1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * https://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.text.similarity;
18
19 import java.util.Arrays;
20
21 /**
22 * An algorithm for measuring the difference between two character sequences using the <a href="https://en.wikipedia.org/wiki/Levenshtein_distance">Levenshtein
23 * Distance</a>.
24 *
25 * <p>
26 * This is the number of changes needed to change one sequence into another, where each change is a single character modification (deletion, insertion or
27 * substitution).
28 * </p>
29 * <p>
30 * This code has been adapted from Apache Commons Lang 3.3.
31 * </p>
32 *
33 * @since 1.0
34 * @see <a href="https://en.wikipedia.org/wiki/Levenshtein_distance">Levenshtein Distance on Wikipedia</a>
35 * @see <a href="https://xlinux.nist.gov/dads/HTML/Levenshtein.html">Levenshtein Distance on NIST</a>
36 */
37 public class LevenshteinDistance implements EditDistance<Integer> {
38
39 /**
40 * The singleton instance.
41 */
42 private static final LevenshteinDistance INSTANCE = new LevenshteinDistance();
43
44 /**
45 * Gets the default instance.
46 *
47 * @return The default instance.
48 */
49 public static LevenshteinDistance getDefaultInstance() {
50 return INSTANCE;
51 }
52
53 /**
54 * Finds the Levenshtein distance between two CharSequences if it's less than or equal to a given threshold.
55 *
56 * <p>
57 * This implementation follows from Algorithms on Strings, Trees and Sequences by Dan Gusfield and Chas Emerick's implementation of the Levenshtein distance
58 * algorithm from <a href="http://www.merriampark.com/ld.htm">http://www.merriampark.com/ld.htm</a>
59 * </p>
60 *
61 * <pre>
62 * limitedCompare(null, *, *) = IllegalArgumentException
63 * limitedCompare(*, null, *) = IllegalArgumentException
64 * limitedCompare(*, *, -1) = IllegalArgumentException
65 * limitedCompare("","", 0) = 0
66 * limitedCompare("aaapppp", "", 8) = 7
67 * limitedCompare("aaapppp", "", 7) = 7
68 * limitedCompare("aaapppp", "", 6)) = -1
69 * limitedCompare("elephant", "hippo", 7) = 7
70 * limitedCompare("elephant", "hippo", 6) = -1
71 * limitedCompare("hippo", "elephant", 7) = 7
72 * limitedCompare("hippo", "elephant", 6) = -1
73 * </pre>
74 *
75 * @param left the first SimilarityInput, must not be null.
76 * @param right the second SimilarityInput, must not be null.
77 * @param threshold the target threshold, must not be negative.
78 * @return result distance, or -1
79 */
80 private static <E> int limitedCompare(SimilarityInput<E> left, SimilarityInput<E> right, final int threshold) { // NOPMD
81 if (left == null || right == null) {
82 throw new IllegalArgumentException("CharSequences must not be null");
83 }
84 if (threshold < 0) {
85 throw new IllegalArgumentException("Threshold must not be negative");
86 }
87
88 /*
89 * 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
90 * 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
91 * 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
92 * time until the distance is found; this is O(dm), where d is the distance.
93 *
94 * 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
95 * of the leftmost member We must ignore the entry above the rightmost member
96 *
97 * 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
98 * shorter of the two, the stripe will always run off to the upper right instead of the lower left of the matrix.
99 *
100 * 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
101 * matrix would look like so:
102 *
103 * <pre> 1 2 3 4 5 1 |#|#| | | | 2 |#|#|#| | | 3 | |#|#|#| | 4 | | |#|#|#| 5 | | | |#|#| 6 | | | | |#| 7 | | | | | | </pre>
104 *
105 * 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.
106 *
107 * Additionally, this implementation decreases memory usage by using two single-dimensional arrays and swapping them back and forth instead of
108 * 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
109 * the matrix and initially filling the arrays with large values so that entries we don't compute are ignored.
110 *
111 * See Algorithms on Strings, Trees and Sequences by Dan Gusfield for some discussion.
112 */
113
114 int n = left.length(); // length of left
115 int m = right.length(); // length of right
116
117 // if one string is empty, the edit distance is necessarily the length
118 // of the other
119 if (n == 0) {
120 return m <= threshold ? m : -1;
121 }
122 if (m == 0) {
123 return n <= threshold ? n : -1;
124 }
125
126 if (n > m) {
127 // swap the two strings to consume less memory
128 final SimilarityInput<E> tmp = left;
129 left = right;
130 right = tmp;
131 n = m;
132 m = right.length();
133 }
134
135 // the edit distance cannot be less than the length difference
136 if (m - n > threshold) {
137 return -1;
138 }
139
140 int[] p = new int[n + 1]; // 'previous' cost array, horizontally
141 int[] d = new int[n + 1]; // cost array, horizontally
142 int[] tempD; // placeholder to assist in swapping p and d
143
144 // fill in starting table values
145 final int boundary = Math.min(n, threshold) + 1;
146 for (int i = 0; i < boundary; i++) {
147 p[i] = i;
148 }
149 // these fills ensure that the value above the rightmost entry of our
150 // stripe will be ignored in following loop iterations
151 Arrays.fill(p, boundary, p.length, Integer.MAX_VALUE);
152 Arrays.fill(d, Integer.MAX_VALUE);
153
154 // iterates through t
155 for (int j = 1; j <= m; j++) {
156 final E rightJ = right.at(j - 1); // jth character of right
157 d[0] = j;
158
159 // compute stripe indices, constrain to array size
160 final int min = Math.max(1, j - threshold);
161 final int max = j > Integer.MAX_VALUE - threshold ? n : Math.min(n, j + threshold);
162
163 // ignore entry left of leftmost
164 if (min > 1) {
165 d[min - 1] = Integer.MAX_VALUE;
166 }
167
168 int lowerBound = Integer.MAX_VALUE;
169 // iterates through [min, max] in s
170 for (int i = min; i <= max; i++) {
171 if (left.at(i - 1).equals(rightJ)) {
172 // diagonally left and up
173 d[i] = p[i - 1];
174 } else {
175 // 1 + minimum of cell to the left, to the top, diagonally
176 // left and up
177 d[i] = 1 + Math.min(Math.min(d[i - 1], p[i]), p[i - 1]);
178 }
179 lowerBound = Math.min(lowerBound, d[i]);
180 }
181 // if the lower bound is greater than the threshold, then exit early
182 if (lowerBound > threshold) {
183 return -1;
184 }
185
186 // copy current distance counts to 'previous row' distance counts
187 tempD = p;
188 p = d;
189 d = tempD;
190 }
191
192 // if p[n] is greater than the threshold, there's no guarantee on it
193 // being the correct
194 // distance
195 if (p[n] <= threshold) {
196 return p[n];
197 }
198 return -1;
199 }
200
201 /**
202 * Finds the Levenshtein distance between two Strings.
203 *
204 * <p>
205 * A higher score indicates a greater distance.
206 * </p>
207 *
208 * <p>
209 * The previous implementation of the Levenshtein distance algorithm was from
210 * <a href="https://web.archive.org/web/20120526085419/http://www.merriampark.com/ldjava.htm">
211 * https://web.archive.org/web/20120526085419/http://www.merriampark.com/ldjava.htm</a>
212 * </p>
213 *
214 * <p>
215 * This implementation only need one single-dimensional arrays of length s.length() + 1
216 * </p>
217 *
218 * <pre>
219 * unlimitedCompare(null, *) = IllegalArgumentException
220 * unlimitedCompare(*, null) = IllegalArgumentException
221 * unlimitedCompare("","") = 0
222 * unlimitedCompare("","a") = 1
223 * unlimitedCompare("aaapppp", "") = 7
224 * unlimitedCompare("frog", "fog") = 1
225 * unlimitedCompare("fly", "ant") = 3
226 * unlimitedCompare("elephant", "hippo") = 7
227 * unlimitedCompare("hippo", "elephant") = 7
228 * unlimitedCompare("hippo", "zzzzzzzz") = 8
229 * unlimitedCompare("hello", "hallo") = 1
230 * </pre>
231 *
232 * @param left the first CharSequence, must not be null.
233 * @param right the second CharSequence, must not be null.
234 * @return result distance, or -1.
235 * @throws IllegalArgumentException if either CharSequence input is {@code null}.
236 */
237 private static <E> int unlimitedCompare(SimilarityInput<E> left, SimilarityInput<E> right) {
238 if (left == null || right == null) {
239 throw new IllegalArgumentException("CharSequences must not be null");
240 }
241 /*
242 * This implementation use two variable to record the previous cost counts, So this implementation use less memory than previous impl.
243 */
244 int n = left.length(); // length of left
245 int m = right.length(); // length of right
246
247 if (n == 0) {
248 return m;
249 }
250 if (m == 0) {
251 return n;
252 }
253 if (n > m) {
254 // swap the input strings to consume less memory
255 final SimilarityInput<E> tmp = left;
256 left = right;
257 right = tmp;
258 n = m;
259 m = right.length();
260 }
261 final int[] p = new int[n + 1];
262 // indexes into strings left and right
263 int i; // iterates through left
264 int j; // iterates through right
265 int upperLeft;
266 int upper;
267 E rightJ; // jth character of right
268 int cost; // cost
269 for (i = 0; i <= n; i++) {
270 p[i] = i;
271 }
272 for (j = 1; j <= m; j++) {
273 upperLeft = p[0];
274 rightJ = right.at(j - 1);
275 p[0] = j;
276
277 for (i = 1; i <= n; i++) {
278 upper = p[i];
279 cost = left.at(i - 1).equals(rightJ) ? 0 : 1;
280 // minimum of cell to the left+1, to the top+1, diagonally left and up +cost
281 p[i] = Math.min(Math.min(p[i - 1] + 1, p[i] + 1), upperLeft + cost);
282 upperLeft = upper;
283 }
284 }
285 return p[n];
286 }
287
288 /**
289 * Threshold.
290 */
291 private final Integer threshold;
292
293 /**
294 * Constructs a default instance that uses a version of the algorithm that does not use a threshold parameter.
295 *
296 * @see LevenshteinDistance#getDefaultInstance()
297 * @deprecated Use {@link #getDefaultInstance()}.
298 */
299 @Deprecated
300 public LevenshteinDistance() {
301 this(null);
302 }
303
304 /**
305 * Constructs a new instance. If the threshold is not null, distance calculations will be limited to a maximum length. If the threshold is null, the
306 * unlimited version of the algorithm will be used.
307 *
308 * @param threshold If this is null then distances calculations will not be limited. This may not be negative.
309 */
310 public LevenshteinDistance(final Integer threshold) {
311 if (threshold != null && threshold < 0) {
312 throw new IllegalArgumentException("Threshold must not be negative");
313 }
314 this.threshold = threshold;
315 }
316
317 /**
318 * Computes the Levenshtein distance between two Strings.
319 *
320 * <p>
321 * A higher score indicates a greater distance.
322 * </p>
323 *
324 * <p>
325 * The previous implementation of the Levenshtein distance algorithm was from
326 * <a href="http://www.merriampark.com/ld.htm">http://www.merriampark.com/ld.htm</a>
327 * </p>
328 *
329 * <p>
330 * Chas Emerick has written an implementation in Java, which avoids an OutOfMemoryError which can occur when my Java implementation is used with very large
331 * strings.<br>
332 * This implementation of the Levenshtein distance algorithm is from
333 * <a href="http://www.merriampark.com/ldjava.htm">http://www.merriampark.com/ldjava.htm</a>
334 * </p>
335 *
336 * <pre>
337 * distance.apply(null, *) = IllegalArgumentException
338 * distance.apply(*, null) = IllegalArgumentException
339 * distance.apply("","") = 0
340 * distance.apply("","a") = 1
341 * distance.apply("aaapppp", "") = 7
342 * distance.apply("frog", "fog") = 1
343 * distance.apply("fly", "ant") = 3
344 * distance.apply("elephant", "hippo") = 7
345 * distance.apply("hippo", "elephant") = 7
346 * distance.apply("hippo", "zzzzzzzz") = 8
347 * distance.apply("hello", "hallo") = 1
348 * </pre>
349 *
350 * @param left the first input, must not be null.
351 * @param right the second input, must not be null.
352 * @return result distance, or -1.
353 * @throws IllegalArgumentException if either String input {@code null}.
354 */
355 @Override
356 public Integer apply(final CharSequence left, final CharSequence right) {
357 return apply(SimilarityInput.input(left), SimilarityInput.input(right));
358 }
359
360 /**
361 * Computes the Levenshtein distance between two inputs.
362 *
363 * <p>
364 * A higher score indicates a greater distance.
365 * </p>
366 *
367 * <pre>
368 * distance.apply(null, *) = IllegalArgumentException
369 * distance.apply(*, null) = IllegalArgumentException
370 * distance.apply("","") = 0
371 * distance.apply("","a") = 1
372 * distance.apply("aaapppp", "") = 7
373 * distance.apply("frog", "fog") = 1
374 * distance.apply("fly", "ant") = 3
375 * distance.apply("elephant", "hippo") = 7
376 * distance.apply("hippo", "elephant") = 7
377 * distance.apply("hippo", "zzzzzzzz") = 8
378 * distance.apply("hello", "hallo") = 1
379 * </pre>
380 *
381 * @param <E> The type of similarity score unit.
382 * @param left the first input, must not be null.
383 * @param right the second input, must not be null.
384 * @return result distance, or -1.
385 * @throws IllegalArgumentException if either String input {@code null}.
386 * @since 1.13.0
387 */
388 public <E> Integer apply(final SimilarityInput<E> left, final SimilarityInput<E> right) {
389 if (threshold != null) {
390 return limitedCompare(left, right, threshold);
391 }
392 return unlimitedCompare(left, right);
393 }
394
395 /**
396 * Gets the distance threshold.
397 *
398 * @return The distance threshold.
399 */
400 public Integer getThreshold() {
401 return threshold;
402 }
403
404 }