How can I generate all possible combinations of elements from a 1D array, considering both order and duplicates?

Generating Combinations from a 1D Array

Introduction

Combinations of elements from a given array find applications in various domains such as combinatorics and optimization.

Problem Statement

Given a 1D array, the objective is to determine all possible combinations of the elements, ensuring that both order and duplicates are considered.

Solution

To generate all combinations while factoring in order and duplicates, a systematic approach is necessary. One such approach involves utilizing recursion along with array manipulation:

<code class="php"><?php $array = array('Alpha', 'Beta', 'Gamma');

function depth_picker($arr, $temp_string, &$collect) {
    if ($temp_string != "") 
        $collect []= $temp_string;

    for ($i=0, $iMax = sizeof($arr); $i < $iMax; $i++) {
        $arrcopy = $arr;
        $elem = array_splice($arrcopy, $i, 1); // removes and returns the i'th element
        if (sizeof($arrcopy) > 0) {
            depth_picker($arrcopy, $temp_string ." " . $elem[0], $collect);
        } else {
            $collect []= $temp_string. " " . $elem[0];
        }   
    }   
}

$collect = array();
depth_picker($array, "", $collect);
print_r($collect);

?></code>

Explanation

1. The depth_picker function recursively traverses the array and constructs combinations based on the order of elements.
2. Each recursive call operates on a copy of the array, removing one element at a time.
3. If the array copy is non-empty, recursion continues with the modified array and the current string with the removed element appended.
4. If the array copy is empty, the current string with the last element appended is added to the collect array.
5. The print_r function displays the collected combinations.

Output

Using the provided array, the code generates the following combinations:

Array
(
    [0] =>  Alpha
    [1] =>  Alpha Beta
    [2] =>  Alpha Beta Gamma
    [3] =>  Alpha Beta Gamma Sigma
    [4] =>  Alpha Beta Sigma
    [5] =>  Alpha Beta Sigma Gamma
    [6] =>  Alpha Gamma
    [7] =>  Alpha Gamma Beta
    [8] =>  Alpha Gamma Beta Sigma
    [9] =>  Alpha Gamma Sigma
    [10] =>  Alpha Gamma Sigma Beta
    [11] =>  Alpha Sigma
    [12] =>  Alpha Sigma Beta
    [13] =>  Alpha Sigma Beta Gamma
    [14] =>  Alpha Sigma Gamma
    [15] =>  Alpha Sigma Gamma Beta
    [16] =>  Beta
    [17] =>  Beta Alpha
    [18] =>  Beta Alpha Gamma
    [19] =>  Beta Alpha Gamma Sigma
    [20] =>  Beta Alpha Sigma
    [21] =>  Beta Alpha Sigma Gamma
    [22] =>  Beta Gamma
    [23] =>  Beta Gamma Alpha
    [24] =>  Beta Gamma Alpha Sigma
    [25] =>  Beta Gamma Sigma
    [26] =>  Beta Gamma Sigma Alpha
    [27] =>  Beta Sigma
    [28] =>  Beta Sigma Alpha
    [29] =>  Beta Sigma Alpha Gamma
    [30] =>  Beta Sigma Gamma
    [31] =>  Beta Sigma Gamma Alpha
    [32] =>  Gamma
    [33] =>  Gamma Alpha
    [34] =>  Gamma Alpha Beta
    [35] =>  Gamma Alpha Beta Sigma
    [36] =>  Gamma Alpha Sigma
    [37] =>  Gamma Alpha Sigma Beta
    [38] =>  Gamma Beta
    [39] =>  Gamma Beta Alpha
    [40] =>  Gamma Beta Alpha Sigma
    [41] =>  Gamma Beta Sigma
    [42] =>  Gamma Beta Sigma Alpha
    [43] =>  Gamma Sigma
    [44] =>  Gamma Sigma Alpha
    [45] =>  Gamma Sigma Alpha Beta
    [46] =>  Gamma Sigma Beta
    [47] =>  Gamma Sigma Beta Alpha
    [48] =>  Sigma
    [49] =>  Sigma Alpha
    [50] =>  Sigma Alpha Beta
    [51] =>  Sigma Alpha Beta Gamma
    [52] =>  Sigma Alpha Gamma
    [53] =>  Sigma Alpha Gamma Beta
    [54] =>  Sigma Beta
    [55] =>  Sigma Beta Alpha
    [56] =>  Sigma Beta Alpha Gamma
    [57] =>  Sigma Beta Gamma
    [58] =>  Sigma Beta Gamma Alpha
    [59] =>  Sigma Gamma
    [60] =>  Sigma Gamma Alpha
    [61] =>  Sigma Gamma Alpha Beta
    [62] =>  Sigma Gamma Beta
    [63] =>  Sigma Gamma Beta Alpha
)

This output contains all possible combinations and arrangements, fulfilling the specified requirements of the problem.

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