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Apache Commons Text is a library focused on algorithms working on strings.
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/*
* 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 org.apache.commons.text.similarity;
import java.util.Arrays;
/**
* An algorithm for measuring the difference between two character sequences.
*
*
* 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).
*
*
* This code has been adapted from Apache Commons Lang 3.3.
*
*
* @since 1.0
*/
public class LevenshteinDistance implements EditDistance {
/**
* Singleton instance.
*/
private static final LevenshteinDistance INSTANCE = new LevenshteinDistance();
/**
* Gets the default instance.
*
* @return The default instance
*/
public static LevenshteinDistance getDefaultInstance() {
return INSTANCE;
}
/**
* Find the Levenshtein distance between two CharSequences if it's less than or equal to a given threshold.
*
*
* This implementation follows from Algorithms on Strings, Trees and Sequences by Dan Gusfield and Chas Emerick's implementation of the Levenshtein distance
* algorithm from http://www.merriampark.com/ld.htm
*
*
*
* 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
*
*
* @param left the first SimilarityInput, must not be null
* @param right the second SimilarityInput, must not be null
* @param threshold the target threshold, must not be negative
* @return result distance, or -1
*/
private static int limitedCompare(SimilarityInput left, SimilarityInput right, final int threshold) { // NOPMD
if (left == null || right == null) {
throw new IllegalArgumentException("CharSequences 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:
*
* 1 2 3 4 5 1 |#|#| | | | 2 |#|#|#| | | 3 | |#|#|#| | 4 | | |#|#|#| 5 | | | |#|#| 6 | | | | |#| 7 | | | | | |
*
* 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;
}
if (m == 0) {
return n <= threshold ? n : -1;
}
if (n > m) {
// swap the two strings to consume less memory
final SimilarityInput tmp = left;
left = right;
right = tmp;
n = m;
m = right.length();
}
// the edit distance cannot be less than the length difference
if (m - n > threshold) {
return -1;
}
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 E rightJ = right.at(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);
// ignore entry left of leftmost
if (min > 1) {
d[min - 1] = Integer.MAX_VALUE;
}
int lowerBound = Integer.MAX_VALUE;
// iterates through [min, max] in s
for (int i = min; i <= max; i++) {
if (left.at(i - 1).equals(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]);
}
lowerBound = Math.min(lowerBound, d[i]);
}
// if the lower bound is greater than the threshold, then exit early
if (lowerBound > threshold) {
return -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;
}
/**
* Finds the Levenshtein distance between two Strings.
*
*
* A higher score indicates a greater distance.
*
*
*
* The previous implementation of the Levenshtein distance algorithm was from
*
* https://web.archive.org/web/20120526085419/http://www.merriampark.com/ldjava.htm
*
*
*
* This implementation only need one single-dimensional arrays of length s.length() + 1
*
*
*
* 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
*
*
* @param left the first CharSequence, must not be null
* @param right the second CharSequence, must not be null
* @return result distance, or -1
* @throws IllegalArgumentException if either CharSequence input is {@code null}
*/
private static int unlimitedCompare(SimilarityInput left, SimilarityInput right) {
if (left == null || right == null) {
throw new IllegalArgumentException("CharSequences 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;
}
if (m == 0) {
return n;
}
if (n > m) {
// swap the input strings to consume less memory
final SimilarityInput 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;
E 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.at(j - 1);
p[0] = j;
for (i = 1; i <= n; i++) {
upper = p[i];
cost = left.at(i - 1).equals(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];
}
/**
* 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()
* @deprecated Use {@link #getDefaultInstance()}.
*/
@Deprecated
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;
}
/**
* Computes the Levenshtein distance between two Strings.
*
*
* A higher score indicates a greater distance.
*
*
*
* The previous implementation of the Levenshtein distance algorithm was from
* http://www.merriampark.com/ld.htm
*
*
*
* 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.
* This implementation of the Levenshtein distance algorithm is from
* http://www.merriampark.com/ldjava.htm
*
*
*
* 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
*
*
* @param left the first input, must not be null
* @param right the second input, must not be null
* @return result distance, or -1
* @throws IllegalArgumentException if either String input {@code null}
*/
@Override
public Integer apply(final CharSequence left, final CharSequence right) {
return apply(SimilarityInput.input(left), SimilarityInput.input(right));
}
/**
* Computes the Levenshtein distance between two inputs.
*
*
* A higher score indicates a greater distance.
*
*
*
* 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
*
*
* @param The type of similarity score unit.
* @param left the first input, must not be null.
* @param right the second input, must not be null.
* @return result distance, or -1.
* @throws IllegalArgumentException if either String input {@code null}.
* @since 1.13.0
*/
public Integer apply(final SimilarityInput left, final SimilarityInput right) {
if (threshold != null) {
return limitedCompare(left, right, threshold);
}
return unlimitedCompare(left, right);
}
/**
* Gets the distance threshold.
*
* @return The distance threshold
*/
public Integer getThreshold() {
return threshold;
}
}
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