php-doc-en/reference/strings/functions/levenshtein.xml

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  <refentry id="function.levenshtein">
   <refnamediv>
    <refname>levenshtein</refname> 
    <refpurpose>
     Calculate Levenshtein distance between two strings
    </refpurpose>
   </refnamediv>
   <refsect1>
    <title>Description</title>
     <methodsynopsis>
      <type>int</type><methodname>levenshtein</methodname>
      <methodparam><type>string</type><parameter>str1</parameter></methodparam>
      <methodparam><type>string</type><parameter>str2</parameter></methodparam>
     </methodsynopsis>
     <methodsynopsis>
      <type>int</type><methodname>levenshtein</methodname>
      <methodparam><type>string</type><parameter>str1</parameter></methodparam>
      <methodparam><type>string</type><parameter>str2</parameter></methodparam>
      <methodparam><type>int</type><parameter>cost_ins</parameter></methodparam>
      <methodparam><type>int</type><parameter>cost_rep</parameter></methodparam>
      <methodparam><type>int</type><parameter>cost_del</parameter></methodparam>
     </methodsynopsis>
     <methodsynopsis>
      <type>int</type><methodname>levenshtein</methodname>
      <methodparam><type>string</type><parameter>str1</parameter></methodparam>
      <methodparam><type>string</type><parameter>str2</parameter></methodparam>
      <methodparam><type>function</type><parameter>cost</parameter></methodparam>
     </methodsynopsis>
    <para>
     This function returns the Levenshtein-Distance between the
     two argument strings or -1, if one of the argument strings
     is longer than the limit of 255 characters (255 should be
     more than enough for name or dictionary comparison, and 
     nobody serious would be doing genetic analysis with PHP).
    </para>
    <para>
     The Levenshtein distance is defined as the minimal number of
     characters you have to replace, insert or delete to transform
     <parameter>str1</parameter> into <parameter>str2</parameter>.
     The complexity of the algorithm is <literal>O(m*n)</literal>,
     where <literal>n</literal> and <literal>m</literal> are the
     length of <parameter>str1</parameter> and
     <parameter>str2</parameter> (rather good when compared to
     <function>similar_text</function>, which is O(max(n,m)**3),
     but still expensive).
    </para>
    <para>
     In its simplest form the function will take only the two
     strings as parameter and will calculate just the number of
     insert, replace and delete operations needed to transform
     <parameter>str1</parameter> into <parameter>str2</parameter>.
    </para>
    <para> 
     A second variant will take three additional parameters that
     define the cost of insert, replace and delete operations.  This
     is more general and adaptive than variant one, but not as
     efficient.
    </para>
    <para> 
     The third variant (which is not implemented yet) will be the most
     general and adaptive, but also the slowest alternative.  It will
     call a user-supplied function that will determine the cost for
     every possible operation.
    </para>
    <para>
     The user-supplied function will be called with the following
     arguments:
     <itemizedlist>
      <listitem>
       <simpara>
        operation to apply: 'I', 'R' or 'D'
       </simpara>
      </listitem>
      <listitem>
       <simpara>
        actual character in string 1
       </simpara>
      </listitem>
      <listitem>
       <simpara>
        actual character in string 2
       </simpara>
      </listitem>
      <listitem>
       <simpara>
        position in string 1
       </simpara>
      </listitem>
      <listitem>
       <simpara>
        position in string 2
       </simpara>
      </listitem>
      <listitem>
       <simpara>
        remaining characters in string 1
       </simpara>
      </listitem>
      <listitem>
       <simpara>
        remaining characters in string 2
       </simpara>
      </listitem>
     </itemizedlist>
     The user-supplied function has to return a positive integer
     describing the cost for this particular operation, but it may
     decide to use only some of the supplied arguments.
    </para>
    <para> 
     The user-supplied function approach offers the possibility to
     take into account the relevance of and/or difference between
     certain symbols (characters) or even the context those symbols
     appear in to determine the cost of insert, replace and delete
     operations, but at the cost of losing all optimizations done
     regarding cpu register utilization and cache misses that have
     been worked into the other two variants.
    </para>
    <para>
     See also <function>soundex</function>,
     <function>similar_text</function>, and
     <function>metaphone</function>.
    </para>
   </refsect1>
  </refentry>

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