如何获取多个多维数组的所有可能交集？

Question

我在 PHP 中有两个数组，如下所示：

$array1 = array(array("1", "3", "4"), array("1", "4"));
$array2 = array(array("5", "4", "3", "2"), array("5", "3"));

现在我想得到这两个多维数组所有可能的交集。意味着我总共会得到 4 个数组：

$array1[0] & $array2[0]
$array1[1] & $array2[0]
$array1[0] & $array2[1]
$array1[1] & $array2[1]

我可以使用 array_intersect() 从一维数组中获取交集。但是如何才能得到多个多维数组的所有可能的交集呢？

Answer 1

这个foreach解决了我的问题

$array1= array(array("1","3","4"),array("1","4"));
$array2= array(array("5","4","3","2"),array("5","3"));
$result = array();
echo "<pre>";
foreach($array1 as $array1)
{
    foreach($array2 as $array3)
    {
        print_r($array3);
        $result[] = array_intersect($array1,$array3);
    }
}

print_r($result);

如果您有更好的解决方案，请改进它

Answer 2

这里我们创建了一个包含所有数组组合的数组，所以我们稍后可以取这些数组的交集。

数组组合

首先我们需要创建所有可能的数组组合。即：

c_{array 1} * c_{array 2} * ... * c_{array n}

_{"c" 就是数组的count()}

因此在您的具体示例中它将是：

c_{array 1} * c_{array 2} => 2 * 2 => 4 combinations

现在我们需要获取所有这些组合并将它们放入一个数组中。为此，我们从一个空的 $combinations 数组开始。然后我们遍历数组中的所有组合并将下一个数组合并到其中，直到我们得到所需的组合长度，在本例中为我们拥有的数组数量。

举个例子：

Array with the elements (Empty array is '[]'):

[
    [[1, 3, 4], [1, 4]],     //array 1
    [[5, 4, 3, 2], [5, 3]],  //array 2
]

           1* combination array    2* new array     //↓new combinations
                    ↓                   ↓           //↓for the next iteration
                                                    │
array NAN*:

    Combinations:
                  - []                              │  -> []
                                                       │
array 1:            ┌──────────────────────────────────┘
                    │                       
    Combinations:   v                       
                  - []             + [1, 3, 4]      │  -> [[1, 3, 4]]  
                  - []             + [1, 4]         │  -> [[1, 4]]   
                                                       │
array 2:            ┌──────────────────────────────────┘
                    │                       
    Combinations:   v                       
                  - [[1, 3, 4]]    + [5, 4, 3, 2]   │  -> [[1, 3, 4], [5, 4, 3, 2]]
                  - [[1, 3, 4]]    + [5, 3]         │  -> [[1, 3, 4], [5, 3]]
                  - [[1, 4]]       + [5, 4, 3, 2]   │  -> [[1, 4], [5, 4, 3, 2]]
                  - [[1, 4]]       + [5, 3]         │  -> [[1, 4], [5, 3]] 
                                                    //↑ All combinations here

_{* NAN: 不是数字}

因此，正如您在上面的示例中看到的那样，我们现在拥有所有组合，其长度为我们拥有的所有数组的数量（4 个组合，长度为 2 个元素）。

如上例所示获取组合的代码为：

//The for loop makes sure we get the desired length of each combination
//(The amount of arrays which we have. Here 2)
for ($count = 0, $length = count($data); $count < $length; $count++) {  

    $tmp = [];

    foreach ($combinations as $v1) {  //1* combinations array

        foreach ($data[$count] as $v2)  //2* new array
            $tmp[] = array_merge($v1, [$v2]);  //Creating new combinations

    }

    $combinations = $tmp;  //Assigning the new combinations for the next iteration

}

在您的特定示例中生成此数组：

Array
(
[0] => Array  //Combination 1
    (
        [0] => Array
            (
                [0] => 1
                [1] => 3
                [2] => 4
            )

        [1] => Array
            (
                [0] => 5
                [1] => 4
                [2] => 3
                [3] => 2
            )

    )

[1] => Array  //Combination 2
    (
        [0] => Array
            (
                [0] => 1
                [1] => 3
                [2] => 4
            )

        [1] => Array
            (
                [0] => 5
                [1] => 3
            )

    )

[2] => Array  //Combination 3
    (
        [0] => Array
            (
                [0] => 1
                [1] => 4
            )

        [1] => Array
            (
                [0] => 5
                [1] => 4
                [2] => 3
                [3] => 2
            )

    )

[3] => Array  //Combination 4
    (
        [0] => Array
            (
                [0] => 1
                [1] => 4
            )

        [1] => Array
            (
                [0] => 5
                [1] => 3
            )

    )

)

数组交集

现在我们有了所有组合，我们可以使用 array_map() and get the array_intersect() of each combination. And since we don't know from how many arrays we want the intersection, we just use call_user_func_array() 遍历组合数组，例如

$intersections = array_map(function($v){
    //intersection of each combination, which we created
    return call_user_func_array("array_intersect", $v);
}, $combinations);

完整代码：

<?php

    $array1 = [[1, 3, 4], [1, 4]];
    $array2 = [[5, 4, 3, 2], [5, 3]];


    function getIntersections($data = []) {
        $combinations = [[]];

        for ($count = 0, $length = count($data); $count < $length; $count++) {
            $tmp = [];
            foreach ($combinations as $v1) {
                foreach ($data[$count] as $v2)
                    $tmp[] = array_merge($v1, [$v2]);
            }
            $combinations = $tmp;
        }

        $intersections = array_map(function($v){
            return call_user_func_array("array_intersect", $v);
        }, $combinations);

        return $intersections;

    }

    $intersections = getIntersections([$array1, $array2]);
    print_r($intersections);

?>

输出：

Array
(
    [0] => Array  //Intersection of: [1, 3, 4] && [5, 4, 3, 2]
        (
            [1] => 3
            [2] => 4
        )

    [1] => Array  //Intersection of: [1, 3, 4] && [5, 3]
        (
            [1] => 3
        )

    [2] => Array  //Intersection of: [1, 4] && [5, 4, 3, 2]
        (
            [1] => 4
        )

    [3] => Array  //Intersection of: [1, 4] && [5, 3]
        (
        )

)

如何获取多个多维数组的所有可能交集？

How to get all possible intersections of multiple multidimensional arrays?

php

arrays

array-intersect

multidimensional-array

数组组合

数组交集