Rabin-Karp算法的PHP实现

Question

嗨，我正在写一个PHP类来实现Rabin-Karp算法。我有关于重新散列部分的问题。此代码不包括匹配字符的一部分。我不得不停下来，因为它从来没有匹配散列代码，因为与重新散列的问题。有没有人能帮我解决这个问题。

<?php
 class RabinKarp
 {
    /** 
    * @var String
    */ 
    private $pattern ;
    private $patternHash ;
    private $text ;
    private $previousHash ;

    /** 
    * @var Integer
    */ 
    private $radix ;
    private $prime ;
    private $position ;

    /** 
    * Constructor 
    *
    * @param String $pattern - The pattern
    *
    */ 
    public function __construct($pattern) 
    {
        $this->pattern = $pattern;
        $this->radix = 256;
        $this->prime = 100007;
        $this->previousHash = "";
        $this->position = 0;
        $this->patternHash = $this->generateHash($pattern);
    }

    private function generateHash($key)
    {
        $charArray = str_split($key);
        $hash = 0;
        foreach($charArray as $char)
        {
             $hash = ($this->radix * $hash + ord($char)) % $this->prime;
        }

        return $hash;
    }

    public function search($character)
    {
        $this->text .= $character;
        if(strlen($this->text) < strlen($this->pattern))
        {
            return false;
        }
        else
        {
            $txtHash = 0;
            echo $this->previousHash . "<br/>";
            if(empty($this->previousHash))
            {
                $txtHash = $this->generateHash($this->text);
                $this->previousHash = $txtHash;
                $this->position = 0;
            }
            else
            {
                // The issue is here 
                $charArray = str_split($this->text);
                $txtHash = (($txtHash  + $this->prime) - $this->radix * strlen($this->pattern) * ord($charArray[$this->position]) % $this->prime) % $this->prime;
                $txtHash = ($txtHash * $this->radix + ord($character)) % $this->prime; 

                $this->previousHash = $txtHash;
            }

            if($txtHash == $this->patternHash)
            {
                echo "Hash Match found";
            }
        }

    }

 }

$x = new RabinKarp("ABC");
$x->search("Z");
$x->search("A");
$x->search("B");
$x->search("C");
?>

谢谢。

Answer 1

您要删除的字符(c表示缩写)对散列的贡献值为

ord(c) * radix^(length(pattern)-1)

因为字符在第一次进入匹配窗口时贡献了ord(c)，对于进入匹配窗口的每个length(pattern)-1字符，散列-因此也包括其贡献-与radix相乘，直到c最终离开它。

但是你在减去ord(c) * radix * length(pattern)

$charArray = str_split($this->text);
$txtHash = (($txtHash  + $this->prime)
             - $this->radix * strlen($this->pattern)
             * ord($charArray[$this->position]) % $this->prime)
           % $this->prime;
$txtHash = ($txtHash * $this->radix + ord($character)) % $this->prime;

此外，在计算中，您使用了变量$txtHash，该变量设置为0，应该是$this->previousHash，并且必须递增文本位置。

原则上，

$charArray = str_split($this->text);
$txtHash = (($this->previousHash  + $this->prime)
             - pow($this->radix, strlen($this->pattern)-1)
             * ord($charArray[$this->position]) % $this->prime)
           % $this->prime;
$txtHash = ($txtHash * $this->radix + ord($character)) % $this->prime;

$this->previousHash = $txtHash;
$this->position += 1;

是你必须要做的。

但是，除非模式非常短，否则pow($this->radix,strlen($this->pattern)-1)将溢出，因此您必须用模幂函数替换pow($this-radix, strlen($this->pattern)-1)

function mod_pow($base,$exponent,$modulus)
{
    $aux = 1;
    while($exponent > 0) {
        if ($exponent % 2 == 1) {
            $aux = ($aux * $base) % $modulus;
        }
        $base = ($base * $base) % $modulus;
        $exponent = $exponent/2;
    }
    return $aux;
}

(如果$modulus，也就是这里的$this->prime太大，这仍然会溢出)。相关的代码行将变为

$txtHash = (($this->previousHash  + $this->prime)
             - mod_pow($this->radix, strlen($this->pattern)-1, $this->prime)
             * ord($charArray[$this->position]) % $this->prime)
           % $this->prime;

那么你就会有一个潜在的巨大的低效

$this->text .= $character;
...
    $charArray = str_split($this->text);

如果字符串变得很长，连接和拆分可能需要很长时间(不确定PHP如何实现字符串和字符串操作，但它们可能不是恒定的时间)。您可能应该只保留字符串的相关部分，即在重新计算散列后删除第一个字符。