LevenshteinDistance.java
/*
* 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.
*/
package tech.tablesaw.util;
import java.util.Arrays;
/**
* An algorithm for measuring the difference between two character sequences.
*
* <p>This is the number of changes needed to change one sequence into another, where each change is
* a single character modification (deletion, insertion or substitution).
*
* <p>This code has been adapted from Apache Commons Lang 3.3.
*
* @since 1.0
*/
public class LevenshteinDistance {
/** Default instance. */
private static final LevenshteinDistance DEFAULT_INSTANCE = new LevenshteinDistance();
/** Threshold. */
private final Integer threshold;
/**
* This returns the default instance that uses a version of the algorithm that does not use a
* threshold parameter.
*
* @see LevenshteinDistance#getDefaultInstance()
*/
public LevenshteinDistance() {
this(null);
}
/**
* If the threshold is not null, distance calculations will be limited to a maximum length. If the
* threshold is null, the unlimited version of the algorithm will be used.
*
* @param threshold If this is null then distances calculations will not be limited. This may not
* be negative.
*/
public LevenshteinDistance(final Integer threshold) {
if (threshold != null && threshold < 0) {
throw new IllegalArgumentException("Threshold must not be negative");
}
this.threshold = threshold;
}
/**
* Find the Levenshtein distance between two Strings.
*
* <p>A higher score indicates a greater distance.
*
* <p>The previous implementation of the Levenshtein distance algorithm was from <a
* href="http://www.merriampark.com/ld.htm">http://www.merriampark.com/ld.htm</a>
*
* <p>Chas Emerick has written an implementation in Java, which avoids an OutOfMemoryError which
* can occur when my Java implementation is used with very large strings.<br>
* This implementation of the Levenshtein distance algorithm is from <a
* href="http://www.merriampark.com/ldjava.htm">http://www.merriampark.com/ldjava.htm</a>
*
* <pre>
* distance.apply(null, *) = IllegalArgumentException
* distance.apply(*, null) = IllegalArgumentException
* distance.apply("","") = 0
* distance.apply("","a") = 1
* distance.apply("aaapppp", "") = 7
* distance.apply("frog", "fog") = 1
* distance.apply("fly", "ant") = 3
* distance.apply("elephant", "hippo") = 7
* distance.apply("hippo", "elephant") = 7
* distance.apply("hippo", "zzzzzzzz") = 8
* distance.apply("hello", "hallo") = 1
* </pre>
*
* @param left the first string, must not be null
* @param right the second string, must not be null
* @return result distance, or -1
* @throws IllegalArgumentException if either String input {@code null}
*/
public Integer apply(final CharSequence left, final CharSequence right) {
if (threshold != null) {
return limitedCompare(left, right, threshold);
}
return unlimitedCompare(left, right);
}
/**
* Gets the default instance.
*
* @return the default instance
*/
public static LevenshteinDistance getDefaultInstance() {
return DEFAULT_INSTANCE;
}
/**
* Gets the distance threshold.
*
* @return the distance threshold
*/
public Integer getThreshold() {
return threshold;
}
/**
* Find the Levenshtein distance between two CharSequences if it's less than or equal to a given
* threshold.
*
* <p>This implementation follows from Algorithms on Strings, Trees and Sequences by Dan Gusfield
* and Chas Emerick's implementation of the Levenshtein distance algorithm from <a
* href="http://www.merriampark.com/ld.htm" >http://www.merriampark.com/ld.htm</a>
*
* <pre>
* limitedCompare(null, *, *) = IllegalArgumentException
* limitedCompare(*, null, *) = IllegalArgumentException
* limitedCompare(*, *, -1) = IllegalArgumentException
* limitedCompare("","", 0) = 0
* limitedCompare("aaapppp", "", 8) = 7
* limitedCompare("aaapppp", "", 7) = 7
* limitedCompare("aaapppp", "", 6)) = -1
* limitedCompare("elephant", "hippo", 7) = 7
* limitedCompare("elephant", "hippo", 6) = -1
* limitedCompare("hippo", "elephant", 7) = 7
* limitedCompare("hippo", "elephant", 6) = -1
* </pre>
*
* @param left the first string, must not be null
* @param right the second string, must not be null
* @param threshold the target threshold, must not be negative
* @return result distance, or -1
*/
private static int limitedCompare(
CharSequence left, CharSequence right, final int threshold) { // NOPMD
if (left == null || right == null) {
throw new IllegalArgumentException("Strings must not be null");
}
if (threshold < 0) {
throw new IllegalArgumentException("Threshold must not be negative");
}
/*
* This implementation only computes the distance if it's less than or
* equal to the threshold value, returning -1 if it's greater. The
* advantage is performance: unbounded distance is O(nm), but a bound of
* k allows us to reduce it to O(km) time by only computing a diagonal
* stripe of width 2k + 1 of the cost table. It is also possible to use
* this to compute the unbounded Levenshtein distance by starting the
* threshold at 1 and doubling each time until the distance is found;
* this is O(dm), where d is the distance.
*
* One subtlety comes from needing to ignore entries on the border of
* our stripe eg. p[] = |#|#|#|* d[] = *|#|#|#| We must ignore the entry
* to the left of the leftmost member We must ignore the entry above the
* rightmost member
*
* Another subtlety comes from our stripe running off the matrix if the
* strings aren't of the same size. Since string s is always swapped to
* be the shorter of the two, the stripe will always run off to the
* upper right instead of the lower left of the matrix.
*
* As a concrete example, suppose s is of length 5, t is of length 7,
* and our threshold is 1. In this case we're going to walk a stripe of
* length 3. The matrix would look like so:
*
* <pre>
* 1 2 3 4 5
* 1 |#|#| | | |
* 2 |#|#|#| | |
* 3 | |#|#|#| |
* 4 | | |#|#|#|
* 5 | | | |#|#|
* 6 | | | | |#|
* 7 | | | | | |
* </pre>
*
* Note how the stripe leads off the table as there is no possible way
* to turn a string of length 5 into one of length 7 in edit distance of
* 1.
*
* Additionally, this implementation decreases memory usage by using two
* single-dimensional arrays and swapping them back and forth instead of
* allocating an entire n by m matrix. This requires a few minor
* changes, such as immediately returning when it's detected that the
* stripe has run off the matrix and initially filling the arrays with
* large values so that entries we don't compute are ignored.
*
* See Algorithms on Strings, Trees and Sequences by Dan Gusfield for
* some discussion.
*/
int n = left.length(); // length of left
int m = right.length(); // length of right
// if one string is empty, the edit distance is necessarily the length
// of the other
if (n == 0) {
return m <= threshold ? m : -1;
} else if (m == 0) {
return n <= threshold ? n : -1;
}
if (n > m) {
// swap the two strings to consume less memory
final CharSequence tmp = left;
left = right;
right = tmp;
n = m;
m = right.length();
}
int[] p = new int[n + 1]; // 'previous' cost array, horizontally
int[] d = new int[n + 1]; // cost array, horizontally
int[] tempD; // placeholder to assist in swapping p and d
// fill in starting table values
final int boundary = Math.min(n, threshold) + 1;
for (int i = 0; i < boundary; i++) {
p[i] = i;
}
// these fills ensure that the value above the rightmost entry of our
// stripe will be ignored in following loop iterations
Arrays.fill(p, boundary, p.length, Integer.MAX_VALUE);
Arrays.fill(d, Integer.MAX_VALUE);
// iterates through t
for (int j = 1; j <= m; j++) {
final char rightJ = right.charAt(j - 1); // jth character of right
d[0] = j;
// compute stripe indices, constrain to array size
final int min = Math.max(1, j - threshold);
final int max = j > Integer.MAX_VALUE - threshold ? n : Math.min(n, j + threshold);
// the stripe may lead off of the table if s and t are of different
// sizes
if (min > max) {
return -1;
}
// ignore entry left of leftmost
if (min > 1) {
d[min - 1] = Integer.MAX_VALUE;
}
// iterates through [min, max] in s
for (int i = min; i <= max; i++) {
if (left.charAt(i - 1) == rightJ) {
// diagonally left and up
d[i] = p[i - 1];
} else {
// 1 + minimum of cell to the left, to the top, diagonally
// left and up
d[i] = 1 + Math.min(Math.min(d[i - 1], p[i]), p[i - 1]);
}
}
// copy current distance counts to 'previous row' distance counts
tempD = p;
p = d;
d = tempD;
}
// if p[n] is greater than the threshold, there's no guarantee on it
// being the correct
// distance
if (p[n] <= threshold) {
return p[n];
}
return -1;
}
/**
* Find the Levenshtein distance between two Strings.
*
* <p>A higher score indicates a greater distance.
*
* <p>The previous implementation of the Levenshtein distance algorithm was from <a
* href="https://web.archive.org/web/20120526085419/http://www.merriampark.com/ldjava.htm">
* https://web.archive.org/web/20120526085419/http://www.merriampark.com/ldjava.htm</a>
*
* <p>This implementation only need one single-dimensional arrays of length s.length() + 1
*
* <pre>
* unlimitedCompare(null, *) = IllegalArgumentException
* unlimitedCompare(*, null) = IllegalArgumentException
* unlimitedCompare("","") = 0
* unlimitedCompare("","a") = 1
* unlimitedCompare("aaapppp", "") = 7
* unlimitedCompare("frog", "fog") = 1
* unlimitedCompare("fly", "ant") = 3
* unlimitedCompare("elephant", "hippo") = 7
* unlimitedCompare("hippo", "elephant") = 7
* unlimitedCompare("hippo", "zzzzzzzz") = 8
* unlimitedCompare("hello", "hallo") = 1
* </pre>
*
* @param left the first String, must not be null
* @param right the second String, must not be null
* @return result distance, or -1
* @throws IllegalArgumentException if either String input {@code null}
*/
private static int unlimitedCompare(CharSequence left, CharSequence right) {
if (left == null || right == null) {
throw new IllegalArgumentException("Strings must not be null");
}
/*
This implementation use two variable to record the previous cost counts,
So this implementation use less memory than previous impl.
*/
int n = left.length(); // length of left
int m = right.length(); // length of right
if (n == 0) {
return m;
} else if (m == 0) {
return n;
}
if (n > m) {
// swap the input strings to consume less memory
final CharSequence tmp = left;
left = right;
right = tmp;
n = m;
m = right.length();
}
final int[] p = new int[n + 1];
// indexes into strings left and right
int i; // iterates through left
int j; // iterates through right
int upperLeft;
int upper;
char rightJ; // jth character of right
int cost; // cost
for (i = 0; i <= n; i++) {
p[i] = i;
}
for (j = 1; j <= m; j++) {
upperLeft = p[0];
rightJ = right.charAt(j - 1);
p[0] = j;
for (i = 1; i <= n; i++) {
upper = p[i];
cost = left.charAt(i - 1) == rightJ ? 0 : 1;
// minimum of cell to the left+1, to the top+1, diagonally left and up +cost
p[i] = Math.min(Math.min(p[i - 1] + 1, p[i] + 1), upperLeft + cost);
upperLeft = upper;
}
}
return p[n];
}
}