使用阶乘原理通过阶乘获取一个一维数组中全部的组合情况

代码如下

<?php
/**
 * 使用阶乘原理，通过阶乘获取一个一维数组中全部的组合情况
 *
 * Created by PhpStorm.
 * User: Alex
 * Date: 2020/3/9
 * Time: 13:08
 */

namespace App\Handlers;


class FactorialHandler
{

    /**
     * 使用阶乘原理获取一维数组中全部的组合情况
     *
     * @param array $arr
     * @return array
     */
    public function getArrAllCombineByFactor(array $arr) : array
    {
        // 大于等于1 => n! = 1*2*3*4*5…………*(n-1)*n
        if (count($arr) > 1) {
            $combineArr = [];
            foreach ($arr as $k => $v) {
                // 除当前 key 以外的单元数组
                $temArr = $this->arrRmoveValueByKey($arr, $k);
                $sonCombineArr = $this->getArrAllCombineByFactor($temArr);
                foreach ($sonCombineArr as $value) {
                    $combineArr[] = $v . '|' . $value;
                }
            }
            return $combineArr;
        } else {
            return $arr;
        }
    }

    /**
     * 通过数组的 key 移除掉当前 key 所在的单元，返回除 key 单元以外的单元数组
     *
     * @param array $arr  原始数组
     * @param $k  需要移除数组单元的 key
     * @return array
     */
    public function arrRmoveValueByKey(array $arr, $k) : array
    {
        unset($arr[$k]);
        $arr = array_values($arr);
        return $arr;
    }

}

使用

$arr = ['1_1', '2_3', '4_6'];

$factorialInstance = new FactorialHandler();
$result = $factorialInstance->getArrAllCombineByFactor($arr);

var_dump($result);

返回结果

array:6 [
  0 => "1_1|2_3|4_6"
  1 => "1_1|4_6|2_3"
  2 => "2_3|1_1|4_6"
  3 => "2_3|4_6|1_1"
  4 => "4_6|1_1|2_3"
  5 => "4_6|2_3|1_1"
]

一维数组所有的组合情况（排列组合）

$array = array('Alpha', 'Beta', 'Gamma', 'Sigma');

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

    for ($i=0; $i<sizeof($arr);$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);

返回的结果

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

    .
    .
    .

    [59] =>  Sigma Gamma
    [60] =>  Sigma Gamma Alpha
    [61] =>  Sigma Gamma Alpha Beta
    [62] =>  Sigma Gamma Beta
    [63] =>  Sigma Gamma Beta Alpha
)