SPARSE MATRIX

• 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.

Matrix (4 × 4):            0 1   2  3    0    0  0  3  0    1    0  0  0  0    2   0  4  0  5    3   7  0  0  0  most values are 0.

Only these are non-zero:    Value at(Row,Col) 3 at (0,2) 4 at (2,1) 5 at (2,3) 7 at (3,0)

0           1      2         Row   Col   Value    0      0          2     3     1     2          1     4     2     2          3     5     3     3           0     7

[

 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;

}