与后缀数组的top-down遍历相比,后缀树的自顶向下遍历相对直接一些。下面的实现中首先确定每一个内部结点的左右后缀边界下标(prepare方法),然后先序遍历所有内部结点。
实现:
import java.util.ArrayList; import java.util.LinkedList; import java.util.List; /** * * Top-Down traversal of a suffix tree * (The suffix tree is built with ukk algorithm) * * * Copyright (c) 2011 ljs (http://blog.csdn.net/ljsspace/) * Licensed under GPL (http://www.opensource.org/licenses/gpl-license.php) * * @author ljs * 2011-07-25 * */ public class TopDownTraverseSuffixTree { private class SuffixNode { private StringBuilder sb; private List<SuffixNode> children = new LinkedList<SuffixNode>(); private SuffixNode link; private int start; private int end; private int pathlen; private int lb; private int rb; public SuffixNode(StringBuilder sb,int start,int end,int pathlen){ this.sb = sb; this.start = start; this.end = end; this.pathlen = pathlen; } public SuffixNode(StringBuilder sb){ this.sb = sb; this.start = -1; this.end = -1; this.pathlen = 0; } public int getLength(){ if(start == -1) return 0; else return end - start + 1; } public String getString(){ if(start != -1){ return this.sb.substring(start,end+1); }else{ return ""; } } public boolean isRoot(){ return start == -1; } public String getCoordinate(){ return "[" + start+".." + end + "/" + this.pathlen + "]"; } public String toString(){ return getString() + "(" + getCoordinate() + ",link:" + ((this.link==null)?"N/A":this.link.getCoordinate()) + ",children:" + children.size() +")"; } } private class State{ private SuffixNode u; //parent(v) //private SuffixNode w; private SuffixNode v; //private int k; //the global index of text starting from 0 to text.length() //private boolean finished; } private SuffixNode root; private StringBuilder sb = new StringBuilder(); //build a suffix-tree for a string of text public void buildSuffixTree(String text) throws Exception{ int m = text.length(); if(m==0) return; if(root==null){ root = new SuffixNode(sb); root.link = root; //link to itself } List<SuffixNode> leaves = new ArrayList<SuffixNode>(); //add first node sb.append(text.charAt(0)); SuffixNode node = new SuffixNode(sb,0,0,1); leaves.add(node); root.children.add(node); int j_star = 0; //j_{i-1} SuffixNode u = root; SuffixNode v = root; for(int i=1;i<=m-1;i++){ //do phase i sb.append(text.charAt(i)); //step 1: do implicit extensions for(SuffixNode leafnode:leaves){ leafnode.end++; leafnode.pathlen++; } //step 2: do explicit extensions until rule #3 is applied State state = new State(); //for the first explicit extension, we reuse the last phase's u and do slowscan //also note: suffix link doesn't span two phases. int j=j_star+1; SuffixNode s = u; int k = s.pathlen + j; state.u = s; state.v = s; SuffixNode newleaf = slowscan(state,s,k); if(newleaf == null){ //if rule #3 is applied, then we can terminate this phase j_star = j - 1; //Note: no need to update state.v because it is not going to be used //at the next phase u = state.u; continue; }else{ j_star = j; leaves.add(newleaf); u = state.u; v = state.v; } j++; //for other explicit extensions, we start with fast scan. for(;j<=i;j++){ s = u.link; int uvLen=v.pathlen - u.pathlen; if(u.isRoot() && !v.isRoot()){ uvLen--; } //starting with index k of the text k = s.pathlen + j; //init state state.u = s; state.v = s; //if uvLen = 0 //execute fast scan newleaf = fastscan(state,s,uvLen,k); //establish the suffix link with v v.link = state.v; if(newleaf == null){ //if rule #3 is applied, then we can terminate this phase j_star = j - 1; u = state.u; break; }else{ j_star = j; leaves.add(newleaf); u = state.u; v = state.v; } } } } //slow scan from currNode until state.v is found //return the new leaf if a new one is created right after v; //return null otherwise (i.e. when rule #3 is applied) private SuffixNode slowscan(State state,SuffixNode currNode,int k){ SuffixNode newleaf = null; boolean done = false; int keyLen = sb.length() - k; for(int i=0;i<currNode.children.size();i++){ SuffixNode child = currNode.children.get(i); //use min(child.key.length, key.length) int childKeyLen = child.getLength(); int len = childKeyLen<keyLen?childKeyLen:keyLen; int delta = 0; for(;delta<len;delta++){ if(sb.charAt(k+delta) != sb.charAt(child.start+delta)){ break; } } if(delta==0){//this child doesn't match any character with the new key //order keys by lexi-order if(sb.charAt(k) < sb.charAt(child.start)){ //e.g. child="e" (currNode="abc") // abc abc // / \ =========> / | \ // e f insert "c" c e f int pathlen = sb.length() - k + currNode.pathlen; SuffixNode node = new SuffixNode(sb,k,sb.length()-1,pathlen); currNode.children.add(i,node); //state.u = currNode; //currNode is already registered as state.u, so commented out state.v = currNode; newleaf = node; done = true; break; }else{ //key.charAt(0)>child.key.charAt(0) //don't forget to add the largest new key after iterating all children continue; } }else{//current child's key partially matches with the new key if(delta==len){ if(keyLen==childKeyLen){ //e.g. child="ab" // ab ab // / \ =========> / \ // e f insert "ab" e f //terminate this phase (implicit tree with rule #3) state.u = child; state.v = currNode; }else if(keyLen>childKeyLen){ //TODO: still need an example to test this condition //e.g. child="ab" // ab ab // / \ ==========> / | \ // e f insert "abc" c e f //recursion state.u = child; state.v = child; k += childKeyLen; //state.k = k; newleaf = slowscan(state,child,k); } else{ //keyLen<childKeyLen //e.g. child="abc" // abc abc // / \ =========> / \ // e f insert "ab" e f // //terminate this phase (implicit tree with rule #3) //state.u = currNode; state.v = currNode; } }else{//0<delta<len //e.g. child="abc" // abc ab // / \ ==========> / \ // e f insert "abd" c d // / \ // e f //insert the new node: ab int nodepathlen = child.pathlen - (child.getLength()-delta); SuffixNode node = new SuffixNode(sb, child.start,child.start + delta - 1,nodepathlen); node.children = new LinkedList<SuffixNode>(); int leafpathlen = (sb.length() - (k + delta)) + nodepathlen; SuffixNode leaf = new SuffixNode(sb, k+delta,sb.length()-1,leafpathlen); //update child node: c child.start += delta; if(sb.charAt(k+delta)<sb.charAt(child.start)){ node.children.add(leaf); node.children.add(child); }else{ node.children.add(child); node.children.add(leaf); } //update parent currNode.children.set(i, node); //state.u = currNode; //currNode is already registered as state.u, so commented out state.v = node; newleaf = leaf; } done = true; break; } } if(!done){ int pathlen = sb.length() - k + currNode.pathlen; SuffixNode node = new SuffixNode(sb,k,sb.length()-1,pathlen); currNode.children.add(node); //state.u = currNode; //currNode is already registered as state.u, so commented out state.v = currNode; newleaf = node; } return newleaf; } //fast scan until state.v is found; //return the new leaf if a new one is created right after v; //return null otherwise (i.e. when rule #3 is applied) private SuffixNode fastscan(State state,SuffixNode currNode,int uvLen,int k){ if(uvLen==0){ //state.u = currNode; //currNode is already registered as state.u, so commented out //continue with slow scan return slowscan(state,currNode,k); } SuffixNode newleaf = null; boolean done = false; for(int i=0;i<currNode.children.size();i++){ SuffixNode child = currNode.children.get(i); if(sb.charAt(child.start) == sb.charAt(k)){ int len = child.getLength(); if(uvLen==len){ //then we find v //uvLen = 0; state.u = child; //state.v = child; k += len; //state.k = k; //continue with slow scan newleaf = slowscan(state,child,k); }else if(uvLen<len){ //we know v must be an internal node; branching and cut child short //e.g. child="abc",uvLen = 2 // abc ab // / \ ================> / \ // e f suffix part: "abd" c d // / \ // e f //insert the new node: ab; child is now c int nodepathlen = child.pathlen - (child.getLength()-uvLen); SuffixNode node = new SuffixNode(sb, child.start,child.start + uvLen - 1,nodepathlen); node.children = new LinkedList<SuffixNode>(); int leafpathlen = (sb.length() - (k + uvLen)) + nodepathlen; SuffixNode leaf = new SuffixNode(sb, k+uvLen,sb.length()-1,leafpathlen); //update child node: c child.start += uvLen; if(sb.charAt(k+uvLen)<sb.charAt(child.start)){ node.children.add(leaf); node.children.add(child); }else{ node.children.add(child); node.children.add(leaf); } //update parent currNode.children.set(i, node); //uvLen = 0; //state.u = currNode; //currNode is already registered as state.u, so commented out state.v = node; newleaf = leaf; }else{//uvLen>len //e.g. child="abc", uvLen = 4 // abc // / \ ================> // e f suffix part: "abcde" // // //jump to next node uvLen -= len; state.u = child; //state.v = child; k += len; //state.k = k; newleaf = fastscan(state,child,uvLen,k); } done = true; break; } } if(!done){ //TODO: still need an example to test this condition //add a leaf under the currNode int pathlen = sb.length() - k + currNode.pathlen; SuffixNode node = new SuffixNode(sb,k,sb.length()-1,pathlen); currNode.children.add(node); //state.u = currNode; //currNode is already registered as state.u, so commented out state.v = currNode; newleaf = node; } return newleaf; } private int maxk=0; //the suffix array index private void prepare(SuffixNode currNode){ for(int i=0;i<currNode.children.size();i++){ SuffixNode child = currNode.children.get(i); prepare(child); } if(!currNode.children.isEmpty()){ currNode.lb = currNode.children.get(0).lb; currNode.rb = currNode.children.get(currNode.children.size()-1).rb; }else{ currNode.lb = currNode.rb = maxk; maxk++; } } public void topDownTraverse(){ //prepare lb and rb for each internal node prepare(root); topDownTraverse(root); } public void topDownTraverse(SuffixNode currNode){ if(!currNode.children.isEmpty()) visit(currNode); for(int i=0;i<currNode.children.size();i++){ SuffixNode child = currNode.children.get(i); if(!child.children.isEmpty()){ topDownTraverse(child); } } } //visit internal node private void visit(SuffixNode node){ String interval = String.format("%d-[%d..%d]", node.pathlen,node.lb,node.rb); if(node.children.size()>0){ StringBuilder sb = new StringBuilder(); int internalNodes = 0; for(SuffixNode child:node.children){ if(!child.children.isEmpty()){ internalNodes++; String childInterval = String.format("%d-[%d..%d]", child.pathlen,child.lb,child.rb); sb.append(childInterval); sb.append(","); } } if(internalNodes>0){ sb.deleteCharAt(sb.length()-1); System.out.format("%s, children={%s}%n", interval,sb.toString()); }else{ System.out.format("%s%n", interval); } }else{ System.out.format("%s%n", interval); } } //for test purpose only public void printTree(){ System.out.format("The suffix tree for S = %s is: %n",this.sb); this.print(0, this.root); } private void print(int level, SuffixNode node){ for (int i = 0; i < level; i++) { System.out.format(" "); } System.out.format("|"); for (int i = 0; i < level; i++) { System.out.format("-"); } System.out.format("%s(%d..%d/%d)%n", node.getString(),node.start,node.end,node.pathlen); //System.out.format("(%d,%d)%n", node.start,node.end); for (SuffixNode child : node.children) { print(level + 1, child); } } public static void main(String[] args) throws Exception { //test suffix-tree System.out.println("****************************"); String text = "mississippi#"; //the last char must be unique! TopDownTraverseSuffixTree stree = new TopDownTraverseSuffixTree(); stree.buildSuffixTree(text); //stree.printTree(); System.out.format("%nInternal Nodes for text: %s %n",text); stree.topDownTraverse(); System.out.println(); System.out.println("****************************"); text = "GACCCACCACC#"; //the last char must be unique! stree = new TopDownTraverseSuffixTree(); stree.buildSuffixTree(text); //stree.printTree(); System.out.format("Internal Nodes for text: %s %n",text); stree.topDownTraverse(); System.out.println(); System.out.println("****************************"); text = "abcdefghijklmmnopqrstuvwxyz#"; //the last char must be unique! stree = new TopDownTraverseSuffixTree(); stree.buildSuffixTree(text); //stree.printTree(); System.out.format("Internal Nodes for text: %s %n",text); stree.topDownTraverse(); System.out.println("****************************"); text = "yabbadabbado#"; //the last char must be unique! stree = new TopDownTraverseSuffixTree(); stree.buildSuffixTree(text); //stree.printTree(); System.out.format("Internal Nodes for text: %s %n",text); stree.topDownTraverse(); System.out.println("****************************"); text = "AAAAAAAAAAAAAAAAAAAAAAAAAA#"; //the last char must be unique! stree = new TopDownTraverseSuffixTree(); stree.buildSuffixTree(text); //stree.printTree(); System.out.format("Internal Nodes for text: %s %n",text); stree.topDownTraverse(); System.out.println("****************************"); text = "GGGGGGGGGGGGCGCAAAAGCGAGCAGAGAGAAAAAAAAAAAAAAAAAAAAAA#"; //the last char must be unique! stree = new TopDownTraverseSuffixTree(); stree.buildSuffixTree(text); //stree.printTree(); System.out.format("Internal Nodes for text: %s %n",text); stree.topDownTraverse(); } }
测试:
****************************
Internal Nodes for text: mississippi#
0-[0..11], children={1-[1..4],1-[6..7],1-[8..11]}
1-[1..4], children={4-[3..4]}
4-[3..4]
1-[6..7]
1-[8..11], children={2-[8..9],3-[10..11]}
2-[8..9]
3-[10..11]
****************************
Internal Nodes for text: GACCCACCACC#
0-[0..11], children={3-[1..3],1-[4..10]}
3-[1..3]
1-[4..10], children={4-[5..6],2-[7..10]}
4-[5..6]
2-[7..10], children={5-[8..9]}
5-[8..9]
****************************
Internal Nodes for text: abcdefghijklmmnopqrstuvwxyz#
0-[0..27], children={1-[13..14]}
1-[13..14]
****************************
Internal Nodes for text: yabbadabbado#
0-[0..12], children={1-[1..4],1-[5..8],1-[9..10]}
1-[1..4], children={5-[1..2],2-[3..4]}
5-[1..2]
2-[3..4]
1-[5..8], children={3-[5..6],4-[7..8]}
3-[5..6]
4-[7..8]
1-[9..10]
****************************
Internal Nodes for text: AAAAAAAAAAAAAAAAAAAAAAAAAA#
0-[0..26], children={1-[1..26]}
1-[1..26], children={2-[2..26]}
2-[2..26], children={3-[3..26]}
3-[3..26], children={4-[4..26]}
4-[4..26], children={5-[5..26]}
5-[5..26], children={6-[6..26]}
6-[6..26], children={7-[7..26]}
7-[7..26], children={8-[8..26]}
8-[8..26], children={9-[9..26]}
9-[9..26], children={10-[10..26]}
10-[10..26], children={11-[11..26]}
11-[11..26], children={12-[12..26]}
12-[12..26], children={13-[13..26]}
13-[13..26], children={14-[14..26]}
14-[14..26], children={15-[15..26]}
15-[15..26], children={16-[16..26]}
16-[16..26], children={17-[17..26]}
17-[17..26], children={18-[18..26]}
18-[18..26], children={19-[19..26]}
19-[19..26], children={20-[20..26]}
20-[20..26], children={21-[21..26]}
21-[21..26], children={22-[22..26]}
22-[22..26], children={23-[23..26]}
23-[23..26], children={24-[24..26]}
24-[24..26], children={25-[25..26]}
25-[25..26]
****************************
Internal Nodes for text: GGGGGGGGGGGGCGCAAAAGCGAGCAGAGAGAAAAAAAAAAAAAAAAAAAAAA#
0-[0..53], children={1-[1..30],1-[31..34],1-[35..53]}
1-[1..30], children={2-[2..25],2-[26..30]}
2-[2..25], children={3-[3..24]}
3-[3..24], children={4-[4..23]}
4-[4..23], children={5-[5..22]}
5-[5..22], children={6-[6..22]}
6-[6..22], children={7-[7..22]}
7-[7..22], children={8-[8..22]}
8-[8..22], children={9-[9..22]}
9-[9..22], children={10-[10..22]}
10-[10..22], children={11-[11..22]}
11-[11..22], children={12-[12..22]}
12-[12..22], children={13-[13..22]}
13-[13..22], children={14-[14..22]}
14-[14..22], children={15-[15..22]}
15-[15..22], children={16-[16..22]}
16-[16..22], children={17-[17..22]}
17-[17..22], children={18-[18..22]}
18-[18..22], children={19-[19..22]}
19-[19..22], children={20-[20..22]}
20-[20..22], children={21-[21..22]}
21-[21..22]
2-[26..30], children={3-[26..28],3-[29..30]}
3-[26..28], children={5-[27..28]}
5-[27..28]
3-[29..30]
1-[31..34], children={2-[31..32],2-[33..34]}
2-[31..32]
2-[33..34]
1-[35..53], children={2-[35..38],2-[39..42],2-[43..53]}
2-[35..38], children={3-[36..38]}
3-[36..38], children={4-[36..37]}
4-[36..37]
2-[39..42], children={3-[39..40],3-[41..42]}
3-[39..40]
3-[41..42]
2-[43..53], children={3-[44..53]}
3-[44..53], children={4-[45..53]}
4-[45..53], children={5-[46..53]}
5-[46..53], children={6-[47..53]}
6-[47..53], children={7-[48..53]}
7-[48..53], children={8-[49..53]}
8-[49..53], children={9-[50..53]}
9-[50..53], children={10-[51..53]}
10-[51..53], children={11-[52..53]}
11-[52..53]