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In information theory and computer science, the Levenshtein distance is a metric for measuring the amount of difference between two sequences (i.e. an edit distance). The Levenshtein distance between two strings is defined as the minimum number of edits needed to transform one string into the other, with the allowable edit operations being insertion, deletion, or substitution of a single character.
For example, the Levenshtein distance between "kitten" and "sitting" is 3, since the following three edits change one into the other, and there is no way to do it with fewer than three edits:
kitten sitten (substitution of 'k' with 's')
sitten sittin (substitution of 'e' with 'i')
sittin sitting (insert 'g' at the end).
The Levenshtein distance between "rosettacode", "raisethysword" is 8; The distance between two strings is same as that when both strings is reversed.package org.apache.lucene.search.spell;
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* Levenstein edit distance class.
*/
public final class LevensteinDistance implements StringDistance {
/**
* Optimized to run a bit faster than the static getDistance().
* In one benchmark times were 5.3sec using ctr vs 8.5sec w/ static method, thus 37% faster.
*/
public LevensteinDistance () {
}
//*****************************
// Compute Levenshtein distance: see org.apache.commons.lang.StringUtils#getLevenshteinDistance(String, String)
//*****************************
@Override
public float getDistance (String target, String other) {
char[] sa;
int n;
int p[]; //'previous' cost array, horizontally
int d[]; // cost array, horizontally
int _d[]; //placeholder to assist in swapping p and d
/*
The difference between this impl. and the previous is that, rather
than creating and retaining a matrix of size s.length()+1 by t.length()+1,
we maintain two single-dimensional arrays of length s.length()+1. The first, d,
is the 'current working' distance array that maintains the newest distance cost
counts as we iterate through the characters of String s. Each time we increment
the index of String t we are comparing, d is copied to p, the second int[]. Doing so
allows us to retain the previous cost counts as required by the algorithm (taking
the minimum of the cost count to the left, up one, and diagonally up and to the left
of the current cost count being calculated). (Note that the arrays aren't really
copied anymore, just switched...this is clearly much better than cloning an array
or doing a System.arraycopy() each time through the outer loop.)
Effectively, the difference between the two implementations is this one does not
cause an out of memory condition when calculating the LD over two very large strings.
*/
sa = target.toCharArray();
n = sa.length;
p = new int[n+1];
d = new int[n+1];
final int m = other.length();
if (n == 0 || m == 0) {
if (n == m) {
return 1;
}
else {
return 0;
}
}
// indexes into strings s and t
int i; // iterates through s
int j; // iterates through t
char t_j; // jth character of t
int cost; // cost
for (i = 0; i<=n; i++) {
p[i] = i;
}
for (j = 1; j<=m; j++) {
t_j = other.charAt(j-1);
d[0] = j;
for (i=1; i<=n; i++) {
cost = sa[i-1]==t_j ? 0 : 1;
// minimum of cell to the left+1, to the top+1, diagonally left and up +cost
d[i] = Math.min(Math.min(d[i-1]+1, p[i]+1), p[i-1]+cost);
}
// copy current distance counts to 'previous row' distance counts
_d = p;
p = d;
d = _d;
}
// our last action in the above loop was to switch d and p, so p now
// actually has the most recent cost counts
return 1.0f - ((float) p[n] / Math.max(other.length(), sa.length));
}
@Override
public int hashCode() {
return 163 * getClass().hashCode();
}
@Override
public boolean equals(Object obj) {
if (this == obj) return true;
if (null == obj) return false;
return (getClass() == obj.getClass());
}
@Override
public String toString() {
return "levenstein";
}
}