How to Generate All Combinations from Multiple Arrays in PHP Recursively?

Generating Combinations from Multiple Arrays in PHP

Introduction

The task of generating all combinations of items from multiple arrays is often encountered during combinatorial optimization problems. This article presents a recursive solution that addresses the need for a function that can handle a variable number of source arrays.

Problem Statement

Given several arrays with different numbers of elements, find all combinations of items, where the number of combinations equals the product of the number of elements in each array. For instance, given the following arrays:

$arrayA = array('A1','A2','A3');
$arrayB = array('B1','B2','B3');
$arrayC = array('C1','C2');

We aim to generate an array of 18 combinations:

[
    ['A1', 'B1', 'C1'],
    ['A1', 'B1', 'C2'],
    ['A1', 'B2', 'C1'],
    ...
]

Recursive Solution

The following recursive function generates all possible combinations of items:

function combinations($arrays, $i = 0) {
    // If reaching the last array, return the array itself
    if (!isset($arrays[$i])) {
        return array();
    }

    // If at the parent array, return the recursive call to the following array
    if ($i == count($arrays) - 1) {
        return $arrays[$i];
    }

    // Get combinations from subsequent arrays
    $tmp = combinations($arrays, $i + 1);

    $result = array();

    // Concatenate each array from tmp with each element from $arrays[$i]
    foreach ($arrays[$i] as $v) {
        foreach ($tmp as $t) {
            $result[] = is_array($t) ?
                array_merge(array($v), $t) :
                array($v, $t);
        }
    }

    return $result;
}

Demonstration

The following code demonstrates the usage of the combinations function:

print_r(
    combinations(
        array(
            array('A1','A2','A3'),
            array('B1','B2','B3'),
            array('C1','C2')
        )
    )
);

This will output the expected array of 18 combinations.

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