A matrix is a two-dimensional data object having m rows and n columns, therefore a total of m*n values. If most of the values of a matrix are 0 then we say that the matrix is sparse.
Consider a definition of Sparse where a matrix is considered sparse if the number of 0s is more than half of the elements in the matrix,
Examples:
Input : 1 0 3 0 0 4 6 0 0 Output : Yes There are 5 zeros. This count is more than half of matrix size. Input : 1 2 3 0 7 8 5 0 7 Output: No
To check whether a matrix is a sparse matrix, we only need to check the total number of elements that are equal to zero. If this count is more than (m * n)/2, we return true.
// CPP code to check if a matrix is // sparse. #include <iostream> using namespace std;
const int MAX = 100;
bool isSparse( int array[][MAX], int m, int n)
{ int counter = 0;
// Count number of zeros in the matrix
for ( int i = 0; i < m; ++i)
for ( int j = 0; j < n; ++j)
if (array[i][j] == 0)
++counter;
return (counter > ((m * n) / 2));
} // Driver Function int main()
{ int array[][MAX] = { { 1, 0, 3 },
{ 0, 0, 4 },
{ 6, 0, 0 } };
int m = 3,
n = 3;
if (isSparse(array, m, n))
cout << "Yes" ;
else
cout << "No" ;
} |
Output:
Yes
Time complexity: O(m*n) where m and n are rows and columns respectively of a given matrix
Auxiliary Space: O(1)
Please refer complete article on Check if a given matrix is sparse or not for more details!