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1 Answer
Nishtha Thakur

A sparse matrix is a matrix in which majority of the elements are 0. An example for this is given as follows.

The matrix given below contains 5 zeroes. Since the number of zeroes is more than half the elements of the matrix, it is a sparse matrix.

0 0 9
5 0 8
7 0 0

Algorithm

Begin
   Declare a 2D array a[10][10] to the integer datatype.
      Initialize some values of array.
   Declare i, j, count to the integer datatype.
      Initialize count = 0.
   Declare row, col to the integer datatype.
      Initialize row = 3, col = 3.
   for (i = 0; i < row; ++i) {
      for (j = 0; j < col; ++j)
         if (a[i][j] == 0)
            count++.
         Print “The matrix is:” .
      for (i = 0; i < row; ++i)
         for (j = 0; j < col; ++j)
            Print the values of array.
      Print “The number of zeros in the matrix are”.
   if (count > ((row * col)/ 2)) then
      Print "This is a sparse matrix".
   else
   Print "This is not a sparse matrix".
End.

Example

 Live Demo

#include<iostream>
using namespace std;
int main () {
   int a[10][10] = { {0, 0, 9} , {5, 0, 8} , {7, 0, 0} };
   int i, j, count = 0;
   int row = 3, col = 3;
   for (i = 0; i < row; ++i) {
      for (j = 0; j < col; ++j) {
         if (a[i][j] == 0)
            count++;
      }
   }
   cout<<"The matrix is:"<<endl;
   for (i = 0; i < row; ++i) {
      for (j = 0; j < col; ++j) {
         cout<<a[i][j]<<" ";
      }
      cout<<endl;
   }
   cout<<"The number of zeros in the matrix are "<< count <<endl;
   if (count > ((row * col)/ 2))
      cout<<"This is a sparse matrix"<<endl;
   else
      cout<<"This is not a sparse matrix"<<endl;
   return 0;
}

Output

The matrix is:
0 0 9
5 0 8
7 0 0
The number of zeros in the matrix are 5
This is a sparse matrix

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