Php 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. 

PHP

<?php
// PHP code to check if a matrix is
// sparse.

$MAX = 100;

function isSparse( $array, $m, $n)
{
    $counter = 0;

    // Count number of zeros
    // in the matrix
    for ($i = 0; $i < $m; ++$i)
        for ($j = 0; $j < $n; ++$j)
            if ($array[$i][$j] == 0)
                ++$counter;

    return ($counter > (($m * $n) / 2));
}

    // Driver Code
    $array = array(array(1, 0, 3),
                   array(0, 0, 4),
                   array(6, 0, 0));

    $m = 3;
    $n = 3;
    if (isSparse($array, $m, $n))
        echo "Yes";
    else
        echo "No";

// This code is contributed by anuj_67.
?>

Output:  

Yes

Time Complexity: O(n*m)

Auxiliary Space: O(1)

Please refer complete article on Check if a given matrix is sparse or not for more details!