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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.
136      * </p>
137      *
138      * <pre>
139      * limitedCompare(null, *, *)             = Throws {@link IllegalArgumentException}
140      * limitedCompare(*, null, *)             = Throws {@link IllegalArgumentException}
141      * limitedCompare(*, *, -1)               = Throws {@link 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 
163         /*
164          * 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
165          * 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
166          * 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
167          * time until the distance is found; this is O(dm), where d is the distance.
168          *
169          * One subtlety comes from needing to ignore entries on the border of our stripe, for example,
170          * p[] = |#|#|#|* d[] = *|#|#|#| We must ignore the entry to the left
171          * of the leftmost member We must ignore the entry above the rightmost member
172          *
173          * 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
174          * shorter of the two, the stripe will always run off to the upper right instead of the lower left of the matrix.
175          *
176          * 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
177          * matrix would look like so:
178          *
179          * <pre> 1 2 3 4 5 1 |#|#| | | | 2 |#|#|#| | | 3 | |#|#|#| | 4 | | |#|#|#| 5 | | | |#|#| 6 | | | | |#| 7 | | | | | | </pre>
180          *
181          * 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.
182          *
183          * Additionally, this implementation decreases memory usage by using two single-dimensional arrays and swapping them back and forth instead of
184          * 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
185          * the matrix and initially filling the arrays with large values so that entries we don't compute are ignored.
186          *
187          * See Algorithms on Strings, Trees and Sequences by Dan Gusfield for some discussion.
188          */
189         int n = left.length(); // length of left
190         int m = right.length(); // length of right
191         // if one string is empty, the edit distance is necessarily the length of the other
192         if (n == 0) {
193             return m <= threshold ? new LevenshteinResults(m, m, 0, 0) : new LevenshteinResults(-1, 0, 0, 0);
194         }
195         if (m == 0) {
196             return n <= threshold ? new LevenshteinResults(n, 0, n, 0) : new LevenshteinResults(-1, 0, 0, 0);
197         }
198         boolean swapped = false;
199         if (n > m) {
200             // swap the two strings to consume less memory
201             final SimilarityInput<E> tmp = left;
202             left = right;
203             right = tmp;
204             n = m;
205             m = right.length();
206             swapped = true;
207         }
208         int[] p = new int[n + 1]; // 'previous' cost array, horizontally
209         int[] d = new int[n + 1]; // cost array, horizontally
210         int[] tempD; // placeholder to assist in swapping p and d
211         final int[][] matrix = new int[m + 1][n + 1];
212         // filling the first row and first column values in the matrix
213         for (int index = 0; index <= n; index++) {
214             matrix[0][index] = index;
215         }
216         for (int index = 0; index <= m; index++) {
217             matrix[index][0] = index;
218         }
219         // fill in starting table values
220         final int boundary = Math.min(n, threshold) + 1;
221         for (int i = 0; i < boundary; i++) {
222             p[i] = i;
223         }
224         // these fills ensure that the value above the rightmost entry of our
225         // stripe will be ignored in following loop iterations
226         Arrays.fill(p, boundary, p.length, Integer.MAX_VALUE);
227         Arrays.fill(d, Integer.MAX_VALUE);
228         // iterates through t
229         for (int j = 1; j <= m; j++) {
230             final E rightJ = right.at(j - 1); // jth character of right
231             d[0] = j;
232             // compute stripe indices, constrain to array size
233             final int min = Math.max(1, j - threshold);
234             final int max = j > Integer.MAX_VALUE - threshold ? n : Math.min(n, j + threshold);
235             // the stripe may lead off of the table if s and t are of different sizes
236             if (min > max) {
237                 return new LevenshteinResults(-1, 0, 0, 0);
238             }
239             // ignore entry left of leftmost
240             if (min > 1) {
241                 d[min - 1] = Integer.MAX_VALUE;
242             }
243             // iterates through [min, max] in s
244             for (int i = min; i <= max; i++) {
245                 if (left.at(i - 1).equals(rightJ)) {
246                     // diagonally left and up
247                     d[i] = p[i - 1];
248                 } else {
249                     // 1 + minimum of cell to the left, to the top, diagonally left and up
250                     d[i] = 1 + Math.min(Math.min(d[i - 1], p[i]), p[i - 1]);
251                 }
252                 matrix[j][i] = d[i];
253             }
254             // copy current distance counts to 'previous row' distance counts
255             tempD = p;
256             p = d;
257             d = tempD;
258         }
259         // if p[n] is greater than the threshold, there's no guarantee on it being the correct distance
260         if (p[n] <= threshold) {
261             return findDetailedResults(left, right, matrix, swapped);
262         }
263         return new LevenshteinResults(-1, 0, 0, 0);
264     }
265 
266     /**
267      * Finds the Levenshtein distance between two Strings.
268      *
269      * <p>
270      * A higher score indicates a greater distance.
271      * </p>
272      *
273      * <p>
274      * Chas Emerick has written an implementation in Java, which avoids an OutOfMemoryError which can occur when my Java implementation is used with very large
275      * strings.
276      * </p>
277      *
278      * <pre>
279      * unlimitedCompare(null, *)             = Throws {@link IllegalArgumentException}
280      * unlimitedCompare(*, null)             = Throws {@link IllegalArgumentException}
281      * unlimitedCompare("","")               = 0
282      * unlimitedCompare("","a")              = 1
283      * unlimitedCompare("aaapppp", "")       = 7
284      * unlimitedCompare("frog", "fog")       = 1
285      * unlimitedCompare("fly", "ant")        = 3
286      * unlimitedCompare("elephant", "hippo") = 7
287      * unlimitedCompare("hippo", "elephant") = 7
288      * unlimitedCompare("hippo", "zzzzzzzz") = 8
289      * unlimitedCompare("hello", "hallo")    = 1
290      * </pre>
291      *
292      * @param <E>   The type of similarity score unit.
293      * @param left  the first CharSequence, must not be null.
294      * @param right the second CharSequence, must not be null.
295      * @return result distance, or -1.
296      * @throws IllegalArgumentException if either CharSequence input is {@code null}.
297      */
298     private static <E> LevenshteinResults unlimitedCompare(SimilarityInput<E> left, SimilarityInput<E> right) {
299         if (left == null || right == null) {
300             throw new IllegalArgumentException("CharSequences must not be null");
301         }
302         /*
303          * 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
304          * maintain two single-dimensional arrays of length s.length() + 1. The first, d, is the 'current working' distance array that maintains the newest
305          * 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
306          * 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
307          * 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
308          * switched...this is clearly much better than cloning an array or doing a System.arraycopy() each time through the outer loop.)
309          *
310          * Effectively, the difference between the two implementations is this one does not cause an out of memory condition when calculating the LD over two
311          * very large strings.
312          */
313         int n = left.length(); // length of left
314         int m = right.length(); // length of right
315         if (n == 0) {
316             return new LevenshteinResults(m, m, 0, 0);
317         }
318         if (m == 0) {
319             return new LevenshteinResults(n, 0, n, 0);
320         }
321         boolean swapped = false;
322         if (n > m) {
323             // swap the input strings to consume less memory
324             final SimilarityInput<E> tmp = left;
325             left = right;
326             right = tmp;
327             n = m;
328             m = right.length();
329             swapped = true;
330         }
331         int[] p = new int[n + 1]; // 'previous' cost array, horizontally
332         int[] d = new int[n + 1]; // cost array, horizontally
333         int[] tempD; // placeholder to assist in swapping p and d
334         final int[][] matrix = new int[m + 1][n + 1];
335         // filling the first row and first column values in the matrix
336         for (int index = 0; index <= n; index++) {
337             matrix[0][index] = index;
338         }
339         for (int index = 0; index <= m; index++) {
340             matrix[index][0] = index;
341         }
342         // indexes into strings left and right
343         int i; // iterates through left
344         int j; // iterates through right
345         E rightJ; // jth character of right
346         int cost; // cost
347         for (i = 0; i <= n; i++) {
348             p[i] = i;
349         }
350         for (j = 1; j <= m; j++) {
351             rightJ = right.at(j - 1);
352             d[0] = j;
353             for (i = 1; i <= n; i++) {
354                 cost = left.at(i - 1).equals(rightJ) ? 0 : 1;
355                 // minimum of cell to the left+1, to the top+1, diagonally left and up +cost
356                 d[i] = Math.min(Math.min(d[i - 1] + 1, p[i] + 1), p[i - 1] + cost);
357                 // filling the matrix
358                 matrix[j][i] = d[i];
359             }
360             // copy current distance counts to 'previous row' distance counts
361             tempD = p;
362             p = d;
363             d = tempD;
364         }
365         return findDetailedResults(left, right, matrix, swapped);
366     }
367 
368     /**
369      * Threshold.
370      */
371     private final Integer threshold;
372 
373     /**
374      * Constructs a new instance that uses a version of the algorithm that does not use a threshold parameter.
375      *
376      * @see LevenshteinDetailedDistance#getDefaultInstance()
377      * @deprecated Use {@link #getDefaultInstance()}.
378      */
379     @Deprecated
380     public LevenshteinDetailedDistance() {
381         this(null);
382     }
383 
384     /**
385      * Constructs a new instance for a threshold.
386      * <p>
387      * If the threshold is not null, distance calculations will be limited to a maximum length.
388      * </p>
389      * <p>
390      * If the threshold is null, the unlimited version of the algorithm will be used.
391      * </p>
392      *
393      * @param threshold If this is null then distances calculations will not be limited. This may not be negative.
394      */
395     public LevenshteinDetailedDistance(final Integer threshold) {
396         if (threshold != null && threshold < 0) {
397             throw new IllegalArgumentException("Threshold must not be negative");
398         }
399         this.threshold = threshold;
400     }
401 
402     /**
403      * Computes the Levenshtein distance between two Strings.
404      *
405      * <p>
406      * A higher score indicates a greater distance.
407      * </p>
408      *
409      * <p>
410      * Chas Emerick has written an implementation in Java, which avoids an OutOfMemoryError which can occur when my Java implementation is used with very large
411      * strings.
412      * </p>
413      *
414      * <pre>
415      * distance.apply(null, *)             = Throws {@link IllegalArgumentException}
416      * distance.apply(*, null)             = Throws {@link IllegalArgumentException}
417      * distance.apply("","")               = 0
418      * distance.apply("","a")              = 1
419      * distance.apply("aaapppp", "")       = 7
420      * distance.apply("frog", "fog")       = 1
421      * distance.apply("fly", "ant")        = 3
422      * distance.apply("elephant", "hippo") = 7
423      * distance.apply("hippo", "elephant") = 7
424      * distance.apply("hippo", "zzzzzzzz") = 8
425      * distance.apply("hello", "hallo")    = 1
426      * </pre>
427      *
428      * @param left  the first input, must not be null.
429      * @param right the second input, must not be null.
430      * @return result distance, or -1.
431      * @throws IllegalArgumentException if either String input {@code null}.
432      */
433     @Override
434     public LevenshteinResults apply(final CharSequence left, final CharSequence right) {
435         return apply(SimilarityInput.input(left), SimilarityInput.input(right));
436     }
437 
438     /**
439      * Computes the Levenshtein distance between two Strings.
440      *
441      * <p>
442      * A higher score indicates a greater distance.
443      * </p>
444      *
445      * <p>
446      * Chas Emerick has written an implementation in Java, which avoids an OutOfMemoryError which can occur when my Java implementation is used with very large
447      * strings.
448      * </p>
449      *
450      * <pre>
451      * distance.apply(null, *)             = Throws {@link IllegalArgumentException}
452      * distance.apply(*, null)             = Throws {@link IllegalArgumentException}
453      * distance.apply("","")               = 0
454      * distance.apply("","a")              = 1
455      * distance.apply("aaapppp", "")       = 7
456      * distance.apply("frog", "fog")       = 1
457      * distance.apply("fly", "ant")        = 3
458      * distance.apply("elephant", "hippo") = 7
459      * distance.apply("hippo", "elephant") = 7
460      * distance.apply("hippo", "zzzzzzzz") = 8
461      * distance.apply("hello", "hallo")    = 1
462      * </pre>
463      *
464      * @param <E>   The type of similarity score unit.
465      * @param left  the first input, must not be null.
466      * @param right the second input, must not be null.
467      * @return result distance, or -1.
468      * @throws IllegalArgumentException if either String input {@code null}.
469      * @since 1.13.0
470      */
471     public <E> LevenshteinResults apply(final SimilarityInput<E> left, final SimilarityInput<E> right) {
472         if (threshold != null) {
473             return limitedCompare(left, right, threshold);
474         }
475         return unlimitedCompare(left, right);
476     }
477 
478     /**
479      * Gets the distance threshold.
480      *
481      * @return The distance threshold.
482      */
483     public Integer getThreshold() {
484         return threshold;
485     }
486 }