PHP Program to Check the 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 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 = [[1, 0, 3], [0, 0, 4], [6, 0, 0]];

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

?>

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!