Finding if an array is ordered

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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);
 
    }
}

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2 Responses

January 9th, 2009 at 2:23 am

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.

Sameer Borate’s Blog: Finding if an array is ordered : Dragonfly Networks

January 9th, 2009 at 3:58 am

[...] the CodeDiesel.com blog today Sameer has posted a quick code snippet that lets you see if a numeric array is already ordered correctly (useful for something like unit [...]

Finding if an array is ordered

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