How to Generate All Combinations of a Specific Size from a Single Set in PHP?

How to Generate All Combinations of a Specific Size from a Single Set in PHP

Given an array of characters and a desired combination size, the task is to generate all possible combinations of that specific size. This article explores an algorithm to achieve this using PHP, differentiating it from permutations where repeating characters are not allowed.

Algorithm

The algorithm is based on recursion. Here's a detailed explanation:

1. Initialization: If the algorithm is running for the first time, the initial set of combinations is set to the given character array.
2. Checking Size: If the desired combination size is 1, the current set of combinations is returned as the result.
3. Creating New Combinations: For each combination in the current set and each character in the original array, a new combination is created by concatenating the current combination and the character.
4. Recursive Call: The function is recursively called with the new set of combinations and a decrement of the desired combination size.
5. Result: The final result is the returned output after the recursion completes.

Example Implementation

Below is a working example in PHP:

function sampling($chars, $size, $combinations = array()) {

    if (empty($combinations)) {
        $combinations = $chars;
    }

    if ($size == 1) {
        return $combinations;
    }

    $new_combinations = array();
    foreach ($combinations as $combination) {
        foreach ($chars as $char) {
            $new_combinations[] = $combination . $char;
        }
    }

    return sampling($chars, $size - 1, $new_combinations);

}

// Example
$chars = array('a', 'b', 'c');
$output = sampling($chars, 2);
var_dump($output);

Output:

array(9) {
  [0]=>
  string(2) "aa"
  [1]=>
  string(2) "ab"
  [2]=>
  string(2) "ac"
  [3]=>
  string(2) "ba"
  [4]=>
  string(2) "bb"
  [5]=>
  string(2) "bc"
  [6]=>
  string(2) "ca"
  [7]=>
  string(2) "cb"
  [8]=>
  string(2) "cc"
}

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