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

Algorithm to Generate Combinations of Specific Size from a Set

In statistics, sampling refers to obtaining a subset of a population to represent the entire population. The goal is to generate all possible combinations of a specified size from a given set of elements.

To achieve this, we can employ a recursive algorithm, as demonstrated below:

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

    # Initialize the starting combinations as the original set
    if (empty($combinations)) {
        $combinations = $chars;
    }

    # Base case: stop if we've reached the desired size
    if ($size == 1) {
        return $combinations;
    }

    $new_combinations = array();

    # Iterate over existing combinations and add new characters
    foreach ($combinations as $combination) {
        foreach ($chars as $char) {
            $new_combinations[] = $combination . $char;
        }
    }

    # Call the function recursively to generate the next iteration of combinations
    return sampling($chars, $size - 1, $new_combinations);
}

Example:

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

# Display the generated combinations
var_dump($output);
/*
Expected 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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