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copied!<p>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 <code>array_*</code> functions. I've tried to put the more interesting Big-O near the top. This list is not complete.</p> <p>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 <code>array_key_exists</code> at N=1 and N=1,000,000 is ~50% time increase.</p> <p><strong>Interesting Points</strong>:</p> <ol> <li><code>isset</code>/<code>array_key_exists</code> is much faster than <code>in_array</code> and <code>array_search</code></li> <li><code>+</code>(union) is a bit faster than <code>array_merge</code> (and looks nicer). But it does work differently so keep that in mind.</li> <li><code>shuffle</code> is on the same Big-O tier as <code>array_rand</code></li> <li><code>array_pop</code>/<code>array_push</code> is faster than <code>array_shift</code>/<code>array_unshift</code> due to re-index penalty</li> </ol> <p><strong>Lookups</strong>:</p> <p><code>array_key_exists</code> 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.</p> <p><code>isset( $array[$index] )</code> 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. </p> <p><code>in_array</code> O(n) - this is because it does a linear search though the array until it finds the value.</p> <p><code>array_search</code> O(n) - it uses the same core function as in_array but returns value.</p> <p><strong>Queue functions</strong>:</p> <p><code>array_push</code> O(∑ var_i, for all i)</p> <p><code>array_pop</code> O(1) </p> <p><code>array_shift</code> O(n) - it has to reindex all the keys</p> <p><code>array_unshift</code> O(n + ∑ var_i, for all i) - it has to reindex all the keys</p> <p><strong>Array Intersection, Union, Subtraction</strong>:</p> <p><code>array_intersect_key</code> 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)</p> <p><code>array_intersect</code> if intersection 100% do O(n^2*∑param_i_count, for all i), if intersection 0% intersect O(n^2)</p> <p><code>array_intersect_assoc</code> 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)</p> <p><code>array_diff</code> O(π param_i_size, for all i) - That's product of all the param_sizes</p> <p><code>array_diff_key</code> O(∑ param_i_size, for i != 1) - this is because we don't need to iterate over the first array.</p> <p><code>array_merge</code> O( ∑ array_i, i != 1 ) - doesn't need to iterate over the first array</p> <p><code>+</code> (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</p> <p><code>array_replace</code> O( ∑ array_i, for all i )</p> <p><strong>Random</strong>:</p> <p><code>shuffle</code> O(n)</p> <p><code>array_rand</code> O(n) - Requires a linear poll.</p> <p><strong>Obvious Big-O</strong>:</p> <p><code>array_fill</code> O(n)</p> <p><code>array_fill_keys</code> O(n)</p> <p><code>range</code> O(n)</p> <p><code>array_splice</code> O(offset + length)</p> <p><code>array_slice</code> O(offset + length) or O(n) if length = NULL</p> <p><code>array_keys</code> O(n)</p> <p><code>array_values</code> O(n)</p> <p><code>array_reverse</code> O(n)</p> <p><code>array_pad</code> O(pad_size)</p> <p><code>array_flip</code> O(n)</p> <p><code>array_sum</code> O(n)</p> <p><code>array_product</code> O(n)</p> <p><code>array_reduce</code> O(n)</p> <p><code>array_filter</code> O(n)</p> <p><code>array_map</code> O(n)</p> <p><code>array_chunk</code> O(n) </p> <p><code>array_combine</code> O(n)</p> <p>I'd like to thank <a href="https://www.creativemachineslab.com/eureqa.html" rel="noreferrer">Eureqa</a> for making it easy to find the Big-O of the functions. It's an amazing <em>free</em> program that can find the best fitting function for arbitrary data.</p> <p>EDIT:</p> <p>For those who doubt that PHP array lookups are <code>O(N)</code>, I've written a benchmark to test that (they are still effectively <code>O(1)</code> for most realistic values).</p> <p><img src="https://i.stack.imgur.com/PgRQd.png" alt="php array lookup graph"></p> <pre><code>$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 ); } </code></pre>

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