如何解决如何找到一组特定大小的元素集合,其中包括集合中可能的最大集合?
给定一个基数在1到6之间的有限集族,它们本身是可能元素的更大有限集的子集,我的目标是创建包含性最强的元素集,即所创建元素的集合。集合可用于从集合系列中创建最可能的集合。我不确定我是否正确地陈述了这个问题,因为自从我在学校学习这类问题以来已经有很长时间了,但是让我尝试通过一个例子来澄清一下。
以下是一组集合的示例,最大元素数为6:
{1029}
{1029}
{1049}
{1029,1049}
{1029,1049,1118,1125}
{1029,1112,1125,1505}
{1029,1094,1505,1525}
{1029,1138,1525}
{1049,1182,1525,1531}
这些集合是由更大的有限元素集创建的:
{1029,1531}
目标是创建不超过6个元素的集合,这些元素可用于重新创建族中的最大集合数。这是一个答案集的示例:
Created Set 1: {1029,1505}
创建的集合的元素可用于重新创建系列中的6个集合。
{1029}
{1029}
{1049}
{1029,1505}
希望这是有道理的。显然,集合的族和可能元素的集合要大得多。我还需要重复创建集合的过程,直到可以重新创建系列中的所有集合。
我真的在寻找一种算法解决方案,用任何编程语言或伪代码编写都是特别有用的,但是即使是我可以用来转换为代码的数学公式也很有帮助。如果我能弄清楚这种类型的问题的名字,我什至会很高兴,这样我自己就可以对它进行更有效的研究。谢谢!
解决方法
如我所见,这很简单。从术语上讲,我将给定的集合称为原始集合,然后将这些集合称为制造的集合。此问题与布景保护问题之间的主要区别在于,您不需要从原始的布景中选取所选择的布景。
当且仅当原始集合是所选集合的子集时,才可以从所选集合中“创建”原始集合。类似地,如果原始集合是所选集合并集的子集,则可以从所选集合的集合中创建原始集合。因此,如果原始集的并集是所选集的并集的子集,则可以创建所有原始集。因此,您可以通过采用原始集合的并集,然后将该联盟(按您希望的任何方式)划分为不超过6个元素的集合的集合来制造所选集合。
,好的,所以我想出了一个答案,尽管它可能不是有史以来最优化的解决方案。如果有人可以帮助我更快地运行它,或者可以帮助我以能够找到最佳前三名的方式编写它,我将不胜感激。这是我的代码,请注意,我正在使用数据结构“ Set”,可从https://github.com/php-ds
获得class ProductionOptimizer{
private int $CARDINALITY=6;
private CombinationsIterator $combinationsIterator;
private array $tickets;
private Set $threads;
public function __construct(array $array){
$this->tickets=$array;
$start = microtime(TRUE);
$this->threads=new Set();
foreach ($array as $ticketThreads){
foreach ($ticketThreads as $thread)
$this->threads->add($thread);
}
$end = microtime(TRUE);
// print_r($this->threads);
echo PHP_EOL."Creating the Set took " . ($end - $start) . " seconds to complete.";
$this->combinationsIterator=new CombinationsIterator($this->getThreadsAsArray(),6);
}
public function outputThreads() : void {
print_r($this->threads);
}
public function getThreadsAsArray() : array {
return $this->threads->toArray();
}
public function getCombinationsIterator() : CombinationsIterator{
return $this->combinationsIterator;
}
public function createNewCombinationsIterator(array $array,int $subsetCardinality=null) : CombinationsIterator {
if(is_null($subsetCardinality)) $subsetCardinality=$this->CARDINALITY;
$this->combinationsIterator=new CombinationsIterator($array,$subsetCardinality);
return $this->combinationsIterator;
}
public function removeFromSet(array $array){
// var_dump($this->threads);
echo "Removing Threads(before count :".$this->threads->count().")...".PHP_EOL;
$this->threads->remove(...$array);
// var_dump($this->threads);
echo "Removing Threads(after count: ".$this->threads->count().")...".PHP_EOL;
$this->combinationsIterator=new CombinationsIterator($this->getThreadsAsArray(),6);
}
public function getSet() : Set {
return $this->threads;
}
public function getThreads() : Set {
return $this->threads;
}
/* not need if using Set class */
/*
Set:
The code took 4.5061111450195E-5 seconds to complete.
This Function:
The code took 0.0054061412811279 seconds to complete.
*/
public function deduplicateArray($array){
array_walk_recursive($array,function($v) use (&$r){$r[]=$v;});
return array_values(array_unique($r));
}
}
class CombinationsIterator implements Iterator
{
protected $c = null;
protected $s = null;
protected $n = 0;
protected $k = 0;
protected $pos = 0;
function __construct($s,$k) {
if(is_array($s)) {
$this->s = array_values($s);
$this->n = count($this->s);
} else {
$this->s = (string) $s;
$this->n = strlen($this->s);
}
$this->k = $k;
$this->rewind();
}
function key() {
return $this->pos;
}
function current() {
$r = array();
for($i = 0; $i < $this->k; $i++)
$r[] = $this->s[$this->c[$i]];
return is_array($this->s) ? $r : implode('',$r);
}
function next() {
if($this->_next())
$this->pos++;
else
$this->pos = -1;
}
function rewind() {
$this->c = range(0,$this->k);
$this->pos = 0;
}
function valid() {
return $this->pos >= 0;
}
protected function _next() {
$i = $this->k - 1;
while ($i >= 0 && $this->c[$i] == $this->n - $this->k + $i)
$i--;
if($i < 0)
return false;
$this->c[$i]++;
while($i++ < $this->k - 1)
$this->c[$i] = $this->c[$i - 1] + 1;
return true;
}
}
,这是一些要测试的示例数据。这将获得前3个有序序列,并在每次迭代时从集合的范围中删除匹配的集合:
function humanReadableMemory($size)
{
$unit=array('b','kb','mb','gb','tb','pb');
return @round($size/pow(1024,($i=floor(log($size,1024)))),2).' '.$unit[$i];
}
$tickets = [
[1029],[1029],[1029,1049],1049,1080,1112,1125,1188],1125],1188,1278],1056,1138,1158,1182,1514,1531],1071,1076],1074,1075,1092,1093,1242,1523,1525],1094,1158],1221,1505],1278,1298],1298,1516],1138],1517],1317,1505,1242],1270,1524],1370,1317],[1038,1076,1177,1182],[1045,1048,1097,1100],[1046,[1049],[1049]
];
$po=new ProductionOptimizer($tickets);
$start = microtime(TRUE);
$end = microtime(TRUE);
echo "Current Memory Usage: ".humanReadableMemory(memory_get_usage()).PHP_EOL;
echo "Peak Memory Usage: ".humanReadableMemory(memory_get_peak_usage()).PHP_EOL;
echo "Starting Iterations and Combination Testing...".PHP_EOL;
$rankedOutput=[];
$start = microtime(TRUE);
for ($i=0;$i<3;$i++) {
$matchCountArray=[];$bestChoice=0;$bestChoiceId=-1;
foreach ($po->getCombinationsIterator() as $comboTest){
$combinationString=implode(",",$comboTest);
$matchCountArray[$combinationString]=0;
$comboTestSet=new Set($comboTest);
foreach ($tickets as $ticketIdx=>$ticketElements) {
$ticketElementsSet = new Set($ticketElements);
$testsArray[$combinationString]+=($comboTestSet->contains(...$ticketElements) ? 1 : 0);
}
if ($matchCountArray[$combinationString]>$bestChoice) {
$bestChoice = $matchCountArray[$combinationString];
$bestChoiceId=$combinationString;
} else {
//trying to save memory
unset($matchCountArray[$combinationString]);
}
}
$currentBestChoiceSet=new Set(explode(",$bestChoiceId));
$currentUniverseSet=$po->getSet()->copy();
for($tmpJ=0;$tmpJ<$currentUniverseSet->count();$tmpJ++){
$testAgainstSet=$currentUniverseSet->get($tmpJ);
if ($currentBestChoiceSet->contains(...$testAgainstSet->toArray())){
$currentUniverseSet->remove($testAgainstSet);
}
}
$tickets = [];
foreach ($currentUniverseSet as $singleSet){
$tickets[]=$singleSet->toArray();
}
$po=new ProductionOptimizer($tickets);
$rankedOutput[$i]=["greatest_matching_sequence"=>$bestChoiceId,"coverage_count"=>$bestChoice];
}
echo "RankedOutput:".PHP_EOL;
var_dump($rankedOutput);
echo PHP_EOL;
$end = microtime(TRUE);
echo PHP_EOL."The code took " . ($end - $start) . " seconds to complete.".PHP_EOL;
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