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# C++ Program to Check if a given matrix is sparse or not

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.

## C++

 `// CPP code to check if a matrix is``// sparse.``#include ``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!

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