构造后缀数组的DC3算法实现

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（/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 (/ljsspace/)
* Licensed under GPL (/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 digits
class Tuple{
int isuffix; //the p-th suffix
int[] 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...max
private void countingSort(int d,Tuple[] tA,Tuple[] tB,int max){
//init the counter array
int[] C = new int[max+1];
for(int i=0;i<=max;i++){
C[i] = 0;
}
//stat the count
for(int j=0;j<tA.length;j++){
C[tA[j].digits[d]]++;
}
//process the counter array C
for(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 caculation
private 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 tA
if(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 iterations
private 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 sa
int[] sa = new int[len];
sa[0] = tB[0].isuffix;
int[] rank = new int[len+2]; //add 2 for sentinel
rank[len]=1;rank[len+1] = 1;
int r = 1; //rank starts with 1
rank[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 done
if(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 sa
int[] sa = new int[len];
for(int i=0;i<len;i++){
sa[i] = tB[i].isuffix;
}
return sa;
}
//rank needs sentinel: len+2
public Suffix reduce(int[] rank,int max){
int len = rank.length - 2;
int n1 = (len+1)/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 sa12
Suffix 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 sa12
int 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 sa12
int[] 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 sa0
int 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 sa0
for(int j=0;j<n0;j++){
sa0[j] = 3*sa0[j];
}
//step 3: merge sa12 and sa0
int[] 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){
if(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 2
if(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 char
Tuple[] tA = new Tuple[len];
Tuple[] tB = new Tuple[len]; //placeholder
for(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 array
int[] 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 2
4 44 18 60 40 49 20 13 38 4
5 21 14 4
6 35 28 59 36 42 15 53 4
7 27 5
8 32 11 30 61 2
9 41 54 19 12 34 26 57 31 10 1。