构造后缀数组的DC3算法实现

DC3算法(Difference Cover mod 3)是J. Kärkkäinen和P. Sanders在2003年发表的论文 "Simple Linear Work Suffix Array Construction"中描述的线性时间内构造后缀数组的算法。相对Prefix Doubling（前缀倍增）算法而言，虽然它的渐进时间复杂度比较小，但是常数项比较大。DC3算法的思想类似于找中位数的median of medians算法（http://en.wikipedia.org/wiki/Selection_algorithm），它采用分治思想: 先用递归方式对起始下标等于1(mod 3)和2(mod 3)的后缀排序，从而将原始的后缀集合大小缩小为2/3，设这些后缀排好序的结果为S12，然后在S12的基础上对起始下标等于0(mod 3)的后缀排序（这一步只需作两位数的基数排序，一位为0(mod 3)的起始下标，另外一位为S12的rank值），设这一步得到的排好序的后缀数组为S0，最后将S0和S12归并（类似于归并排序算法）。归并过程通过Difference Cover思想，也是在S12已知的基础上分两个cases得出相邻两个后缀的先后顺序。

实现：

    /** *  * Build Suffix Array using DC3/KS Algorithm  *   *   * Copyright (c) 2011 ljs (http://blog.csdn.net/ljsspace/) * Licensed under GPL (http://www.opensource.org/licenses/gpl-license.php)  *  * @author ljs * 2011-07-18 * */public class DC3 {public static final char MAX_CHAR = '\u00FF';class Suffix{int[] sa;  //Note: the p-th suffix in sa: SA[rank[p]-1]];//p is the index of the array "rank", start with 0;//a text S's p-th suffix is S[p..n], n=S.length-1.int[] rank; boolean done; public Suffix(int[] sa,int[] rank){this.sa = sa;this.rank = rank;}}//a prefix of suffix[isuffix] represented with digitsclass Tuple{int isuffix; //the p-th suffixint[] digits;public Tuple(int suffix,int[] digits){this.isuffix = suffix;this.digits = digits;}public String toString(){StringBuffer sb = new StringBuffer();sb.append(isuffix);sb.append("(");for(int i=0;i<digits.length;i++){sb.append(digits[i]);if(i<digits.length-1)sb.append("-");}sb.append(")");return sb.toString();}}//d: the digit to do countingsort//max: A value's range is 0...maxprivate void countingSort(int d,Tuple[] tA,Tuple[] tB,int max){//init the counter arrayint[] C = new int[max+1];for(int i=0;i<=max;i++){C[i] = 0;}//stat the countfor(int j=0;j<tA.length;j++){C[tA[j].digits[d]]++;}//process the counter array Cfor(int i=1;i<=max;i++){C[i]+=C[i-1];}//distribute the values  for(int j=tA.length-1;j>=0;j--){//C[A[j]] <= A.length tB[--C[tA[j].digits[d]]]=tA[j];}}//tA: input//tB: output for rank caculationprivate void radixSort(Tuple[] tA,Tuple[] tB,int max,int digitsLen){int len = tA.length;int digitsTotalLen = tA[0].digits.length;for(int d=digitsTotalLen-1,j=0;j<digitsLen;d--,j++){this.countingSort(d, tA, tB, max);//assign tB to tAif(j<digitsLen-1){for(int i=0;i<len;i++){tA[i] = tB[i];}}}}//max is the maximum value in any digit of TA.digits[], used for counting sort//tA: input//tB: the place holder, reused between iterationsprivate Suffix rank(Tuple[] tA,Tuple[] tB,int max,int digitsLen){int len = tA.length;radixSort(tA,tB,max,digitsLen);int digitsTotalLen = tA[0].digits.length;//caculate rank and saint[] sa = new int[len];sa[0] = tB[0].isuffix;int[] rank = new int[len+2]; //add 2 for sentinelrank[len]=1;rank[len+1] = 1;int r = 1; //rank starts with 1rank[tB[0].isuffix] = r;for(int i=1;i<len;i++){sa[i] = tB[i].isuffix;boolean equalLast = true;for(int j=digitsTotalLen-digitsLen;j<digitsTotalLen;j++){if(tB[i].digits[j]!=tB[i-1].digits[j]){equalLast = false;break;}}if(!equalLast){r++;}rank[tB[i].isuffix] = r;} Suffix suffix = new Suffix(sa,rank);//judge if we are doneif(r==len){suffix.done = true;}else{suffix.done = false;}return suffix;}private int[] orderSuffixes(Tuple[] tA,Tuple[] tB,int max,int digitsLen){int len = tA.length;radixSort(tA,tB,max,digitsLen);//caculate rank and saint[] sa = new int[len];for(int i=0;i<len;i++){sa[i] = tB[i].isuffix;}return sa; }//rank needs sentinel: len+2public Suffix reduce(int[] rank,int max){int len = rank.length - 2;int n1 = (len+1)/3;int n2 = len/3;Tuple[] tA = new Tuple[n1+n2];Tuple[] tB = new Tuple[n1+n2];for(int i=0,j=1;i<n1;i++,j+=3){int r1 =  rank[j];int r2 =  rank[j+1];int r3 =  rank[j+2];tA[i] = new Tuple(i,new int[]{r1,r2,r3});}for(int i=n1,j=2;i<n1+n2;i++,j+=3){int r1 =  rank[j];int r2 =  rank[j+1];int r3 =  rank[j+2]; tA[i] = new Tuple(i,new int[]{r1,r2,r3});} return rank(tA,tB,max,3);}public int[] skew(int[] rank,int max){int len = rank.length - 2;//step 1: caculate sa12Suffix suffixT12 = reduce(rank,max); int[] sa12 = null;if(!suffixT12.done){int[] rankT12 = suffixT12.rank;int maxT12 = rankT12[suffixT12.sa[suffixT12.sa.length-1]];sa12 = skew(rankT12,maxT12);// debug for string: GACCCACCACC#//s12 = new Suffix();//s12.rank = new int[]{3,6,5,4,7,2,1,1,1};//s12.sa = new int[]{7,6,5,0,3,2,1,4};//s12.done =true;}else{sa12 = suffixT12.sa;}//index conversion for sa12int n1 = (len+1)/3;for(int j=0;j<sa12.length;j++){if(sa12[j]<n1){sa12[j] = 1 + 3*sa12[j];}else{sa12[j] = 2 + 3*(sa12[j]-n1);}}//recaculate rank for sa12int[] rank12 = new int[len+2];rank12[len] = 1;rank12[len+1] = 1;for(int k=0;k<sa12.length;k++){rank12[sa12[k]] = k+1;}   //step 2: caculate sa0int n0=(len+2)/3;Tuple[] tA = new Tuple[n0];Tuple[] tB = new Tuple[n0];for(int i=0,j=0;i<n0;i++,j+=3){int r1 =  rank[j];int r2 =  rank12[j+1]; tA[i] = new Tuple(i,new int[]{r1,r2});}int max12 = rank12[sa12[sa12.length-1]];int[] sa0 = orderSuffixes(tA,tB,max<max12?max12:max,2);//index conversion for sa0for(int j=0;j<n0;j++){sa0[j] = 3*sa0[j];} //step 3: merge sa12 and sa0int[] sa = new int[len];int i=0,j=0;int k=0;while(i<sa12.length && j<sa0.length){int p = sa12[i];int q = sa0[j];if(p%3==1){//case 1if(rank[p]<rank[q]){sa[k++] = p;i++;}else if(rank[p]>rank[q]){sa[k++] = q;j++;}else{if(rank12[p+1]<rank12[q+1]){sa[k++] = p;i++;}else{sa[k++] = q;j++;}}}else{//case 2if(rank[p]<rank[q]){sa[k++] = p;i++;}else if(rank[p]>rank[q]){sa[k++] = q;j++;}else{if(rank[p+1]<rank[q+1]){sa[k++] = p;i++;}else if(rank[p+1]>rank[q+1]){sa[k++] = q;j++;}else{if(rank12[p+2]<rank12[q+2]){sa[k++] = p;i++;}else{sa[k++] = q;j++;}}}}}for(int m=i;m<sa12.length;m++){sa[k++] = sa12[m];}for(int m=j;m<sa0.length;m++){sa[k++] = sa0[m];}return sa;}//Precondition: the last char in text must be less than other chars.public Suffix solve(String text){if(text == null)return null;int len = text.length();if(len == 0) return null;char base = text.charAt(len-1); //the smallest charTuple[] tA = new Tuple[len];Tuple[] tB = new Tuple[len]; //placeholderfor(int i=0;i<len;i++){tA[i] = new Tuple(i,new int[]{0,text.charAt(i)-base});}Suffix suffix = rank(tA,tB,MAX_CHAR-base,1); int max = suffix.rank[suffix.sa[len-1]];int[] sa  = skew(suffix.rank,max);//caculate rank for result suffix arrayint[] r = new int[len];for(int k=0;k<sa.length;k++){r[sa[k]] = k+1;}return new Suffix(sa,r);}public void report(Suffix suffix){int[] sa = suffix.sa;int[] rank = suffix.rank;int len = sa.length;System.out.println("suffix array:");for(int i=0;i<len;i++){System.out.format(" %s", sa[i]);}System.out.println();System.out.println("rank array:");for(int i=0;i<len;i++){System.out.format(" %s", rank[i]);}System.out.println();}public static void main(String[] args) {String text = "GACCCACCACC#";DC3 dc3 = new DC3();Suffix suffix = dc3.solve(text);System.out.format("Text: %s%n",text);dc3.report(suffix);text = "mississippi#";dc3 = new DC3();suffix = dc3.solve(text);System.out.format("Text: %s%n",text);dc3.report(suffix);text = "abcdefghijklmmnopqrstuvwxyz#";dc3 = new DC3();suffix = dc3.solve(text);System.out.format("Text: %s%n",text);dc3.report(suffix);text = "yabbadabbado#";dc3 = new DC3();suffix = dc3.solve(text);System.out.format("Text: %s%n",text);dc3.report(suffix);text = "DFDLKJLJldfasdlfjasdfkldjasfldafjdajfdsfjalkdsfaewefsdafdsfa#";dc3 = new DC3();suffix = dc3.solve(text);System.out.format("Text: %s%n",text);dc3.report(suffix);}}

测试：

Text: GACCCACCACC#
suffix array:
 11 8 5 1 10 7 4 9 6 3 2 0
rank array:
 12 4 11 10 7 3 9 6 2 8 5 1
Text: mississippi#
suffix array:
 11 10 7 4 1 0 9 8 6 3 5 2
rank array:
 6 5 12 10 4 11 9 3 8 7 2 1
Text: abcdefghijklmmnopqrstuvwxyz#
suffix array:
 27 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
rank array:
 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1
Text: yabbadabbado#
suffix array:
 12 1 6 4 9 3 8 2 7 5 10 11 0
rank array:
 13 2 8 6 4 10 3 9 7 5 11 12 1
Text: DFDLKJLJldfasdlfjasdfkldjasfldafjdajfdsfjalkdsfaewefsdafdsfa#
suffix array:
 60 0 2 1 5 7 4 6 3 59 47 54 30 34 41 17 11 25 53 29 33 9 19 23 13 56 44 37 50 48 58 46 10 55 36 39 15 31 20 27 51 40 16 24 32 35 43 21 28 8 22 14 42 52 18 12 57 45 38 26 49
rank array:
 2 4 3 9 7 5 8 6 50 22 33 17 56 25 52 37 43 16 55 23 39 48 51 24 44 18 60 40 49 20 13 38 45 21 14 46 35 28 59 36 42 15 53 47 27 58 32 11 30 61 29 41 54 19 12 34 26 57 31 10 1