Getting All Possible Combinations in PHP: A Comprehensive Solution

Retrieving all possible combinations from a 1D array can be a complex task, especially when considering both combinations and permutations. While there are various approaches to this problem, one highly effective solution involves implementing a recursive function.

The recursive function, depth_picker(), performs depth-first search on the array, exploring all branches and combining elements to form combinations. It maintains a temporary string that is gradually modified with each element, while a collect array stores the final combinations. Let's examine how this function operates:

1. Base Case: If the temporary string is empty, it means that a standalone element is being considered. In this case, it is directly added to the collect array.
2. Recursive Exploration: When an element is to be combined, the function creates a copy of the original array and removes the current element from it. It then recursively calls depth_picker() on the modified array, passing the updated temporary string with the added element. If there are more elements to combine, it continues the recursive process.
3. Combinations and Permutations: By iterating through each element and recursively combining them, depth_picker() effectively generates all possible combinations and permutations without repetition. This approach ensures both variations of strings ('Alpha Beta' and 'Beta Alpha') are included in the final output.
4. Final Result: When the function has explored all combinations, the collect array contains the complete set of all possible combinations from the input array.

Implementation and Execution

To implement this depth-first search and retrieval of combinations, the following PHP code can be employed:

 0) {
            depth_picker($arrcopy, $temp_string ." " . $elem[0], $collect);
        } else {
            $collect []= $temp_string. " " . $elem[0];
        }
    }
}

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

?>

Upon execution, this code outputs the following array of all possible combinations and arrangements:

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 approach provides a comprehensive and efficient solution for obtaining all possible combinations of elements in an array, ensuring that both combinations and different arrangements are included in the output.