );
b.insert( 4 , 2 , 25 );
// Output result
System.out.println( "Addition: " );
a.add(b);
System.out.println( "\nMultiplication: " );
a.multiply(b);
System.out.println( "\nTranspose: " );
sparse_matrix atranspose = a.transpose();
atranspose.print();
}
} // This code is contributed by Sudarshan Khasnis |
# Python3 code to perform add, # multiply and transpose on sparse matrices class sparse_matrix :
def __init__( self , r, c):
# Maximum number of elements in matrix
self . MAX = 100 ;
# Array representation
# of sparse matrix
#[][0] represents row
#[][1] represents col
#[][2] represents value
self .data = [ None for _ in range ( self . MAX )]
for i in range ( self . MAX ):
self .data[i] = [ None for _ in range ( 3 )]
# dimensions of matrix
self .row = r;
self .col = c;
# total number of elements in matrix
self . len = 0 ;
# insert elements into sparse matrix
def insert( self , r, c, val):
# invalid entry
if (r > self .row or c > self .col) :
print ( "Wrong entry" );
else :
# insert row value
self .data[ self . len ][ 0 ] = r;
# insert col value
self .data[ self . len ][ 1 ] = c;
# insert element's value
self .data[ self . len ][ 2 ] = val;
# increment number of data in matrix
self . len + = 1 ;
def add( self , b):
# if matrices don't have same dimensions
if ( self .row ! = b.row or self .col ! = b.col) :
print ( "Matrices can't be added" );
else :
apos = 0 ;
bpos = 0 ;
result = sparse_matrix( self .row, self .col);
while (apos < self . len and bpos < b. len ):
# if b's row and col is smaller
if ( self .data[apos][ 0 ] > b.data[bpos][ 0 ] or ( self .data[apos][ 0 ] = = b.data[bpos][ 0 ] and self .data[apos][ 1 ] > b.data[bpos][ 1 ])):
# insert smaller value into result
result.insert(b.data[bpos][ 0 ],
b.data[bpos][ 1 ],
b.data[bpos][ 2 ]);
bpos + = 1
# if a's row and col is smaller
elif ( self .data[apos][ 0 ] < b.data[bpos][ 0 ] or ( self .data[apos][ 0 ] = = b.data[bpos][ 0 ] and self .data[apos][ 1 ] < b.data[bpos][ 1 ])):
# insert smaller value into result
result.insert( self .data[apos][ 0 ], self .data[apos][ 1 ], self .data[apos][ 2 ]);
apos + = 1 ;
else :
# add the values as row and col is same
addedval = self .data[apos][ 2 ] + b.data[bpos][ 2 ];
if (addedval ! = 0 ):
result.insert( self .data[apos][ 0 ], self .data[apos][ 1 ], addedval);
# then insert
apos + = 1 ;
bpos + = 1 ;
# insert remaining elements
while (apos < self . len ):
result.insert( self .data[apos][ 0 ], self .data[apos][ 1 ], self .data[apos][ 2 ]);
apos + = 1
while (bpos < b. len ):
result.insert(b.data[bpos][ 0 ], b.data[bpos][ 1 ], b.data[bpos][ 2 ]);
bpos + = 1
# print result
result. print ();
def transpose( self ):
# new matrix with inversed row X col
result = sparse_matrix( self .col, self .row);
# same number of elements
result. len = self . len ;
# to count number of elements in each column
count = [ None for _ in range ( self .col + 1 )];
# initialize all to 0
for i in range ( 1 , 1 + self .col):
count[i] = 0 ;
for i in range ( 0 , self . len ):
count[ self .data[i][ 1 ]] + = 1
index = [ None for _ in range ( self .col + 1 )]
# to count number of elements having col smaller
# than particular i
# as there is no col with value < 1
index[ 1 ] = 0 ;
# initialize rest of the indices
for i in range ( 2 , 1 + self .col):
index[i] = index[i - 1 ] + count[i - 1 ];
for i in range ( self . len ):
# insert a data at rpos and increment its value
rpos = index[ self .data[i][ 1 ]]
index[ self .data[i][ 1 ]] + = 1
# transpose row=col
result.data[rpos][ 0 ] = self .data[i][ 1 ];
# transpose col=row
result.data[rpos][ 1 ] = self .data[i][ 0 ];
# same value
result.data[rpos][ 2 ] = self .data[i][ 2 ];
# the above method ensures
# sorting of transpose matrix
# according to row-col value
return result;
def multiply( self , b):
if ( self .col ! = b.row):
# Invalid multiplication
print ( "Can't multiply, Invalid dimensions" );
return ;
# transpose b to compare row
# and col values and to add them at the end
b = b.transpose();
# result matrix of dimension row X b.col
# however b has been transposed, hence row X b.row
result = sparse_matrix( self .row, b.row);
# iterate over all elements of A
for apos in range ( self . len ):
# current row of result matrix
r = self .data[apos][ 0 ];
# iterate over all elements of B
for bpos in range (b. len ):
# current column of result matrix
# data[][0] used as b is transposed
c = b.data[bpos][ 0 ];
# temporary pointers created to add all
# multiplied values to obtain current
# element of result matrix
tempa = apos;
tempb = bpos;
sum = 0 ;
# iterate over all elements with
# same row and col value
# to calculate result[r]
while (tempa < self . len and self .data[tempa][ 0 ] = = r and tempb < b. len and b.data[tempb][ 0 ] = = c):
if ( self .data[tempa][ 1 ] < b.data[tempb][ 1 ]):
# skip a
tempa + = 1
elif ( self .data[tempa][ 1 ] > b.data[tempb][ 1 ]):
# skip b
tempb + = 1
else :
# same col, so multiply and
# increment
sum + = self .data[tempa][ 2 ] * b.data[tempb][ 2 ];
tempa + = 1
tempb + = 1
# insert sum obtained in result[r]
# if its not equal to 0
if ( sum ! = 0 ):
result.insert(r, c, sum );
while (bpos < b. len and b.data[bpos][ 0 ] = = c):
# jump to next column
bpos + = 1
while (apos < self . len and self .data[apos][ 0 ] = = r):
# jump to next row
apos + = 1
result. print ();
# printing matrix
def print ( self ):
print ( "Dimension:" , self .row, "x" , self .col);
print ( "Sparse Matrix: \nRow Column Value" );
for i in range ( self . len ):
print ( self .data[i][ 0 ], self .data[i][ 1 ], self .data[i][ 2 ]);
# create two sparse matrices and insert values a = sparse_matrix( 4 , 4 );
b = sparse_matrix( 4 , 4 );
a.insert( 1 , 2 , 10 );
a.insert( 1 , 4 , 12 );
a.insert( 3 , 3 , 5 );
a.insert( 4 , 1 , 15 );
a.insert( 4 , 2 , 12 );
b.insert( 1 , 3 , 8 );
b.insert( 2 , 4 , 23 );
b.insert( 3 , 3 , 9 );
b.insert( 4 , 1 , 20 );
b.insert( 4 , 2 , 25 );
# Output result print ( "Addition: " );
a.add(b); print ( "\nMultiplication: " );
a.multiply(b); print ( "\nTranspose: " );
atranspose = a.transpose();
atranspose. print ();
# This code is contributed by phasing17 |
// C# code to perform add, // multiply and transpose on sparse matrices public class sparse_matrix {
// Maximum number of elements in matrix
static int MAX = 100;
// Array representation
// of sparse matrix
//[,0] represents row
//[,1] represents col
//[,2] represents value
int [,] data = new int [MAX,3];
// dimensions of matrix
int row, col;
// total number of elements in matrix
int len;
public sparse_matrix( int r, int c)
{
// initialize row
row = r;
// initialize col
col = c;
// initialize length to 0
len = 0;
}
// insert elements into sparse matrix
public void insert( int r, int c, int val)
{
// invalid entry
if (r > row || c > col) {
System.Console.WriteLine( "Wrong entry" );
}
else {
// insert row value
data[len,0] = r;
// insert col value
data[len,1] = c;
// insert element's value
data[len,2] = val;
// increment number of data in matrix
len++;
}
}
public void add(sparse_matrix b)
{
// if matrices don't have same dimensions
if (row != b.row || col != b.col) {
System.Console.WriteLine( "Matrices can't be added" );
}
else {
int apos = 0, bpos = 0;
sparse_matrix result = new sparse_matrix(row, col);
while (apos < len && bpos < b.len) {
// if b's row and col is smaller
if (data[apos,0] > b.data[bpos,0] ||
(data[apos,0] == b.data[bpos,0] &&
data[apos,1] > b.data[bpos,1]))
{
// insert smaller value into result
result.insert(b.data[bpos,0],
b.data[bpos,1],
b.data[bpos,2]);
bpos++;
}
// if a's row and col is smaller
else if (data[apos,0] < b.data[bpos,0] ||
(data[apos,0] == b.data[bpos,0] &&
data[apos,1] < b.data[bpos,1]))
{
// insert smaller value into result
result.insert(data[apos,0],
data[apos,1],
data[apos,2]);
apos++;
}
else {
// add the values as row and col is same
int addedval = data[apos,2] + b.data[bpos,2];
if (addedval != 0)
result.insert(data[apos,0],
data[apos,1],
addedval);
// then insert
apos++;
bpos++;
}
}
// insert remaining elements
while (apos < len)
result.insert(data[apos,0],
data[apos,1],
data[apos++,2]);
while (bpos < b.len)
result.insert(b.data[bpos,0],
b.data[bpos,1],
b.data[bpos++,2]);
// print result
result.print();
}
}
public sparse_matrix transpose()
{
// new matrix with inversed row X col
sparse_matrix result = new sparse_matrix(col, row);
// same number of elements
result.len = len;
// to count number of elements in each column
int [] count = new int [col + 1];
// initialize all to 0
for ( int i = 1; i <= col; i++)
count[i] = 0;
for ( int i = 0; i < len; i++)
count[data[i,1]]++;
int [] index = new int [col + 1];
// to count number of elements having col smaller
// than particular i
// as there is no col with value < 1
index[1] = 0;
// initialize rest of the indices
for ( int i = 2; i <= col; i++)
index[i] = index[i - 1] + count[i - 1];
for ( int i = 0; i < len; i++) {
// insert a data at rpos and increment its value
int rpos = index[data[i,1]]++;
// transpose row=col
result.data[rpos,0] = data[i,1];
// transpose col=row
result.data[rpos,1] = data[i,0];
// same value
result.data[rpos,2] = data[i,2];
}
// the above method ensures
// sorting of transpose matrix
// according to row-col value
return result;
}
public void multiply(sparse_matrix b)
{
if (col != b.row) {
// Invalid multiplication
System.Console.WriteLine( "Can't multiply, "
+ "Invalid dimensions" );
return ;
}
// transpose b to compare row
// and col values and to add them at the end
b = b.transpose();
int apos, bpos;
// result matrix of dimension row X b.col
// however b has been transposed, hence row X b.row
sparse_matrix result = new sparse_matrix(row, b.row);
// iterate over all elements of A
for (apos = 0; apos < len;) {
// current row of result matrix
int r = data[apos,0];
// iterate over all elements of B
for (bpos = 0; bpos < b.len;) {
// current column of result matrix
// data[,0] used as b is transposed
int c = b.data[bpos,0];
// temporary pointers created to add all
// multiplied values to obtain current
// element of result matrix
int tempa = apos;
int tempb = bpos;
int sum = 0;
// iterate over all elements with
// same row and col value
// to calculate result[r]
while (tempa < len && data[tempa,0] == r
&& tempb < b.len && b.data[tempb,0] == c) {
if (data[tempa,1] < b.data[tempb,1])
// skip a
tempa++;
else if (data[tempa,1] > b.data[tempb,1])
// skip b
tempb++;
else
// same col, so multiply and increment
sum += data[tempa++,2] * b.data[tempb++,2];
}
// insert sum obtained in result[r]
// if its not equal to 0
if (sum != 0)
result.insert(r, c, sum);
while (bpos < b.len && b.data[bpos,0] == c)
// jump to next column
bpos++;
}
while (apos < len && data[apos,0] == r)
// jump to next row
apos++;
}
result.print();
}
// printing matrix
public void print()
{
System.Console.WriteLine( "Dimension: " + row + "x" + col);
System.Console.WriteLine( "Sparse Matrix: \nRow Column Value" );
for ( int i = 0; i < len; i++) {
System.Console.WriteLine(data[i,0] + " "
+ data[i,1] + " " + data[i,2]);
}
}
public static void Main()
{
// create two sparse matrices and insert values
sparse_matrix a = new sparse_matrix(4, 4);
sparse_matrix b = new sparse_matrix(4, 4);
a.insert(1, 2, 10);
a.insert(1, 4, 12);
a.insert(3, 3, 5);
a.insert(4, 1, 15);
a.insert(4, 2, 12);
b.insert(1, 3, 8);
b.insert(2, 4, 23);
b.insert(3, 3, 9);
b.insert(4, 1, 20);
b.insert(4, 2, 25);
// Output result
System.Console.WriteLine( "Addition: " );
a.add(b);
System.Console.WriteLine( "\nMultiplication: " );
a.multiply(b);
System.Console.WriteLine( "\nTranspose: " );
sparse_matrix atranspose = a.transpose();
atranspose.print();
}
} // This code is contributed by mits |
// JavaScript code to perform add, // multiply and transpose on sparse matrices class sparse_matrix { constructor(r, c)
{
// Maximum number of elements in matrix
this .MAX = 100;
// Array representation
// of sparse matrix
//[][0] represents row
//[][1] represents col
//[][2] represents value
this .data = new Array( this .MAX);
for ( var i = 0; i < this .MAX; i++)
this .data[i] = new Array(3);
// dimensions of matrix
this .row = r;
this .col = c;
// total number of elements in matrix
this .len = 0;
}
// insert elements into sparse matrix
insert(r, c, val)
{
// invalid entry
if (r > this .row || c > this .col) {
console.log( "Wrong entry" );
}
else {
// insert row value
this .data[ this .len][0] = r;
// insert col value
this .data[ this .len][1] = c;
// insert element's value
this .data[ this .len][2] = val;
// increment number of data in matrix
this .len++;
}
}
add(b)
{
// if matrices don't have same dimensions
if ( this .row != b.row || this .col != b.col) {
console.log( "Matrices can't be added" );
}
else {
let apos = 0, bpos = 0;
let result
= new sparse_matrix( this .row, this .col);
while (apos < this .len && bpos < b.len) {
// if b's row and col is smaller
if ( this .data[apos][0] > b.data[bpos][0]
|| ( this .data[apos][0]
== b.data[bpos][0]
&& this .data[apos][1]
> b.data[bpos][1]))
{
// insert smaller value into result
result.insert(b.data[bpos][0],
b.data[bpos][1],
b.data[bpos][2]);
bpos++;
}
// if a's row and col is smaller
else if ( this .data[apos][0]
< b.data[bpos][0]
|| ( this .data[apos][0]
== b.data[bpos][0]
&& this .data[apos][1]
< b.data[bpos][1]))
{
// insert smaller value into result
result.insert( this .data[apos][0],
this .data[apos][1],
this .data[apos][2]);
apos++;
}
else {
// add the values as row and col is same
let addedval = this .data[apos][2]
+ b.data[bpos][2];
if (addedval != 0)
result.insert( this .data[apos][0],
this .data[apos][1],
addedval);
// then insert
apos++;
bpos++;
}
}
// insert remaining elements
while (apos < this .len)
result.insert( this .data[apos][0],
this .data[apos][1],
this .data[apos++][2]);
while (bpos < b.len)
result.insert(b.data[bpos][0],
b.data[bpos][1],
b.data[bpos++][2]);
// print result
result.print();
}
}
transpose()
{
// new matrix with inversed row X col
let result = new sparse_matrix( this .col, this .row);
// same number of elements
result.len = this .len;
// to count number of elements in each column
let count = new Array( this .col + 1);
// initialize all to 0
for ( var i = 1; i <= this .col; i++)
count[i] = 0;
for ( var i = 0; i < this .len; i++)
count[ this .data[i][1]]++;
let index = new Array( this .col + 1);
// to count number of elements having col smaller
// than particular i
// as there is no col with value < 1
index[1] = 0;
// initialize rest of the indices
for ( var i = 2; i <= this .col; i++)
index[i] = index[i - 1] + count[i - 1];
for ( var i = 0; i < this .len; i++) {
// insert a data at rpos and increment its value
var rpos = index[ this .data[i][1]]++;
// transpose row=col
result.data[rpos][0] = this .data[i][1];
// transpose col=row
result.data[rpos][1] = this .data[i][0];
// same value
result.data[rpos][2] = this .data[i][2];
}
// the above method ensures
// sorting of transpose matrix
// according to row-col value
return result;
}
multiply(b)
{
if ( this .col != b.row) {
// Invalid multiplication
console.log( "Can't multiply, "
+ "Invalid dimensions" );
return ;
}
// transpose b to compare row
// and col values and to add them at the end
b = b.transpose();
let apos, bpos;
// result matrix of dimension row X b.col
// however b has been transposed, hence row X b.row
let result = new sparse_matrix( this .row, b.row);
// iterate over all elements of A
for (apos = 0; apos < this .len;) {
// current row of result matrix
let r = this .data[apos][0];
// iterate over all elements of B
for (bpos = 0; bpos < b.len;) {
// current column of result matrix
// data[][0] used as b is transposed
let c = b.data[bpos][0];
// temporary pointers created to add all
// multiplied values to obtain current
// element of result matrix
let tempa = apos;
let tempb = bpos;
let sum = 0;
// iterate over all elements with
// same row and col value
// to calculate result[r]
while (tempa < this .len
&& this .data[tempa][0] == r
&& tempb < b.len
&& b.data[tempb][0] == c) {
if ( this .data[tempa][1]
< b.data[tempb][1])
// skip a
tempa++;
else if ( this .data[tempa][1]
> b.data[tempb][1])
// skip b
tempb++;
else
// same col, so multiply and
// increment
sum += this .data[tempa++][2]
* b.data[tempb++][2];
}
// insert sum obtained in result[r]
// if its not equal to 0
if (sum != 0)
result.insert(r, c, sum);
while (bpos < b.len && b.data[bpos][0] == c)
// jump to next column
bpos++;
}
while (apos < this .len
&& this .data[apos][0] == r)
// jump to next row
apos++;
}
result.print();
}
// printing matrix
print()
{
console.log( "Dimension: " + this .row + "x"
+ this .col);
console.log( "Sparse Matrix: \nRow Column Value" );
for ( var i = 0; i < this .len; i++) {
console.log( this .data[i][0] + " "
+ this .data[i][1] + " "
+ this .data[i][2]);
}
}
}; // create two sparse matrices and insert values let a = new sparse_matrix(4, 4);
let b = new sparse_matrix(4, 4);
a.insert(1, 2, 10); a.insert(1, 4, 12); a.insert(3, 3, 5); a.insert(4, 1, 15); a.insert(4, 2, 12); b.insert(1, 3, 8); b.insert(2, 4, 23); b.insert(3, 3, 9); b.insert(4, 1, 20); b.insert(4, 2, 25); // Output result console.log( "Addition: " );
a.add(b); console.log( "\nMultiplication: " );
a.multiply(b); console.log( "\nTranspose: " );
let atranspose = a.transpose(); atranspose.print(); // This code is contributed by phasing17 |
Addition: Dimension: 4x4 Sparse Matrix: Row Column Value 1 2 10 1 3 8 1 4 12 2 4 23 3 3 14 4 1 35 4 2 37 Multiplication: Dimension: 4x4 Sparse Matrix: Row Column Value 1 1 240 1 2 300 1 4 230 3 3 45 4 3 120 4 4 276 Transpose: Dimension: 4x4 Sparse Matrix: Row Column Value 1 4 15 2 1 10 2 4 12 3 3 5 4 1 12
Worst case time complexity: Addition operation traverses the matrices linearly, hence, has a time complexity of O(n), where n is the number of non-zero elements in the larger matrix amongst the two. Transpose has a time complexity of O(n+m), where n is the number of columns and m is the number of non-zero elements in the matrix. Multiplication, however, has a time complexity of O(x*n + y*m), where (x, m) is number of columns and terms in the second matrix; and (y, n) is number of rows and terms in the first matrix.