#include <iostream>
using namespace std;
int main()
{
int matrix[3][3];
int zero = 0;
int total = 9;
cout << "Enter 3 x 3 matrix:" << endl;
// Input matrix
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
cin >> matrix[i][j];
if (matrix[i][j] == 0)
{
zero++;
}
}
}
// Check sparse matrix
if (zero > total / 2)
{
cout << "Matrix is a Sparse Matrix.";
}
else
{
cout << "Matrix is not a Sparse Matrix.";
}
return 0;
}
#include <iostream>
using namespace std;
int main()
{
int matrix1[3][3]; int matrix2[3][3];
int sparse1[10][3]; int sparse2[10][3]; int result[10][3];
int k1 = 0; int k2 = 0; int k3 = 0;
// Input Matrix 1
cout << "Enter first 3 x 3 matrix:" << endl;
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
cin >> matrix1[i][j];
}
}
// Input Matrix 2
cout << "Enter second 3 x 3 matrix:" << endl;
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
cin >> matrix2[i][j];
}
}
// Convert Matrix 1 into Sparse Matrix
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
if (matrix1[i][j] != 0)
{
sparse1[k1][0] = i; // Row
sparse1[k1][1] = j; // Column
sparse1[k1][2] = matrix1[i][j]; // Value
k1++;
}
}
}
// Convert Matrix 2 into Sparse Matrix
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
if (matrix2[i][j] != 0)
{
sparse2[k2][0] = i; // Row
sparse2[k2][1] = j; // Column
sparse2[k2][2] = matrix2[i][j]; // Value
k2++;
}
}
}
// Add two sparse matrices
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
int value = matrix1[i][j] + matrix2[i][j];
if (value != 0)
{
result[k3][0] = i; // Row
result[k3][1] = j; // Column
result[k3][2] = value; // Value
k3++;
}
}
}
// Display Sparse Matrix 1
cout << "\nSparse Matrix 1:" << endl;
cout << "Row\tColumn\tValue" << endl;
for (int i = 0; i < k1; i++)
{
cout << sparse1[i][0] << "\t"
<< sparse1[i][1] << "\t"
<< sparse1[i][2] << endl;
}
// Display Sparse Matrix 2
cout << "\nSparse Matrix 2:" << endl;
cout << "Row\tColumn\tValue" << endl;
for (int i = 0; i < k2; i++)
{
cout << sparse2[i][0] << "\t"
<< sparse2[i][1] << "\t"
<< sparse2[i][2] << endl;
}
// Display Result
cout << "\nAddition of Two Sparse Matrices:" << endl;
cout << "Row\tColumn\tValue" << endl;
for (int i = 0; i < k3; i++)
{
cout << result[i][0] << "\t"
<< result[i][1] << "\t"
<< result[i][2] << endl;
}
return 0;
}
#include <iostream>
int main()
{ int matrix[3][3]; int sparse[10][3]; int k = 0;
cout << "Enter 3 x 3 matrix:" << endl;
# 3 rows ,3 columns , Total = 9 elements
// Input matrix
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
cin >> matrix[i][j];
}
}
// Find non-zero elements
for (int i = 0; i < 3; i++)
{
#i represents the row number.
for (int j = 0; j < 3; j++)
# j represents the column number.
{
if (matrix[i][j] != 0) # If the matrix element is not zero, store it.
{
#k keeps track of the next position to store a non-zero element.
sparse[k][0] = i; #sparse[k][0] → Row
sparse[k][1] = j; #sparse[k][1] → Column
sparse[k][2] = matrix[i][j]; #sparse[k][2] → Value
k++;
}
}
}
// Display sparse matrix
cout << "\nSparse Matrix:" << endl;
cout << "Row\t Column\t Value" << endl;
for (int i = 0; i < k; i++)
{ cout << sparse[i][0] << "\t"
<< sparse[i][1] << "\t"
<< sparse[i][2] << endl;
}
return 0;
}
A matrix is just a table of numbers (rows × columns).
A sparse matrix is a matrix where most of the elements are 0.
Instead of storing all elements (including 0s), we store only the non-zero elements with their row, column, and value.
[
At(Row,column) Value
At (0,2) → compact[0][0]=0, compact[1][0]=2, compact[2][0]=3]
#include <stdio.h>
int main() {
int rows = 4, cols = 4;
// Original sparse matrix
int sparse[4][4] = {
{0, 0, 3, 0},
{0, 0, 0, 0},
{0, 4, 0, 5},
{7, 0, 0, 0}
};
// Count non-zero elements
int size = 0; //size is used to count how many non-zero elements
for (int i = 0; i < rows; i++)
for (int j = 0; j < cols; j++)
if (sparse[i][j] != 0)
size++;
[ //Value at(Row,Col)
3 at (0,2) value = 3 → not zero → size = 1
4 at (2,1) value = 4 → not zero → size = 2
5 at (2,3) value = 5 → not zero → size = 3
7 at (3,0) value = 7 → not zero → size = 4 ]
// Compact matrix (3 × size)
int compact[3][size];// 3-> row,column,value
int k = 0; // k keeps track of which column we are filling in the compact matrix
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
if (sparse[i][j] != 0) {
compact[0][k] = i; // store Row index
compact[1][k] = j; // store Column index
compact[2][k] = sparse[i][j]; // store Value
k++; //k++ → move to next column
}
}
}
[
At(Row,column) Value
At (0,2) → compact[0][0]=0, compact[1][0]=2, compact[2][0]=3]
// Print compact matrix
printf("Row Col Value");
for (int i = 0; i < size; i++)
{
printf("%d %d %d\n", compact[0][i], compact[1][i], compact[2][i]);
}
return 0;
}
