Check If a Matrix is Sparse in C++

What is Sparse Matrix?

A sparse matrix is a matrix in which the majority of the elements are zero. In other words, if more than half of the elements in a matrix are 0, it is called a sparse matrix. In this article, we will show you how to write a C++ program to check whether a given matrix is sparse or not.

Let's understand this with an example. The matrix shown below contains 5 zeros. Since the number of zeros is more than half of the total elements (9), it is a sparse matrix:

1 0 2
5 0 0
0 0 9

Steps to Check if a Matrix is Sparse

We can check if a matrix is sparse by counting how many elements are zero and comparing that count to the total number of elements. Here's how we did it:

• First, we define the matrix a and initialize it with values.
• Next, we use loops to count how many elements in the matrix are zero.
• Then, we compare the count of zeros with half of the total number of elements. If the number of zeros is greater than half, the matrix is sparse otherwise it is not.
• Finally, we print the matrix, the zero count, and the result.

C++ Program to Check if a Matrix is Sparse

In this example, we write a complete C++ program that helps us check whether a matrix is sparse or not.

#include<iostream>
using namespace std;

int main () {
   // Initialize the matrix with some values
   int a[10][10] = { {2, 0, 0} , {0, 3, 8} , {0, 9, 0} };
   int i, j, count = 0;
   int r = 3, c = 3;
   // Count the number of zeros in the matrix
   for (i = 0; i < r; ++i) {
      for (j = 0; j < c; ++j) {
         if (a[i][j] == 0)
            count++;
      }
   }
   // Print the matrix
   cout<<"The matrix is:"<<endl;
   for (i = 0; i < r; ++i) {
      for (j = 0; j < c; ++j) {
         cout<<a[i][j]<<" ";
      }
      cout<<endl;
   }
   // Show how many zeros are in the matrix
   cout<<"There are "<<count<<" zeros in the matrix"<<endl;

   // Check if the matrix is sparse or not
   if (count > ((r * c) / 2))
      cout<<"This is a sparse matrix"<<endl;
   else
      cout<<"This is not a sparse matrix"<<endl;
   return 0;
}

Below you will see the output of the above program which checks and confirms whether the given matrix is sparse or not.

The matrix is:
2 0 0 
0 3 8 
0 9 0 
There are 5 zeros in the matrix
This is a sparse matrix

Time Complexity: O(r1*c1) because we use two nested loops.

Space Complexity: O(1) because we use constant amount of space.