Combinatorics

Combinatorics is a PHP Experts, Inc., Project meant for the ease of access of Combinatorics algorithms.

See https://en.wikipedia.org/wiki/Combinatorics

Memory Consumption

Storing thousands of possibilities can be extremely memory intensive.

However, this project utilizes PHP Generators and uses only a few kilobytes to calculate and output millions of potential combinations (See the Benchmarks section below).

Generating All Possible Combinations

What are all the possibilities of A, B, C and D? More than you might think! 64. Add two more letters and you've got 1,956 possibilities.

How many different parking spot orderings can 8 cars occupy on any given day? Find out in the Usage section below!

Installation

Via Composer

composer require phpexperts/combinatorics

Usage

$generator = new CombinationsGenerator();

foreach ($generator->generate($styles) as $combination) {
    // If you can do what you need to do with the combinations here, without immediately storing
    // them into an array, then your memory usage will never exceed the amount needed store one 
    // combination.
}

You can see real-world usage of this project in the test suite of the Console Painter project](https://github.com/PHPExpertsInc/ConsolePainter).

Use cases

Testing

phpunit --testdox

To actually see what's going on -and- run the stress tests, run

phpunit --debug

Note: It takes over 5 minutes on an Intel i7 to run all of the stress tests.

Benchmarks

Level 1: Generating combinations for A
[
  Number of possibilities => 2
  Time (ms)               => 0.051975250244141
  Time (s)                => 5.1975250244141E-5
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]
Level 2: Generating combinations for A, B
[
  Number of possibilities => 4
  Time (ms)               => 0.047922134399414
  Time (s)                => 4.7922134399414E-5
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]
Level 3: Generating combinations for A, B, C
[
  Number of possibilities => 15
  Time (ms)               => 0.22578239440918
  Time (s)                => 0.00022578239440918
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]
Level 4: Generating combinations for A, B, C, D
[
  Number of possibilities => 64
  Time (ms)               => 1.0910034179688
  Time (s)                => 0.0010910034179688
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]
Level 5: Generating combinations for A, B, C, D, E
[
  Number of possibilities => 325
  Time (ms)               => 6.5748691558838
  Time (s)                => 0.0065748691558838
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]
Level 6: Generating combinations for A, B, C, D, E, F
[
  Number of possibilities => 1956
  Time (ms)               => 47.721147537231
  Time (s)                => 0.047721147537231
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]
Level 7: Generating combinations for A, B, C, D, E, F, G
[
  Number of possibilities => 13699
  Time (ms)               => 395.29585838318
  Time (s)                => 0.39529585838318
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]
Level 8: Generating combinations for A, B, C, D, E, F, G, H
[
  Number of possibilities => 109600
  Time (ms)               => 3834.4430923462
  Time (s)                => 3.8344430923462
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]
Level 9: Generating combinations for A, B, C, D, E, F, G, H, I
[
  Number of possibilities => 986409
  Time (ms)               => 37884.353876114
  Time (s)                => 37.884353876114
  Memory consumed         => 320
  Peak Memory (Diff)      => 0
]
Level 10: Generating combinations for A, B, C, D, E, F, G, H, I, J
[
  Number of possibilities => 9864100
  Time (ms)               => 422606.03785515
  Time (s)                => 422.60603785515
  Memory consumed         => 0
  Peak Memory (Diff)      => 0
]

Contributors

Theodore R. Smith theodore@phpexperts.pro
GPG Fingerprint: 4BF8 2613 1C34 87AC D28F 2AD8 EB24 A91D D612 5690
CEO: PHP Experts, Inc.

{ "transactionId" : "$transactionId", "crmId" : "$crmId", "zAccountId" : "$zuoraAccountId", "facilityId" : "$facilityId", "promo_code" : "$promo_code", "transactionTotal" : "$total_cost_for_facebook", "transactionProducts" : [$transactionProducts], "transactionAffiliation" : "U.S. LawShield" }

License

MIT license. Please see the license file for more information.