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
18 package org.apache.commons.text.similarity;
19
20 import java.util.Arrays;
21
22 /**
23 * An algorithm for measuring the difference between two character sequences.
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 *
30 * @since 1.0
31 */
32 public class LevenshteinDetailedDistance implements EditDistance<LevenshteinResults> {
33
34 /**
35 * The singleton instance.
36 */
37 private static final LevenshteinDetailedDistance INSTANCE = new LevenshteinDetailedDistance();
38
39 /**
40 * Finds count for each of the three [insert, delete, substitute] operations needed. This is based on the matrix formed based on the two character sequence.
41 *
42 * @param <E> The type of similarity score unit.
43 * @param left character sequence which need to be converted from.
44 * @param right character sequence which need to be converted to.
45 * @param matrix two dimensional array containing.
46 * @param swapped tells whether the value for left character sequence and right character sequence were swapped to save memory.
47 * @return result object containing the count of insert, delete and substitute and total count needed.
48 */
49 private static <E> LevenshteinResults findDetailedResults(final SimilarityInput<E> left, final SimilarityInput<E> right, final int[][] matrix,
50 final boolean swapped) {
51 int delCount = 0;
52 int addCount = 0;
53 int subCount = 0;
54 int rowIndex = right.length();
55 int columnIndex = left.length();
56 int dataAtLeft = 0;
57 int dataAtTop = 0;
58 int dataAtDiagonal = 0;
59 int data = 0;
60 boolean deleted = false;
61 boolean added = false;
62 while (rowIndex >= 0 && columnIndex >= 0) {
63 if (columnIndex == 0) {
64 dataAtLeft = -1;
65 } else {
66 dataAtLeft = matrix[rowIndex][columnIndex - 1];
67 }
68 if (rowIndex == 0) {
69 dataAtTop = -1;
70 } else {
71 dataAtTop = matrix[rowIndex - 1][columnIndex];
72 }
73 if (rowIndex > 0 && columnIndex > 0) {
74 dataAtDiagonal = matrix[rowIndex - 1][columnIndex - 1];
75 } else {
76 dataAtDiagonal = -1;
77 }
78 if (dataAtLeft == -1 && dataAtTop == -1 && dataAtDiagonal == -1) {
79 break;
80 }
81 data = matrix[rowIndex][columnIndex];
82 // case in which the character at left and right are the same,
83 // in this case none of the counters will be incremented.
84 if (columnIndex > 0 && rowIndex > 0 && left.at(columnIndex - 1).equals(right.at(rowIndex - 1))) {
85 columnIndex--;
86 rowIndex--;
87 continue;
88 }
89 // handling insert and delete cases.
90 deleted = false;
91 added = false;
92 if (data - 1 == dataAtLeft && data <= dataAtDiagonal && data <= dataAtTop || dataAtDiagonal == -1 && dataAtTop == -1) { // NOPMD
93 columnIndex--;
94 if (swapped) {
95 addCount++;
96 added = true;
97 } else {
98 delCount++;
99 deleted = true;
100 }
101 } else if (data - 1 == dataAtTop && data <= dataAtDiagonal && data <= dataAtLeft || dataAtDiagonal == -1 && dataAtLeft == -1) { // NOPMD
102 rowIndex--;
103 if (swapped) {
104 delCount++;
105 deleted = true;
106 } else {
107 addCount++;
108 added = true;
109 }
110 }
111 // substituted case
112 if (!added && !deleted) {
113 subCount++;
114 columnIndex--;
115 rowIndex--;
116 }
117 }
118 return new LevenshteinResults(addCount + delCount + subCount, addCount, delCount, subCount);
119 }
120
121 /**
122 * Gets the default instance.
123 *
124 * @return The default instace
125 */
126 public static LevenshteinDetailedDistance getDefaultInstance() {
127 return INSTANCE;
128 }
129
130 /**
131 * Finds the Levenshtein distance between two CharSequences if it's less than or equal to a given threshold.
132 *
133 * <p>
134 * This implementation follows from Algorithms on Strings, Trees and Sequences by Dan Gusfield and Chas Emerick's implementation of the Levenshtein distance
135 * algorithm from <a href="http://www.merriampark.com/ld.htm" >http://www.merriampark.com/ld.htm</a>
136 * </p>
137 *
138 * <pre>
139 * limitedCompare(null, *, *) = IllegalArgumentException
140 * limitedCompare(*, null, *) = IllegalArgumentException
141 * limitedCompare(*, *, -1) = IllegalArgumentException
142 * limitedCompare("","", 0) = 0
143 * limitedCompare("aaapppp", "", 8) = 7
144 * limitedCompare("aaapppp", "", 7) = 7
145 * limitedCompare("aaapppp", "", 6)) = -1
146 * limitedCompare("elephant", "hippo", 7) = 7
147 * limitedCompare("elephant", "hippo", 6) = -1
148 * limitedCompare("hippo", "elephant", 7) = 7
149 * limitedCompare("hippo", "elephant", 6) = -1
150 * </pre>
151 *
152 * @param <E> The type of similarity score unit.
153 * @param left the first CharSequence, must not be null.
154 * @param right the second CharSequence, must not be null.
155 * @param threshold the target threshold, must not be negative.
156 * @return result distance, or -1.
157 */
158 private static <E> LevenshteinResults limitedCompare(SimilarityInput<E> left, SimilarityInput<E> right, final int threshold) { // NOPMD
159 if (left == null || right == null) {
160 throw new IllegalArgumentException("CharSequences must not be null");
161 }
162 if (threshold < 0) {
163 throw new IllegalArgumentException("Threshold must not be negative");
164 }
165 /*
166 * 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
167 * 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
168 * 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
169 * time until the distance is found; this is O(dm), where d is the distance.
170 *
171 * 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
172 * of the leftmost member We must ignore the entry above the rightmost member
173 *
174 * 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
175 * shorter of the two, the stripe will always run off to the upper right instead of the lower left of the matrix.
176 *
177 * 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
178 * matrix would look like so:
179 *
180 * <pre> 1 2 3 4 5 1 |#|#| | | | 2 |#|#|#| | | 3 | |#|#|#| | 4 | | |#|#|#| 5 | | | |#|#| 6 | | | | |#| 7 | | | | | | </pre>
181 *
182 * 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.
183 *
184 * Additionally, this implementation decreases memory usage by using two single-dimensional arrays and swapping them back and forth instead of
185 * 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
186 * the matrix and initially filling the arrays with large values so that entries we don't compute are ignored.
187 *
188 * See Algorithms on Strings, Trees and Sequences by Dan Gusfield for some discussion.
189 */
190 int n = left.length(); // length of left
191 int m = right.length(); // length of right
192 // if one string is empty, the edit distance is necessarily the length of the other
193 if (n == 0) {
194 return m <= threshold ? new LevenshteinResults(m, m, 0, 0) : new LevenshteinResults(-1, 0, 0, 0);
195 }
196 if (m == 0) {
197 return n <= threshold ? new LevenshteinResults(n, 0, n, 0) : new LevenshteinResults(-1, 0, 0, 0);
198 }
199 boolean swapped = false;
200 if (n > m) {
201 // swap the two strings to consume less memory
202 final SimilarityInput<E> tmp = left;
203 left = right;
204 right = tmp;
205 n = m;
206 m = right.length();
207 swapped = true;
208 }
209 int[] p = new int[n + 1]; // 'previous' cost array, horizontally
210 int[] d = new int[n + 1]; // cost array, horizontally
211 int[] tempD; // placeholder to assist in swapping p and d
212 final int[][] matrix = new int[m + 1][n + 1];
213 // filling the first row and first column values in the matrix
214 for (int index = 0; index <= n; index++) {
215 matrix[0][index] = index;
216 }
217 for (int index = 0; index <= m; index++) {
218 matrix[index][0] = index;
219 }
220 // fill in starting table values
221 final int boundary = Math.min(n, threshold) + 1;
222 for (int i = 0; i < boundary; i++) {
223 p[i] = i;
224 }
225 // these fills ensure that the value above the rightmost entry of our
226 // stripe will be ignored in following loop iterations
227 Arrays.fill(p, boundary, p.length, Integer.MAX_VALUE);
228 Arrays.fill(d, Integer.MAX_VALUE);
229 // iterates through t
230 for (int j = 1; j <= m; j++) {
231 final E rightJ = right.at(j - 1); // jth character of right
232 d[0] = j;
233 // compute stripe indices, constrain to array size
234 final int min = Math.max(1, j - threshold);
235 final int max = j > Integer.MAX_VALUE - threshold ? n : Math.min(n, j + threshold);
236 // the stripe may lead off of the table if s and t are of different sizes
237 if (min > max) {
238 return new LevenshteinResults(-1, 0, 0, 0);
239 }
240 // ignore entry left of leftmost
241 if (min > 1) {
242 d[min - 1] = Integer.MAX_VALUE;
243 }
244 // iterates through [min, max] in s
245 for (int i = min; i <= max; i++) {
246 if (left.at(i - 1).equals(rightJ)) {
247 // diagonally left and up
248 d[i] = p[i - 1];
249 } else {
250 // 1 + minimum of cell to the left, to the top, diagonally left and up
251 d[i] = 1 + Math.min(Math.min(d[i - 1], p[i]), p[i - 1]);
252 }
253 matrix[j][i] = d[i];
254 }
255 // copy current distance counts to 'previous row' distance counts
256 tempD = p;
257 p = d;
258 d = tempD;
259 }
260 // if p[n] is greater than the threshold, there's no guarantee on it being the correct distance
261 if (p[n] <= threshold) {
262 return findDetailedResults(left, right, matrix, swapped);
263 }
264 return new LevenshteinResults(-1, 0, 0, 0);
265 }
266
267 /**
268 * Finds the Levenshtein distance between two Strings.
269 *
270 * <p>
271 * A higher score indicates a greater distance.
272 * </p>
273 *
274 * <p>
275 * The previous implementation of the Levenshtein distance algorithm was from
276 * <a href="http://www.merriampark.com/ld.htm">http://www.merriampark.com/ld.htm</a>
277 * </p>
278 *
279 * <p>
280 * Chas Emerick has written an implementation in Java, which avoids an OutOfMemoryError which can occur when my Java implementation is used with very large
281 * strings.<br>
282 * This implementation of the Levenshtein distance algorithm is from
283 * <a href="http://www.merriampark.com/ldjava.htm">http://www.merriampark.com/ldjava.htm</a>
284 * </p>
285 *
286 * <pre>
287 * unlimitedCompare(null, *) = IllegalArgumentException
288 * unlimitedCompare(*, null) = IllegalArgumentException
289 * unlimitedCompare("","") = 0
290 * unlimitedCompare("","a") = 1
291 * unlimitedCompare("aaapppp", "") = 7
292 * unlimitedCompare("frog", "fog") = 1
293 * unlimitedCompare("fly", "ant") = 3
294 * unlimitedCompare("elephant", "hippo") = 7
295 * unlimitedCompare("hippo", "elephant") = 7
296 * unlimitedCompare("hippo", "zzzzzzzz") = 8
297 * unlimitedCompare("hello", "hallo") = 1
298 * </pre>
299 *
300 * @param <E> The type of similarity score unit.
301 * @param left the first CharSequence, must not be null.
302 * @param right the second CharSequence, must not be null.
303 * @return result distance, or -1.
304 * @throws IllegalArgumentException if either CharSequence input is {@code null}.
305 */
306 private static <E> LevenshteinResults unlimitedCompare(SimilarityInput<E> left, SimilarityInput<E> right) {
307 if (left == null || right == null) {
308 throw new IllegalArgumentException("CharSequences must not be null");
309 }
310 /*
311 * 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
312 * maintain two single-dimensional arrays of length s.length() + 1. The first, d, is the 'current working' distance array that maintains the newest
313 * 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
314 * 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
315 * 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
316 * switched...this is clearly much better than cloning an array or doing a System.arraycopy() each time through the outer loop.)
317 *
318 * Effectively, the difference between the two implementations is this one does not cause an out of memory condition when calculating the LD over two
319 * very large strings.
320 */
321 int n = left.length(); // length of left
322 int m = right.length(); // length of right
323 if (n == 0) {
324 return new LevenshteinResults(m, m, 0, 0);
325 }
326 if (m == 0) {
327 return new LevenshteinResults(n, 0, n, 0);
328 }
329 boolean swapped = false;
330 if (n > m) {
331 // swap the input strings to consume less memory
332 final SimilarityInput<E> tmp = left;
333 left = right;
334 right = tmp;
335 n = m;
336 m = right.length();
337 swapped = true;
338 }
339 int[] p = new int[n + 1]; // 'previous' cost array, horizontally
340 int[] d = new int[n + 1]; // cost array, horizontally
341 int[] tempD; // placeholder to assist in swapping p and d
342 final int[][] matrix = new int[m + 1][n + 1];
343 // filling the first row and first column values in the matrix
344 for (int index = 0; index <= n; index++) {
345 matrix[0][index] = index;
346 }
347 for (int index = 0; index <= m; index++) {
348 matrix[index][0] = index;
349 }
350 // indexes into strings left and right
351 int i; // iterates through left
352 int j; // iterates through right
353 E rightJ; // jth character of right
354 int cost; // cost
355 for (i = 0; i <= n; i++) {
356 p[i] = i;
357 }
358 for (j = 1; j <= m; j++) {
359 rightJ = right.at(j - 1);
360 d[0] = j;
361 for (i = 1; i <= n; i++) {
362 cost = left.at(i - 1).equals(rightJ) ? 0 : 1;
363 // minimum of cell to the left+1, to the top+1, diagonally left and up +cost
364 d[i] = Math.min(Math.min(d[i - 1] + 1, p[i] + 1), p[i - 1] + cost);
365 // filling the matrix
366 matrix[j][i] = d[i];
367 }
368 // copy current distance counts to 'previous row' distance counts
369 tempD = p;
370 p = d;
371 d = tempD;
372 }
373 return findDetailedResults(left, right, matrix, swapped);
374 }
375
376 /**
377 * Threshold.
378 */
379 private final Integer threshold;
380
381 /**
382 * <p>
383 * This returns the default instance that uses a version of the algorithm that does not use a threshold parameter.
384 * </p>
385 *
386 * @see LevenshteinDetailedDistance#getDefaultInstance()
387 * @deprecated Use {@link #getDefaultInstance()}.
388 */
389 @Deprecated
390 public LevenshteinDetailedDistance() {
391 this(null);
392 }
393
394 /**
395 * If the threshold is not null, distance calculations will be limited to a maximum length.
396 *
397 * <p>
398 * If the threshold is null, the unlimited version of the algorithm will be used.
399 * </p>
400 *
401 * @param threshold If this is null then distances calculations will not be limited. This may not be negative.
402 */
403 public LevenshteinDetailedDistance(final Integer threshold) {
404 if (threshold != null && threshold < 0) {
405 throw new IllegalArgumentException("Threshold must not be negative");
406 }
407 this.threshold = threshold;
408 }
409
410 /**
411 * Computes the Levenshtein distance between two Strings.
412 *
413 * <p>
414 * A higher score indicates a greater distance.
415 * </p>
416 *
417 * <p>
418 * The previous implementation of the Levenshtein distance algorithm was from
419 * <a href="http://www.merriampark.com/ld.htm">http://www.merriampark.com/ld.htm</a>
420 * </p>
421 *
422 * <p>
423 * Chas Emerick has written an implementation in Java, which avoids an OutOfMemoryError which can occur when my Java implementation is used with very large
424 * strings.<br>
425 * This implementation of the Levenshtein distance algorithm is from
426 * <a href="http://www.merriampark.com/ldjava.htm">http://www.merriampark.com/ldjava.htm</a>
427 * </p>
428 *
429 * <pre>
430 * distance.apply(null, *) = IllegalArgumentException
431 * distance.apply(*, null) = IllegalArgumentException
432 * distance.apply("","") = 0
433 * distance.apply("","a") = 1
434 * distance.apply("aaapppp", "") = 7
435 * distance.apply("frog", "fog") = 1
436 * distance.apply("fly", "ant") = 3
437 * distance.apply("elephant", "hippo") = 7
438 * distance.apply("hippo", "elephant") = 7
439 * distance.apply("hippo", "zzzzzzzz") = 8
440 * distance.apply("hello", "hallo") = 1
441 * </pre>
442 *
443 * @param left the first input, must not be null.
444 * @param right the second input, must not be null.
445 * @return result distance, or -1.
446 * @throws IllegalArgumentException if either String input {@code null}.
447 */
448 @Override
449 public LevenshteinResults apply(final CharSequence left, final CharSequence right) {
450 return apply(SimilarityInput.input(left), SimilarityInput.input(right));
451 }
452
453 /**
454 * Computes the Levenshtein distance between two Strings.
455 *
456 * <p>
457 * A higher score indicates a greater distance.
458 * </p>
459 *
460 * <p>
461 * The previous implementation of the Levenshtein distance algorithm was from
462 * <a href="http://www.merriampark.com/ld.htm">http://www.merriampark.com/ld.htm</a>
463 * </p>
464 *
465 * <p>
466 * Chas Emerick has written an implementation in Java, which avoids an OutOfMemoryError which can occur when my Java implementation is used with very large
467 * strings.<br>
468 * This implementation of the Levenshtein distance algorithm is from
469 * <a href="http://www.merriampark.com/ldjava.htm">http://www.merriampark.com/ldjava.htm</a>
470 * </p>
471 *
472 * <pre>
473 * distance.apply(null, *) = IllegalArgumentException
474 * distance.apply(*, null) = IllegalArgumentException
475 * distance.apply("","") = 0
476 * distance.apply("","a") = 1
477 * distance.apply("aaapppp", "") = 7
478 * distance.apply("frog", "fog") = 1
479 * distance.apply("fly", "ant") = 3
480 * distance.apply("elephant", "hippo") = 7
481 * distance.apply("hippo", "elephant") = 7
482 * distance.apply("hippo", "zzzzzzzz") = 8
483 * distance.apply("hello", "hallo") = 1
484 * </pre>
485 *
486 * @param <E> The type of similarity score unit.
487 * @param left the first input, must not be null.
488 * @param right the second input, must not be null.
489 * @return result distance, or -1.
490 * @throws IllegalArgumentException if either String input {@code null}.
491 * @since 1.13.0
492 */
493 public <E> LevenshteinResults apply(final SimilarityInput<E> left, final SimilarityInput<E> right) {
494 if (threshold != null) {
495 return limitedCompare(left, right, threshold);
496 }
497 return unlimitedCompare(left, right);
498 }
499
500 /**
501 * Gets the distance threshold.
502 *
503 * @return The distance threshold.
504 */
505 public Integer getThreshold() {
506 return threshold;
507 }
508 }