[英]Algorithm for permutations
I am looking for an efficient combinations function that would take into account the order of the array. 我正在寻找一种有效的组合函数,该函数应考虑数组的顺序。 For example I want to generate all of the combinations of "hello world" but I don't want any of it reversed "world hello".
例如,我想生成“ hello world”的所有组合,但我不希望其中任何一个都反转为“ world hello”。 I currently have a combinations function but it's too much.
我目前有一个组合功能,但是太多了。
Simple example : 简单的例子:
$text = "Hello World"
$arr = explode(" ",$text); // string to array
And gives: 并给出:
$result = combo_function($arr);
var_dump($result);
"Hello World"
"Hello"
"World"
I do NOT want the inverse: 我不希望相反:
"World Hello"
Currently I am using this: 目前,我正在使用此:
// careful, this is very labor intensive ( O(n^k) )
public function buildSearchCombinations(&$set, &$results)
{
for ($i = 0; $i < count($set); $i++) {
$results[] = (string) $set[$i];
$tempset = $set;
array_splice($tempset, $i, 1);
$tempresults = array();
$this->buildSearchCombinations($tempset, $tempresults);
foreach ($tempresults as $res) {
$results[] = trim((string) $set[$i]) . " " . (string) trim($res);
}
}
}
I have a rather odd solution to this: 我对此有一个相当奇怪的解决方案:
<?php
function supersetmember($set, $index) {
$keys = array_reverse(str_split(decbin($index)));
$member = [];
foreach ($keys as $k => $v) {
if ($v == 1) {
$member[] = $set[$k];
}
}
return $member;
}
$text = "Hello World";
$arr = explode(" ",$text);
$total = pow(2,count($arr)); //Total permutations on size of set n is 2^n
$superset = [];
for ($i = 0;$i < $total;$i++) {
$superset[] = supersetmember($arr,$i);
}
print_r($superset);
Explanation: 说明:
There's 2^n sets that constitute a set of size n (including the empty set). 有2 ^ n个集合构成大小为n的集合(包括空集合)。 You can map each of those sets as a natural number from 0 to (n-1).
您可以将每个集合映射为0到(n-1)之间的自然数。 If you convert that number to binary then the digits that are 1 will indicate which members of the original set your subset will contain.
如果将该数字转换为二进制,则数字1将指示您的子集将包含原始集合的哪些成员。 Example:
例:
Set = (A,B); 设置=(A,B);
Superset member 2(decimal) = 10 (binary) which means the subset will include the second but not first member (we read the number from right to left as in from least significant to most significant digit). 超集成员2(十进制)= 10(二进制),这意味着该子集将包括第二个成员但不包括第一个成员(我们从右到左读取数字,从最低有效位到最高有效位)。
The advantage of doing this is that you have a sort of a "fausset" algorithm (function supersetmember) which you give it a set and the subset you want and you get that subset. 这样做的好处是,您有一种“模糊集合”算法(函数超集成员),可以为其提供一个集合和所需的子集,然后获得该子集。
The complexity of getting a single subset in the current version is O(n)
but if you implement it with bit shifting you can reduce it to O(log n)
In total the algorithm will be O(2^n)
which is unavoidable because there are O(2^n)
subsets to be generated. 在当前版本中获取单个子集的复杂度为
O(n)
但如果通过位移实现它,则可以将其降低为O(log n)
总的来说,算法将为O(2^n)
,这是不可避免的,因为有O(2^n)
个子集要生成。
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