Php Program to Check if a given matrix is sparse or not
Last Updated :
30 Jun, 2022
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
$MAX = 100;
function isSparse( $array , $m , $n )
{
$counter = 0;
for ( $i = 0; $i < $m ; ++ $i )
for ( $j = 0; $j < $n ; ++ $j )
if ( $array [ $i ][ $j ] == 0)
++ $counter ;
return ( $counter > (( $m * $n ) / 2));
}
$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" ;
?>
|
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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