I recently wrote a quick code to find if a numeric array is ordered i.e sorted in a ascending or descending order. I needed it to check a sort algorithm I had written. The problem is that the following code has a worst-case running time of *O(N)*. Can we make the running time logarithmic.

```
/* orderedArray.php */
define("ORDER_ASC", 1);
define("ORDER_DSC", 0);
function is_array_ordered($array, $sort_order)
{
$i=0;
$total_elements = count($array);
if($sort_order == ORDER_ASC)
{
//Check for ascending order
while($total_elements > 1)
{
if($array[$i] < $array[$i+1])
{
$i++;
$total_elements--;
}
else
{
return false;
}
}
}
elseif($sort_order == ORDER_DSC)
{
//Check for descending order
while($total_elements > 1)
{
if($array[$i] > $array[$i+1])
{
$i++;
$total_elements--;
}
else
{
return false;
}
}
}
return true;
}
```

The unit test for the same is given below.

```
include 'PHPUnit/Framework.php';
include 'orderedArray.php';
class ArrayTest extends PHPUnit_Framework_TestCase
{
public function testArrayOrder()
{
// Ascending
$test_array = array(0,1,2,3,4,6,7,8,9,10);
$this->assertEquals(is_array_ordered($test_array, ORDER_ASC), true);
$test_array = array(10,9,8,7,6,5,4,3,2,1,0);
$this->assertEquals(is_array_ordered($test_array, ORDER_ASC), false);
$test_array = array(0,1,2,3,4,6,7,8,9,10,1);
$this->assertEquals(is_array_ordered($test_array, ORDER_ASC), false);
$test_array = array(1,0,1,2,3,4,6,7,8,9,10);
$this->assertEquals(is_array_ordered($test_array, ORDER_ASC), false);
// Descending
$test_array = array(10,9,8,7,6,5,4,3,2,1,0);
$this->assertEquals(is_array_ordered($test_array, ORDER_DSC), true);
$test_array = array(0,1,2,3,4,6,7,8,9,10);
$this->assertEquals(is_array_ordered($test_array, ORDER_DSC), false);
$test_array = array(10,9,8,7,6,5,4,3,2,1,0,1);
$this->assertEquals(is_array_ordered($test_array, ORDER_DSC), false);
$test_array = array(1,10,9,8,7,6,5,4,3,2,1,0);
$this->assertEquals(is_array_ordered($test_array, ORDER_DSC), false);
}
}
```

You can’t make the time O(log N) since you have to check every element, which is precisely O(N).

Usually, a logarithmic time means O(N log N), which is worse than O(N) but much better than O(N²). For example, the best sorting algorithms have O(N log N) times (Quicksort with possible degeneration, Heap Sort), while naive ones have O(N²) times.

As for your algorithm:

– You don’t make the difference between strictly increasing (resp. strictly decreasing) and simply non-decreasing (resp. non-increasing).

– AFAIK, it is only valid for arrays indexed by consecutive integers. A foreach would be better suited, keeping the previous element in a temporary variable (which could be more efficient than an array access as PHP does copy-on-write. This should be tested).

– I’d rather use multiple functions than a single parametrized one. This eliminates the need for a constant and limitates the needed logic.

Cheers.