找到分区集的每个可能组合的更好方法

时间:2012-04-20 16:34:16

标签: php algorithm recursion set cartesian

我需要找到N组X长度的所有可能组合,没有重复且按特定顺序,例如。

input:  [["A"], ["B"], ["C"]]
output: [["A","B","C"],["A","B"],["A","C"],["B","C"],["A"],["B"],["C"]]

规则:

  • 分区的数量或大小不固定。
  • 每个组合中每个分区只有一个成员。
  • 更多成员的组合优先级更高。
  • 之前在输入中的成员优先于后来的成员。

更大集合的另一个例子:

input:  [["A","B"],["C","D","E"],["F"]]
output: [["A","C","F"],["A","D","F"],["A","E","F"],["B","C","F"],["B","D","F"],["B","E","F"],["A","C"],["A","D"],["A","E"],["B","C"],["B","D"],["B","E"],["A","F"],["B","F"],["C","F"],["D","F"],["E","F"],["A"],["B"],["C"],["D"],["E"],["F"]]

我已经设法通过将幂集函数的输出与笛卡尔积函数相结合来获得我想要的输出,但结果代码不是非常简洁或漂亮。我想知道这是否可以通过递归更好地完成?

这是我已经拥有的:

$test = json_decode('[["A"]]');
$test1 = json_decode('[["A"], ["B"], ["C"]]');
$test2 = json_decode('[["A", "B"], ["C", "D", "E"], ["F"]]');

/**
 * Returns a power set of the input array.
 */                   
function power_set($in, $minLength = 1) {
  $count = count($in);
  $members = pow(2,$count);
  $return = array();

  for ($i = 0; $i < $members; $i++) {
    $b = sprintf("%0".$count."b",$i);
    $out = array();

    for ($j = 0; $j < $count; $j++) {
      if ($b[$j] == '1') {
        $out[] = $in[$j];
      }
    }
    if (count($out) >= $minLength) {
      $return[] = $out;
    }
  }

  return $return;
}

/**
 * Returns the cartesian product of the input arrays.
 */
function array_cartesian() {
  $_ = func_get_args();

  if(count($_) == 0) {
    return array(array());
  }

  $a = array_shift($_);
  $c = call_user_func_array(__FUNCTION__, $_);
  $r = array();

  foreach($a as $v) {
    foreach($c as $p) {
      $r[] = array_merge(array($v), $p);
    }
  }

  return $r;
}

/**
 * Used with usort() to sort arrays by length, desc.
 * If two arrays are the same length, then a sum of 
 * their keys is taken, with lower values coming first.
 */
function arraySizeDesc($a, $b) {
  if(count($a) === count($b)) {
    if(array_sum($a) === array_sum($b)) {
      return 0;
    }

    return (array_sum($a) > array_sum($b)) ? 1 : -1;
  }

  return (count($a) < count($b)) ? 1 : -1;
}

/**
 * Calculates a powerset of the input array and then uses
 * this to generate cartesian products of each combination
 * until all possible combinations are aquired.
 */
function combinations($in) {
 $out = array();
 $powerSet = power_set(array_keys($in));
 usort($powerSet, 'arraySizeDesc');

 foreach($powerSet as $combination) {
   if(count($combination) < 2) {
     foreach($in[$combination[0]] as $value) {
       $out[] = array($value);
     }
   } else {
     $sets = array();

     foreach($combination as $setId) {
       $sets[] = $in[$setId];
     }

     $out = array_merge($out, call_user_func_array('array_cartesian', $sets));
   }
 }

 return $out;
}

echo "input: ".json_encode($test2);
echo "<br />output: ".json_encode(combinations($test2));

我意识到输出的大小可以非常快速地增长,但是输入通常只包含1-5组1-50个成员,所以它不需要处理大量的集合。

2 个答案:

答案 0 :(得分:1)

基本上,您的方法是生成输入的功率集,然后进行后处理以获得所需的输出。

通过尝试直接解决它,可以采用不同的方法。我遇到的一个解决方案如下。

给定输入A = [A 1 ,...],假设问题已经解决了A \ A 1 。将此解决方案称为S'。我们如何将S'转换为整个A的解S?这主要是通过制作S'的两个副本。我们将A 1 的元素分发到第一个副本中。我们称之为新序列S''。因此,A的解决方案变成S'和S'的串联。

算法,

Input: A = [ A1, A2, ..., An]

combine(A, i, n):

  1. if n < i
  2. return []
  3. if n == i
  4. return singletons(Ai)
  5. S' = combine(A, i + 1, n)
  6. S'' = [a, S'], for each a in Ai
  7. return [S'', S']
  8. 函数singletons返回输入集的一元素子集。所以,如果输入[1,2,3],它将返回[[1],[2],[3]]。

    如果你在这里和那里忽略一些松散的序列连接,那么这个方法应该是明确的......

    祝你好运!

答案 1 :(得分:0)

尝试

$test = array ();
$test [0] = json_decode ( '[["A"]]', true );
$test [1] = json_decode ( '[["A"], ["B"], ["C"]]', true );
$test [2] = json_decode ( '[["A", "B"], ["C", "D", "E"], ["F"]]', true );


echo "<pre>" ;
$set = array ();
getSet ( $test, $set );
$set = array_values(array_unique($set));
$return = powerSet($set,1,3);
print_r ($return);

输出

Array
(
    [0] => Array
        (
            [0] => F
        )

    [1] => Array
        (
            [0] => E
        )

    [2] => Array
        (
            [0] => E
            [1] => F
        )

    [3] => Array
        (
            [0] => D
        )

    [4] => Array
        (
            [0] => D
            [1] => F
        )

    [5] => Array
        (
            [0] => D
            [1] => E
        )

    [6] => Array
        (
            [0] => D
            [1] => E
            [2] => F
        )

    [7] => Array
        (
            [0] => C
        )

    [8] => Array
        (
            [0] => C
            [1] => F
        )

    [9] => Array
        (
            [0] => C
            [1] => E
        )

    [10] => Array
        (
            [0] => C
            [1] => E
            [2] => F
        )

    [11] => Array
        (
            [0] => C
            [1] => D
        )

    [12] => Array
        (
            [0] => C
            [1] => D
            [2] => F
        )

    [13] => Array
        (
            [0] => C
            [1] => D
            [2] => E
        )

    [14] => Array
        (
            [0] => B
        )

    [15] => Array
        (
            [0] => B
            [1] => F
        )

    [16] => Array
        (
            [0] => B
            [1] => E
        )

    [17] => Array
        (
            [0] => B
            [1] => E
            [2] => F
        )

    [18] => Array
        (
            [0] => B
            [1] => D
        )

    [19] => Array
        (
            [0] => B
            [1] => D
            [2] => F
        )

    [20] => Array
        (
            [0] => B
            [1] => D
            [2] => E
        )

    [21] => Array
        (
            [0] => B
            [1] => C
        )

    [22] => Array
        (
            [0] => B
            [1] => C
            [2] => F
        )

    [23] => Array
        (
            [0] => B
            [1] => C
            [2] => E
        )

    [24] => Array
        (
            [0] => B
            [1] => C
            [2] => D
        )

    [25] => Array
        (
            [0] => A
        )

    [26] => Array
        (
            [0] => A
            [1] => F
        )

    [27] => Array
        (
            [0] => A
            [1] => E
        )

    [28] => Array
        (
            [0] => A
            [1] => E
            [2] => F
        )

    [29] => Array
        (
            [0] => A
            [1] => D
        )

    [30] => Array
        (
            [0] => A
            [1] => D
            [2] => F
        )

    [31] => Array
        (
            [0] => A
            [1] => D
            [2] => E
        )

    [32] => Array
        (
            [0] => A
            [1] => C
        )

    [33] => Array
        (
            [0] => A
            [1] => C
            [2] => F
        )

    [34] => Array
        (
            [0] => A
            [1] => C
            [2] => E
        )

    [35] => Array
        (
            [0] => A
            [1] => C
            [2] => D
        )

    [36] => Array
        (
            [0] => A
            [1] => B
        )

    [37] => Array
        (
            [0] => A
            [1] => B
            [2] => F
        )

    [38] => Array
        (
            [0] => A
            [1] => B
            [2] => E
        )

    [39] => Array
        (
            [0] => A
            [1] => B
            [2] => D
        )

    [40] => Array
        (
            [0] => A
            [1] => B
            [2] => C
        )

)

使用的功能

function powerSet($in, $minLength = 1, $max = 10) {
    $count = count ( $in );
    $members = pow ( 2, $count );
    $return = array ();
    for($i = 0; $i < $members; $i ++) {
        $b = sprintf ( "%0" . $count . "b", $i );
        $out = array ();
        for($j = 0; $j < $count; $j ++) {
            if ($b {$j} == '1')
                $out [] = $in [$j];
        }
        if (count ( $out ) >= $minLength && count ( $out ) <= $max) {
            $return [] = $out;
        }

    }
    return $return;
}

function getSet($array, &$vals) {
    foreach ( $array as $key => $value ) {

        if (is_array ( $value )) {

            getSet ( $value, $vals );

        } else {

            $vals [] = $value;
        }
    }

    return $vals;
}