• 后缀数组

    在定义后缀树（Suffix Tree）时，我们给出了一段简洁的描述：

    A suffix tree is a compressed trie for all the suffixes of a text.

    后缀数组（Suffix Array）的定义也同样简洁：

    A suffix array is a sorted array of all suffixes of a text.

    后缀数组由 Manber & Myers 在 1990 年首先提出《Suffix arrays: a new method for on-line string searches》，用以替代后缀树，并且改进了存储空间的需求。其与后缀树的的关系有：

    • 后缀数组可以通过对后缀树做深度优先遍历（DFT: Depth First Traversal）来进行构建，对所有的边（Edge）做字典序（Lexicographical Order）遍历。
    • 通过使用后缀集合和最长公共前缀数组（LCP Array: Longest Common Prefix Array）来构建后缀树，可在 O(n) 时间内完成，例如使用 Ukkonen 算法。构造后缀数组同样也可以在 O(n) 时间内完成。
    • 每个通过后缀树解决的问题，都可以通过组合使用后缀数组和额外的信息（例如：LCP Array）来解决。

    下面用一个例子来解释后缀数组结构。假设文本 Text = "banana"，这里增加一个末尾字符 "$" 以使所有的后缀与前缀不重复，要求 "$" 为 Text 中不存在并且按字典序排序要小于所有其他字符。（假设数组从 1 开始）

    i

     1 

    		  2   3   4 

     5 

     6 

     7 

    Text[i] 

    b

    a

    n

    a

     n

     a

     $

    那么对于 Text = "banana$" 的后缀列表如下：

    suffix

    i

    banana$

    1
    anana$

    2
    nana$

    3
    ana$

    4
    na$

    5
    a$

    6
    $

    7

    对所有后缀进行字典序（Lexicographical Order）排序：

    sorted suffix

    i

    $

    7
    a$

    6
    ana$

    4
    anana$

    2
    banana$

    1
    na$

    5
    nana$

    3

    上表中右侧列即为后缀数组（Suffix Array），SA = [7, 6, 4, 2, 1, 5, 3]。

    i

     1 

    		  2   3   4 

     5 

     6 

     7 

     SA[i] 

    7

    6

    4

    2

     1

     5

     3

    这样，例如 SA[3] 的值为 4，就代表 Text = "banana$" 中从位置 4 开始的后缀 "ana$"。

    在 2009 年，Nong, Ge; Zhang, Sen; Chan, Wai Hong 等发表了论文《Linear Suffix Array Construction by Almost Pure Induced-Sorting》，首次实现了如下 3 个目标：

    • minimal asymptotic complexity Θ(n)
    • lightweight in space, meaning little or no working memory beside the text and the suffix array itself is needed
    • fast in practice

    Yuta Mori 对该算法做了具体的实现。

    代码示例

      1 /*
  2  * SAIS.cs for SAIS-CSharp
  3  * Copyright (c) 2010 Yuta Mori. All Rights Reserved.
  4  *
  5  * Permission is hereby granted, free of charge, to any person
  6  * obtaining a copy of this software and associated documentation
  7  * files (the "Software"), to deal in the Software without
  8  * restriction, including without limitation the rights to use,
  9  * copy, modify, merge, publish, distribute, sublicense, and/or sell
 10  * copies of the Software, and to permit persons to whom the
 11  * Software is furnished to do so, subject to the following
 12  * conditions:
 13  *
 14  * The above copyright notice and this permission notice shall be
 15  * included in all copies or substantial portions of the Software.
 16  *
 17  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 18  * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 19  * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 20  * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 21  * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 22  * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 23  * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 24  * OTHER DEALINGS IN THE SOFTWARE.
 25  */
 26 
 27 namespace SuffixArray
 28 {
 29   internal interface BaseArray
 30   {
 31     int this[int i]
 32     {
 33       set;
 34       get;
 35     }
 36   }
 37 
 38   internal class ByteArray : BaseArray
 39   {
 40     private byte[] m_array;
 41     private int m_pos;
 42     public ByteArray(byte[] array, int pos)
 43     {
 44       m_pos = pos;
 45       m_array = array;
 46     }
 47     ~ByteArray() { m_array = null; }
 48     public int this[int i]
 49     {
 50       set { m_array[i + m_pos] = (byte)value; }
 51       get { return (int)m_array[i + m_pos]; }
 52     }
 53   }
 54 
 55   internal class CharArray : BaseArray
 56   {
 57     private char[] m_array;
 58     private int m_pos;
 59     public CharArray(char[] array, int pos)
 60     {
 61       m_pos = pos;
 62       m_array = array;
 63     }
 64     ~CharArray() { m_array = null; }
 65     public int this[int i]
 66     {
 67       set { m_array[i + m_pos] = (char)value; }
 68       get { return (int)m_array[i + m_pos]; }
 69     }
 70   }
 71 
 72   internal class IntArray : BaseArray
 73   {
 74     private int[] m_array;
 75     private int m_pos;
 76     public IntArray(int[] array, int pos)
 77     {
 78       m_pos = pos;
 79       m_array = array;
 80     }
 81     ~IntArray() { m_array = null; }
 82     public int this[int i]
 83     {
 84       set { m_array[i + m_pos] = value; }
 85       get { return m_array[i + m_pos]; }
 86     }
 87   }
 88 
 89   internal class StringArray : BaseArray
 90   {
 91     private string m_array;
 92     private int m_pos;
 93     public StringArray(string array, int pos)
 94     {
 95       m_pos = pos;
 96       m_array = array;
 97     }
 98     ~StringArray() { m_array = null; }
 99     public int this[int i]
100     {
101       set { }
102       get { return (int)m_array[i + m_pos]; }
103     }
104   }
105 
106   /// <summary>
107   /// An implementation of the induced sorting based suffix array construction algorithm.
108   /// </summary>
109   public static class SAIS
110   {
111     private const int MINBUCKETSIZE = 256;
112 
113     private static
114     void
115     getCounts(BaseArray T, BaseArray C, int n, int k)
116     {
117       int i;
118       for (i = 0; i < k; ++i) { C[i] = 0; }
119       for (i = 0; i < n; ++i) { C[T[i]] = C[T[i]] + 1; }
120     }
121     private static
122     void
123     getBuckets(BaseArray C, BaseArray B, int k, bool end)
124     {
125       int i, sum = 0;
126       if (end != false) { for (i = 0; i < k; ++i) { sum += C[i]; B[i] = sum; } }
127       else { for (i = 0; i < k; ++i) { sum += C[i]; B[i] = sum - C[i]; } }
128     }
129 
130     /* sort all type LMS suffixes */
131     private static
132     void
133     LMSsort(BaseArray T, int[] SA, BaseArray C, BaseArray B, int n, int k)
134     {
135       int b, i, j;
136       int c0, c1;
137       /* compute SAl */
138       if (C == B) { getCounts(T, C, n, k); }
139       getBuckets(C, B, k, false); /* find starts of buckets */
140       j = n - 1;
141       b = B[c1 = T[j]];
142       --j;
143       SA[b++] = (T[j] < c1) ? ~j : j;
144       for (i = 0; i < n; ++i)
145       {
146         if (0 < (j = SA[i]))
147         {
148           if ((c0 = T[j]) != c1) { B[c1] = b; b = B[c1 = c0]; }
149           --j;
150           SA[b++] = (T[j] < c1) ? ~j : j;
151           SA[i] = 0;
152         }
153         else if (j < 0)
154         {
155           SA[i] = ~j;
156         }
157       }
158       /* compute SAs */
159       if (C == B) { getCounts(T, C, n, k); }
160       getBuckets(C, B, k, true); /* find ends of buckets */
161       for (i = n - 1, b = B[c1 = 0]; 0 <= i; --i)
162       {
163         if (0 < (j = SA[i]))
164         {
165           if ((c0 = T[j]) != c1) { B[c1] = b; b = B[c1 = c0]; }
166           --j;
167           SA[--b] = (T[j] > c1) ? ~(j + 1) : j;
168           SA[i] = 0;
169         }
170       }
171     }
172     private static
173     int
174     LMSpostproc(BaseArray T, int[] SA, int n, int m)
175     {
176       int i, j, p, q, plen, qlen, name;
177       int c0, c1;
178       bool diff;
179 
180       /* compact all the sorted substrings into the first m items of SA
181           2*m must be not larger than n (proveable) */
182       for (i = 0; (p = SA[i]) < 0; ++i) { SA[i] = ~p; }
183       if (i < m)
184       {
185         for (j = i, ++i; ; ++i)
186         {
187           if ((p = SA[i]) < 0)
188           {
189             SA[j++] = ~p; SA[i] = 0;
190             if (j == m) { break; }
191           }
192         }
193       }
194 
195       /* store the length of all substrings */
196       i = n - 1; j = n - 1; c0 = T[n - 1];
197       do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) >= c1));
198       for (; 0 <= i; )
199       {
200         do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) <= c1));
201         if (0 <= i)
202         {
203           SA[m + ((i + 1) >> 1)] = j - i; j = i + 1;
204           do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) >= c1));
205         }
206       }
207 
208       /* find the lexicographic names of all substrings */
209       for (i = 0, name = 0, q = n, qlen = 0; i < m; ++i)
210       {
211         p = SA[i]; plen = SA[m + (p >> 1)]; diff = true;
212         if ((plen == qlen) && ((q + plen) < n))
213         {
214           for (j = 0; (j < plen) && (T[p + j] == T[q + j]); ++j) { }
215           if (j == plen) { diff = false; }
216         }
217         if (diff != false) { ++name; q = p; qlen = plen; }
218         SA[m + (p >> 1)] = name;
219       }
220 
221       return name;
222     }
223 
224     /* compute SA and BWT */
225     private static
226     void
227     induceSA(BaseArray T, int[] SA, BaseArray C, BaseArray B, int n, int k)
228     {
229       int b, i, j;
230       int c0, c1;
231       /* compute SAl */
232       if (C == B) { getCounts(T, C, n, k); }
233       getBuckets(C, B, k, false); /* find starts of buckets */
234       j = n - 1;
235       b = B[c1 = T[j]];
236       SA[b++] = ((0 < j) && (T[j - 1] < c1)) ? ~j : j;
237       for (i = 0; i < n; ++i)
238       {
239         j = SA[i]; SA[i] = ~j;
240         if (0 < j)
241         {
242           if ((c0 = T[--j]) != c1) { B[c1] = b; b = B[c1 = c0]; }
243           SA[b++] = ((0 < j) && (T[j - 1] < c1)) ? ~j : j;
244         }
245       }
246       /* compute SAs */
247       if (C == B) { getCounts(T, C, n, k); }
248       getBuckets(C, B, k, true); /* find ends of buckets */
249       for (i = n - 1, b = B[c1 = 0]; 0 <= i; --i)
250       {
251         if (0 < (j = SA[i]))
252         {
253           if ((c0 = T[--j]) != c1) { B[c1] = b; b = B[c1 = c0]; }
254           SA[--b] = ((j == 0) || (T[j - 1] > c1)) ? ~j : j;
255         }
256         else
257         {
258           SA[i] = ~j;
259         }
260       }
261     }
262     private static
263     int
264     computeBWT(BaseArray T, int[] SA, BaseArray C, BaseArray B, int n, int k)
265     {
266       int b, i, j, pidx = -1;
267       int c0, c1;
268       /* compute SAl */
269       if (C == B) { getCounts(T, C, n, k); }
270       getBuckets(C, B, k, false); /* find starts of buckets */
271       j = n - 1;
272       b = B[c1 = T[j]];
273       SA[b++] = ((0 < j) && (T[j - 1] < c1)) ? ~j : j;
274       for (i = 0; i < n; ++i)
275       {
276         if (0 < (j = SA[i]))
277         {
278           SA[i] = ~(c0 = T[--j]);
279           if (c0 != c1) { B[c1] = b; b = B[c1 = c0]; }
280           SA[b++] = ((0 < j) && (T[j - 1] < c1)) ? ~j : j;
281         }
282         else if (j != 0)
283         {
284           SA[i] = ~j;
285         }
286       }
287       /* compute SAs */
288       if (C == B) { getCounts(T, C, n, k); }
289       getBuckets(C, B, k, true); /* find ends of buckets */
290       for (i = n - 1, b = B[c1 = 0]; 0 <= i; --i)
291       {
292         if (0 < (j = SA[i]))
293         {
294           SA[i] = (c0 = T[--j]);
295           if (c0 != c1) { B[c1] = b; b = B[c1 = c0]; }
296           SA[--b] = ((0 < j) && (T[j - 1] > c1)) ? ~((int)T[j - 1]) : j;
297         }
298         else if (j != 0)
299         {
300           SA[i] = ~j;
301         }
302         else
303         {
304           pidx = i;
305         }
306       }
307       return pidx;
308     }
309 
310     /* find the suffix array SA of T[0..n-1] in {0..k-1}^n
311        use a working space (excluding T and SA) of at most 2n+O(1) for a constant alphabet */
312     private static
313     int
314     sais_main(BaseArray T, int[] SA, int fs, int n, int k, bool isbwt)
315     {
316       BaseArray C, B, RA;
317       int i, j, b, m, p, q, name, pidx = 0, newfs;
318       int c0, c1;
319       uint flags = 0;
320 
321       if (k <= MINBUCKETSIZE)
322       {
323         C = new IntArray(new int[k], 0);
324         if (k <= fs) { B = new IntArray(SA, n + fs - k); flags = 1; }
325         else { B = new IntArray(new int[k], 0); flags = 3; }
326       }
327       else if (k <= fs)
328       {
329         C = new IntArray(SA, n + fs - k);
330         if (k <= (fs - k)) { B = new IntArray(SA, n + fs - k * 2); flags = 0; }
331         else if (k <= (MINBUCKETSIZE * 4)) { B = new IntArray(new int[k], 0); flags = 2; }
332         else { B = C; flags = 8; }
333       }
334       else
335       {
336         C = B = new IntArray(new int[k], 0);
337         flags = 4 | 8;
338       }
339 
340       /* stage 1: reduce the problem by at least 1/2
341          sort all the LMS-substrings */
342       getCounts(T, C, n, k); getBuckets(C, B, k, true); /* find ends of buckets */
343       for (i = 0; i < n; ++i) { SA[i] = 0; }
344       b = -1; i = n - 1; j = n; m = 0; c0 = T[n - 1];
345       do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) >= c1));
346       for (; 0 <= i; )
347       {
348         do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) <= c1));
349         if (0 <= i)
350         {
351           if (0 <= b) { SA[b] = j; } b = --B[c1]; j = i; ++m;
352           do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) >= c1));
353         }
354       }
355       if (1 < m)
356       {
357         LMSsort(T, SA, C, B, n, k);
358         name = LMSpostproc(T, SA, n, m);
359       }
360       else if (m == 1)
361       {
362         SA[b] = j + 1;
363         name = 1;
364       }
365       else
366       {
367         name = 0;
368       }
369 
370       /* stage 2: solve the reduced problem
371          recurse if names are not yet unique */
372       if (name < m)
373       {
374         if ((flags & 4) != 0) { C = null; B = null; }
375         if ((flags & 2) != 0) { B = null; }
376         newfs = (n + fs) - (m * 2);
377         if ((flags & (1 | 4 | 8)) == 0)
378         {
379           if ((k + name) <= newfs) { newfs -= k; }
380           else { flags |= 8; }
381         }
382         for (i = m + (n >> 1) - 1, j = m * 2 + newfs - 1; m <= i; --i)
383         {
384           if (SA[i] != 0) { SA[j--] = SA[i] - 1; }
385         }
386         RA = new IntArray(SA, m + newfs);
387         sais_main(RA, SA, newfs, m, name, false);
388         RA = null;
389 
390         i = n - 1; j = m * 2 - 1; c0 = T[n - 1];
391         do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) >= c1));
392         for (; 0 <= i; )
393         {
394           do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) <= c1));
395           if (0 <= i)
396           {
397             SA[j--] = i + 1;
398             do { c1 = c0; } while ((0 <= --i) && ((c0 = T[i]) >= c1));
399           }
400         }
401 
402         for (i = 0; i < m; ++i) { SA[i] = SA[m + SA[i]]; }
403         if ((flags & 4) != 0) { C = B = new IntArray(new int[k], 0); }
404         if ((flags & 2) != 0) { B = new IntArray(new int[k], 0); }
405       }
406 
407       /* stage 3: induce the result for the original problem */
408       if ((flags & 8) != 0) { getCounts(T, C, n, k); }
409       /* put all left-most S characters into their buckets */
410       if (1 < m)
411       {
412         getBuckets(C, B, k, true); /* find ends of buckets */
413         i = m - 1; j = n; p = SA[m - 1]; c1 = T[p];
414         do
415         {
416           q = B[c0 = c1];
417           while (q < j) { SA[--j] = 0; }
418           do
419           {
420             SA[--j] = p;
421             if (--i < 0) { break; }
422             p = SA[i];
423           } while ((c1 = T[p]) == c0);
424         } while (0 <= i);
425         while (0 < j) { SA[--j] = 0; }
426       }
427       if (isbwt == false) { induceSA(T, SA, C, B, n, k); }
428       else { pidx = computeBWT(T, SA, C, B, n, k); }
429       C = null; B = null;
430       return pidx;
431     }
432 
433     /*- Suffixsorting -*/
434     /* byte */
435     /// <summary>
436     /// Constructs the suffix array of a given string in linear time.
437     /// </summary>
438     /// <param name="T">input string</param>
439     /// <param name="SA">output suffix array</param>
440     /// <param name="n">length of the given string</param>
441     /// <returns>0 if no error occurred, -1 or -2 otherwise</returns>
442     public static
443     int
444     sufsort(byte[] T, int[] SA, int n)
445     {
446       if ((T == null) || (SA == null) ||
447           (T.Length < n) || (SA.Length < n)) { return -1; }
448       if (n <= 1) { if (n == 1) { SA[0] = 0; } return 0; }
449       return sais_main(new ByteArray(T, 0), SA, 0, n, 256, false);
450     }
451     /* char */
452     /// <summary>
453     /// Constructs the suffix array of a given string in linear time.
454     /// </summary>
455     /// <param name="T">input string</param>
456     /// <param name="SA">output suffix array</param>
457     /// <param name="n">length of the given string</param>
458     /// <returns>0 if no error occurred, -1 or -2 otherwise</returns>
459     public static
460     int
461     sufsort(char[] T, int[] SA, int n)
462     {
463       if ((T == null) || (SA == null) ||
464           (T.Length < n) || (SA.Length < n)) { return -1; }
465       if (n <= 1) { if (n == 1) { SA[0] = 0; } return 0; }
466       return sais_main(new CharArray(T, 0), SA, 0, n, 65536, false);
467     }
468     /* int */
469     /// <summary>
470     /// Constructs the suffix array of a given string in linear time.
471     /// </summary>
472     /// <param name="T">input string</param>
473     /// <param name="SA">output suffix array</param>
474     /// <param name="n">length of the given string</param>
475     /// <param name="k">alphabet size</param>
476     /// <returns>0 if no error occurred, -1 or -2 otherwise</returns>
477     public static
478     int
479     sufsort(int[] T, int[] SA, int n, int k)
480     {
481       if ((T == null) || (SA == null) ||
482           (T.Length < n) || (SA.Length < n) ||
483          (k <= 0)) { return -1; }
484       if (n <= 1) { if (n == 1) { SA[0] = 0; } return 0; }
485       return sais_main(new IntArray(T, 0), SA, 0, n, k, false);
486     }
487     /* string */
488     /// <summary>
489     /// Constructs the suffix array of a given string in linear time.
490     /// </summary>
491     /// <param name="T">input string</param>
492     /// <param name="SA">output suffix array</param>
493     /// <param name="n">length of the given string</param>
494     /// <returns>0 if no error occurred, -1 or -2 otherwise</returns>
495     public static
496     int
497     sufsort(string T, int[] SA, int n)
498     {
499       if ((T == null) || (SA == null) ||
500           (T.Length < n) || (SA.Length < n)) { return -1; }
501       if (n <= 1) { if (n == 1) { SA[0] = 0; } return 0; }
502       return sais_main(new StringArray(T, 0), SA, 0, n, 65536, false);
503     }
504 
505     /*- Burrows-Wheeler Transform -*/
506     /* byte */
507     /// <summary>
508     /// Constructs the burrows-wheeler transformed string of a given string in linear time.
509     /// </summary>
510     /// <param name="T">input string</param>
511     /// <param name="U">output string</param>
512     /// <param name="A">temporary array</param>
513     /// <param name="n">length of the given string</param>
514     /// <returns>primary index if no error occurred, -1 or -2 otherwise</returns>
515     public static
516     int
517     bwt(byte[] T, byte[] U, int[] A, int n)
518     {
519       int i, pidx;
520       if ((T == null) || (U == null) || (A == null) ||
521          (T.Length < n) || (U.Length < n) || (A.Length < n)) { return -1; }
522       if (n <= 1) { if (n == 1) { U[0] = T[0]; } return n; }
523       pidx = sais_main(new ByteArray(T, 0), A, 0, n, 256, true);
524       U[0] = T[n - 1];
525       for (i = 0; i < pidx; ++i) { U[i + 1] = (byte)A[i]; }
526       for (i += 1; i < n; ++i) { U[i] = (byte)A[i]; }
527       return pidx + 1;
528     }
529     /* char */
530     /// <summary>
531     /// Constructs the burrows-wheeler transformed string of a given string in linear time.
532     /// </summary>
533     /// <param name="T">input string</param>
534     /// <param name="U">output string</param>
535     /// <param name="A">temporary array</param>
536     /// <param name="n">length of the given string</param>
537     /// <returns>primary index if no error occurred, -1 or -2 otherwise</returns>
538     public static
539     int
540     bwt(char[] T, char[] U, int[] A, int n)
541     {
542       int i, pidx;
543       if ((T == null) || (U == null) || (A == null) ||
544          (T.Length < n) || (U.Length < n) || (A.Length < n)) { return -1; }
545       if (n <= 1) { if (n == 1) { U[0] = T[0]; } return n; }
546       pidx = sais_main(new CharArray(T, 0), A, 0, n, 65536, true);
547       U[0] = T[n - 1];
548       for (i = 0; i < pidx; ++i) { U[i + 1] = (char)A[i]; }
549       for (i += 1; i < n; ++i) { U[i] = (char)A[i]; }
550       return pidx + 1;
551     }
552     /* int */
553     /// <summary>
554     /// Constructs the burrows-wheeler transformed string of a given string in linear time.
555     /// </summary>
556     /// <param name="T">input string</param>
557     /// <param name="U">output string</param>
558     /// <param name="A">temporary array</param>
559     /// <param name="n">length of the given string</param>
560     /// <param name="k">alphabet size</param>
561     /// <returns>primary index if no error occurred, -1 or -2 otherwise</returns>
562     public static
563     int
564     bwt(int[] T, int[] U, int[] A, int n, int k)
565     {
566       int i, pidx;
567       if ((T == null) || (U == null) || (A == null) ||
568          (T.Length < n) || (U.Length < n) || (A.Length < n) ||
569          (k <= 0)) { return -1; }
570       if (n <= 1) { if (n == 1) { U[0] = T[0]; } return n; }
571       pidx = sais_main(new IntArray(T, 0), A, 0, n, k, true);
572       U[0] = T[n - 1];
573       for (i = 0; i < pidx; ++i) { U[i + 1] = A[i]; }
574       for (i += 1; i < n; ++i) { U[i] = A[i]; }
575       return pidx + 1;
576     }
577   }
578 }

    测试代码

      1 /*
  2  * suftest.cs for SAIS-CSharp
  3  * Copyright (c) 2010 Yuta Mori. All Rights Reserved.
  4  *
  5  * Permission is hereby granted, free of charge, to any person
  6  * obtaining a copy of this software and associated documentation
  7  * files (the "Software"), to deal in the Software without
  8  * restriction, including without limitation the rights to use,
  9  * copy, modify, merge, publish, distribute, sublicense, and/or sell
 10  * copies of the Software, and to permit persons to whom the
 11  * Software is furnished to do so, subject to the following
 12  * conditions:
 13  *
 14  * The above copyright notice and this permission notice shall be
 15  * included in all copies or substantial portions of the Software.
 16  *
 17  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 18  * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 19  * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 20  * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 21  * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 22  * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 23  * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 24  * OTHER DEALINGS IN THE SOFTWARE.
 25  */
 26 
 27 using SuffixArray;
 28 
 29 namespace suftest
 30 {
 31   class MainClass
 32   {
 33     private static
 34     int
 35     check(byte[] T, int[] SA, int n, bool verbose)
 36     {
 37       int[] C = new int[256];
 38       int i, p, q, t;
 39       int c;
 40 
 41       if (verbose) { System.Console.Write(@"sufcheck: "); }
 42       if (n == 0)
 43       {
 44         if (verbose) { System.Console.WriteLine("Done."); }
 45         return 0;
 46       }
 47 
 48       /* Check arguments. */
 49       if ((T == null) || (SA == null) || (n < 0))
 50       {
 51         if (verbose) { System.Console.WriteLine("Invalid arguments."); }
 52         return -1;
 53       }
 54 
 55       /* check range: [0..n-1] */
 56       for (i = 0; i < n; ++i)
 57       {
 58         if ((SA[i] < 0) || (n <= SA[i]))
 59         {
 60           if (verbose)
 61           {
 62             System.Console.WriteLine("Out of the range [0," + (n - 1) + "].");
 63             System.Console.WriteLine("  SA[" + i + "]=" + SA[i]);
 64           }
 65           return -2;
 66         }
 67       }
 68 
 69       /* check first characters. */
 70       for (i = 1; i < n; ++i)
 71       {
 72         if (T[SA[i - 1]] > T[SA[i]])
 73         {
 74           if (verbose)
 75           {
 76             System.Console.WriteLine("Suffixes in wrong order.");
 77             System.Console.Write("  T[SA[" + (i - 1) + "]=" + SA[i - 1] + "]=" + T[SA[i - 1]]);
 78             System.Console.WriteLine(" > T[SA[" + i + "]=" + SA[i] + "]=" + T[SA[i]]);
 79           }
 80           return -3;
 81         }
 82       }
 83 
 84       /* check suffixes. */
 85       for (i = 0; i < 256; ++i) { C[i] = 0; }
 86       for (i = 0; i < n; ++i) { ++C[T[i]]; }
 87       for (i = 0, p = 0; i < 256; ++i)
 88       {
 89         t = C[i];
 90         C[i] = p;
 91         p += t;
 92       }
 93 
 94       q = C[T[n - 1]];
 95       C[T[n - 1]] += 1;
 96       for (i = 0; i < n; ++i)
 97       {
 98         p = SA[i];
 99         if (0 < p)
100         {
101           c = T[--p];
102           t = C[c];
103         }
104         else
105         {
106           c = T[p = n - 1];
107           t = q;
108         }
109         if ((t < 0) || (p != SA[t]))
110         {
111           if (verbose)
112           {
113             System.Console.WriteLine("Suffixes in wrong position.");
114             System.Console.WriteLine("  SA[" + t + "]=" + ((0 <= t) ? SA[t] : -1) + " or");
115             System.Console.WriteLine("  SA[" + i + "]=" + SA[i]);
116           }
117           return -4;
118         }
119         if (t != q)
120         {
121           ++C[c];
122           if ((n <= C[c]) || (T[SA[C[c]]] != c)) { C[c] = -1; }
123         }
124       }
125       C = null;
126 
127       if (verbose) { System.Console.WriteLine("Done."); }
128       return 0;
129     }
130 
131     public static
132     void
133     Main(string[] args)
134     {
135       int i;
136       for (i = 0; i < args.Length; ++i)
137       {
138         using (System.IO.FileStream fs = new System.IO.FileStream(
139                 args[i],
140                 System.IO.FileMode.Open,
141                 System.IO.FileAccess.Read))
142         {
143           System.Console.Write(args[i] + @": {0:d} bytes ... ", fs.Length);
144           byte[] T = new byte[fs.Length];
145           int[] SA = new int[fs.Length];
146           fs.Read(T, 0, T.Length);
147 
148           System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
149           sw.Start();
150           SAIS.sufsort(T, SA, T.Length);
151           sw.Stop();
152 
153           double sec = (double)sw.ElapsedTicks / (double)System.Diagnostics.Stopwatch.Frequency;
154           System.Console.WriteLine(@"{0:f4} sec", sec);
155 
156           check(T, SA, T.Length, true);
157           T = null;
158           SA = null;
159         }
160       }
161     }
162   }
163 }

    后缀数组的应用

    • 应用1：最长公共前缀
    • 应用2：最长重复子串（不重叠）
    • 应用3：最长重复子串（可重叠）
    • 应用4：至少重复 k 次的最长子串（可重叠）
    • 应用5：最长回文子串
    • 应用6：最长公共子串
    • 应用7：长度不小于 k 的公共子串的个数
    • 应用8：至少出现在 k 个串中的最长子串

    参考资料

    本文《后缀数组》由 Dennis Gao 发表自博客园，未经作者本人同意禁止任何形式的转载，任何自动或人为的爬虫转载行为均为耍流氓。
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  • 原文地址：https://www.cnblogs.com/gaochundong/p/suffix_array.html
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