After using PHP for a while now, I've noticed that not all built-in PHP functions are as fast as expected. Consider these two possible implementations of a function that finds if a number is prime using a cached array of primes.

```
//very slow for large $prime_array
$prime_array = array( 2, 3, 5, 7, 11, 13, .... 104729, ... );
$result_array = array();
foreach( $prime_array => $number ) {
$result_array[$number] = in_array( $number, $large_prime_array );
}
//speed is much less dependent on size of $prime_array, and runs much faster.
$prime_array => array( 2 => NULL, 3 => NULL, 5 => NULL, 7 => NULL,
11 => NULL, 13 => NULL, .... 104729 => NULL, ... );
foreach( $prime_array => $number ) {
$result_array[$number] = array_key_exists( $number, $large_prime_array );
}
```

This is because `in_array`

is implemented with a linear search O(n) which will linearly slow down as `$prime_array`

grows. Where the `array_key_exists`

function is implemented with a hash lookup O(1) which will not slow down unless the hash table gets extremely populated (in which case it's only O(n)).

So far I've had to discover the big-O's via trial and error, and occasionally looking at the source code. Now for the question...

**Is there a list of the theoretical (or practical) big O times for all* the built-in PHP functions?**

*or at least the interesting ones

For example, I find it very hard to predict the big O of functions listed because the possible implementation depends on unknown core data structures of PHP: `array_merge`

, `array_merge_recursive`

, `array_reverse`

, `array_intersect`

, `array_combine`

, `str_replace`

(with array inputs), etc.

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**:

`isset`

/`array_key_exists`

is much faster than`in_array`

and`array_search`

`+`

(union) is a bit faster than`array_merge`

(and looks nicer). But it does work differently so keep that in mind.`shuffle`

is on the same Big-O tier as`array_rand`

`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.

Licensed under: CC-BY-SA with attribution

Not affiliated with: Stack Overflow