Misunderstanding How in_array Works

Brian Moon has a post about how in_array() really, really sucks. This is not a problem with in_array per se, but failing to recognize the proper way to solve a problem like this. Some of the comments has already touched on this matter, but I’ll attempt to further expand and describe the problem.

You have two arrays; a1 and b2. You’re interested in removing all the values from a1 that also are in b2. If you’re doing the naive approach (which Brian Moon describes), you’ll simply do:

foreach($a1 as $key => $value)
{
    foreach($b2 as $key2 => $value2)
    {
        if ($value == $value2)
        {
            unset($a1[$key]);
        }
    }
}

(ignore any potential side effects of manipulating $a1 while looping through it for now)

This will work for small sizes of a1 and b2, but as soon as the number of entries starts to increase (let’s call them m and n), you’ll see that the growth of your function will approach O(m*n), which can be written as O(n²) as both values approach infinity. This is not good and is the same complexity that you’ll find in naive sorting algorithms. This means that for each element you add to the array, your processing time increases quadratically (since you have two loops here). in_array is simply a shortcut for the inner loop (the inner foreach loop) in this example. It loops through each element of the array and checks if it matches the needle we’re searching for.

Compare this to using array_flip on the array to search first, so that the values becomes the keys:

foreach($a1 as $key => $value)
{
    if (isset($b2[$key]))
    {
        unset($a1[$key]);
    }
}

But why is isset($arr[$key]) any faster than using in_array? Doesn’t the application just have to loop through a different set of values instead (this time, the keys instead of the values)? No. This is where hashing comes into the picture. As $key can be any string value in PHP, the string is hashed and resolved to an internal array id. This means that internally, the following is happening:

$arr[$id] => find location by converting $id to an internal array location (on the C-level) => simply index the array by using this value

Instead of going through all the valid keys, the $id is converted once, and then checked to see if there is any value stored at that location. This is a simplification, but explains the concept. The complexity of this conversion may depend on the length of the key (depending on the choice of hashing function), but we’ll ignore this here, and simply give it a complexity of O(1). Looking up the index in the array is also an O(1) operation (it takes the same time, regardless if we’re looking at item #3 or #4818, it’s simply reading from different locations in memory).

This means that while our other loop is still looping through n elements, we’re now just doing a constant lookup in the innerloop. The amount of work done in the inner loop does not depend on the number of elements in b2, and this means that our algorithm instead grows in a linear fashion (O(n)).

Further reading can be found at Wikipedia: Hash function, Big O Notation. I’ll also suggest reading an introductionary book into the field of algorithms and datastructures. The type of book depends on your skillset, but if anyone wants any suggestions, just leave a comment and I’ll add a few as I get home to my bookshelf tonight.

2 thoughts on “Misunderstanding How in_array Works”

  1. Thanks Mats for finishing my post. Had it not been late and I not been just relieved to hunt this down, I would have liked to elaborate the way he did here.

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