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!
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