PHP implements Cartesian product algorithm

Concept

In mathematics, the Cartesian product (Cartesian product) of two sets X and Y, also known as the direct product, is expressed as X × Y. Suppose A and B are any two sets. Take any element x from set A and take any element y from set B to form an ordered pair (x, y). Take such an ordered pair as a new Elements, the set composed of all of them is called the direct product of set A and set B, denoted as A×B, that is, A×B={(x, y)|x∈A and y∈B}.

Assume that set A={a, b} and set B={0, 1, 2}, then the Cartesian product of the two sets is {(a, 0), (a, 1), ( a, 2), (b, 0), (b, 1), (b, 2)}.

Example

Given three domains:

D1 = { 张清玫，刘逸 }
D2 = {计算机专业，信息专业}
D3 = {李勇，刘晨，王敏}

Then the Cartesian product D of D1, D2, D3 = D1×D2×D3, Equal to:

{
    (张清玫, 计算机专业, 李勇),
    (张清玫, 计算机专业, 刘晨),
    (张清玫, 计算机专业, 王敏),
    (张清玫, 信息专业, 李勇),
    (张清玫, 信息专业, 刘晨),
    (张清玫, 信息专业, 王敏),
    (刘逸, 计算机专业, 李勇),
    (刘逸, 计算机专业, 刘晨),
    (刘逸, 计算机专业, 王敏),
    (刘逸, 信息专业, 李勇),
    (刘逸, 信息专业, 刘晨),
    (刘逸, 信息专业, 王敏)
}

In this way, each element in the three sets D1, D2, and D3 is combined correspondingly to form a huge set group. In this example, there will be 2X2X3=12 elements in D. If a set has 1000 elements and there are 3 such sets, the new set composed of their Cartesian product will reach one billion elements. If a set is infinite, then the new set will have infinite elements.

PHP code - Output array form

function Descartes()
{
    $t = func_get_args();                                    // 获取传入的参数
    if (func_num_args() == 1) {                               // 判断参数个数是否为1
        return call_user_func_array(__FUNCTION__, $t[0]);  // 回调当前函数，并把第一个数组作为参数传入
    }
    $a = array_shift($t);        // 将 $t 中的第一个元素移动到 $a 中，$t 中索引值重新排序
    if ( !is_array($a)) {
        $a = [$a];
    }
    $a = array_chunk($a, 1);     // 分割数组 $a ，为每个单元1个元素的新数组
    do {
        $r = [];
        $b = array_shift($t);
        if ( !is_array($b)) {
            $b = [$b];
        }
        foreach ($a as $p) {
            foreach (array_chunk($b, 1) as $q) {
                $r[] = array_merge($p, $q);
            }
        }
        $a = $r;
    } while ($t);
    return $r;
}

Usage:

$arr = [
    [
        '张清玫',
        '刘逸'
    ],
    [
        '计算机专业',
        '信息管理与信息系统专业',
        '电子商务专业'
    ],
    [
        '2018级',
        '2017级'
    ]
];
$r = Descartes($arr);

Effect:

array(12) {
  [0]=>
  array(3) {
    [0]=>
    string(9) "张清玫"
    [1]=>
    string(15) "计算机专业"
    [2]=>
    string(7) "2018级"
  }
  [1]=>
  array(3) {
    [0]=>
    string(9) "张清玫"
    [1]=>
    string(15) "计算机专业"
    [2]=>
    string(7) "2017级"
  }
  [2]=>
  array(3) {
    [0]=>
    string(9) "张清玫"
    [1]=>
    string(33) "信息管理与信息系统专业"
    [2]=>
    string(7) "2018级"
  }
  [3]=>
  array(3) {
    [0]=>
    string(9) "张清玫"
    [1]=>
    string(33) "信息管理与信息系统专业"
    [2]=>
    string(7) "2017级"
  }
  [4]=>
  array(3) {
    [0]=>
    string(9) "张清玫"
    [1]=>
    string(18) "电子商务专业"
    [2]=>
    string(7) "2018级"
  }
  [5]=>
  array(3) {
    [0]=>
    string(9) "张清玫"
    [1]=>
    string(18) "电子商务专业"
    [2]=>
    string(7) "2017级"
  }
  [6]=>
  array(3) {
    [0]=>
    string(6) "刘逸"
    [1]=>
    string(15) "计算机专业"
    [2]=>
    string(7) "2018级"
  }
  [7]=>
  array(3) {
    [0]=>
    string(6) "刘逸"
    [1]=>
    string(15) "计算机专业"
    [2]=>
    string(7) "2017级"
  }
  [8]=>
  array(3) {
    [0]=>
    string(6) "刘逸"
    [1]=>
    string(33) "信息管理与信息系统专业"
    [2]=>
    string(7) "2018级"
  }
  [9]=>
  array(3) {
    [0]=>
    string(6) "刘逸"
    [1]=>
    string(33) "信息管理与信息系统专业"
    [2]=>
    string(7) "2017级"
  }
  [10]=>
  array(3) {
    [0]=>
    string(6) "刘逸"
    [1]=>
    string(18) "电子商务专业"
    [2]=>
    string(7) "2018级"
  }
  [11]=>
  array(3) {
    [0]=>
    string(6) "刘逸"
    [1]=>
    string(18) "电子商务专业"
    [2]=>
    string(7) "2017级"
  }
}

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