List of Big-O for PHP functions

Since it doesn't seem like anyone has done this before I thought it'd be good idea to have it for reference somewhere. I've gone though and either via benchmark or code-skimming to characterize the array_* functions. I've tried to put the more interesting Big-O near the top. This list is not complete.

Note: All the Big-O where calculated assuming a hash lookup is O(1) even though it's really O(n). The coefficient of the n is so low, the ram overhead of storing a large enough array would hurt you before the characteristics of lookup Big-O would start taking effect. For example the difference between a call to array_key_exists at N=1 and N=1,000,000 is ~50% time increase.

Interesting Points:

1. isset/array_key_exists is much faster than in_array and array_search
2. +(union) is a bit faster than array_merge (and looks nicer). But it does work differently so keep that in mind.
3. shuffle is on the same Big-O tier as array_rand
4. array_pop/array_push is faster than array_shift/array_unshift due to re-index penalty

Lookups:

array_key_exists O(n) but really close to O(1) - this is because of linear polling in collisions, but because the chance of collisions is very small, the coefficient is also very small. I find you treat hash lookups as O(1) to give a more realistic big-O. For example the different between N=1000 and N=100000 is only about 50% slow down.

isset( $array[$index] ) O(n) but really close to O(1) - it uses the same lookup as array_key_exists. Since it's language construct, will cache the lookup if the key is hardcoded, resulting in speed up in cases where the same key is used repeatedly.

in_array O(n) - this is because it does a linear search though the array until it finds the value.

array_search O(n) - it uses the same core function as in_array but returns value.

Queue functions:

array_push O(∑ var_i, for all i)

array_pop O(1)

array_shift O(n) - it has to reindex all the keys

array_unshift O(n + ∑ var_i, for all i) - it has to reindex all the keys

Array Intersection, Union, Subtraction:

array_intersect_key if intersection 100% do O(Max(param_i_size)*∑param_i_count, for all i), if intersection 0% intersect O(∑param_i_size, for all i)

array_intersect if intersection 100% do O(n^2*∑param_i_count, for all i), if intersection 0% intersect O(n^2)

array_intersect_assoc if intersection 100% do O(Max(param_i_size)*∑param_i_count, for all i), if intersection 0% intersect O(∑param_i_size, for all i)

array_diff O(π param_i_size, for all i) - That's product of all the param_sizes

array_diff_key O(∑ param_i_size, for i != 1) - this is because we don't need to iterate over the first array.

array_merge O( ∑ array_i, i != 1 ) - doesn't need to iterate over the first array

+ (union) O(n), where n is size of the 2nd array (ie array_first + array_second) - less overhead than array_merge since it doesn't have to renumber

array_replace O( ∑ array_i, for all i )

Random:

shuffle O(n)

array_rand O(n) - Requires a linear poll.

Obvious Big-O:

array_fill O(n)

array_fill_keys O(n)

range O(n)

array_splice O(offset + length)

array_slice O(offset + length) or O(n) if length = NULL

array_keys O(n)

array_values O(n)

array_reverse O(n)

array_pad O(pad_size)

array_flip O(n)

array_sum O(n)

array_product O(n)

array_reduce O(n)

array_filter O(n)

array_map O(n)

array_chunk O(n)

array_combine O(n)

I'd like to thank Eureqa for making it easy to find the Big-O of the functions. It's an amazing free program that can find the best fitting function for arbitrary data.

EDIT:

For those who doubt that PHP array lookups are O(N), I've written a benchmark to test that (they are still effectively O(1) for most realistic values).

$tests = 1000000;
$max = 5000001;


for( $i = 1; $i <= $max; $i += 10000 ) {
    //create lookup array
    $array = array_fill( 0, $i, NULL );

    //build test indexes
    $test_indexes = array();
    for( $j = 0; $j < $tests; $j++ ) {
        $test_indexes[] = rand( 0, $i-1 );
    }

    //benchmark array lookups
    $start = microtime( TRUE );
    foreach( $test_indexes as $test_index ) {
        $value = $array[ $test_index ];
        unset( $value );
    }
    $stop = microtime( TRUE );
    unset( $array, $test_indexes, $test_index );

    printf( "%d,%1.15f\n", $i, $stop - $start ); //time per 1mil lookups
    unset( $stop, $start );
}

The explanation for the case you specifically describe is that associative arrays are implemented as hash tables - so lookup by key (and correspondingly, array_key_exists) is O(1). However, arrays aren't indexed by value, so the only way in the general case to discover whether a value exists in the array is a linear search. There's no surprise there.

I don't think there's specific comprehensive documentation of the algorithmic complexity of PHP methods. However, if it's a big enough concern to warrant the effort, you can always look through the source code.