@jogojapan you brought awesome explanation and visualisation. But as @makagonov mentioned it's missing some rules regarding setting suffix links. It's visible in nice way when going step by step on http://brenden.github.io/ukkonen-animation/ through word 'aabaaabb'. When you go from step 10 to step 11, there is no suffix link from node 5 to node 2 but active point suddenly moves there.
@makagonov since I live in Java world I also tried to follow your implementation to grasp ST building workflow but it was hard to me because of:
- combining edges with nodes
- using index pointers instead of references
- breaks statements;
- continue statements;
So I ended up with such implementation in Java which I hope reflects all steps in clearer way and will reduce learning time for other Java people:
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
public class ST {
public class Node {
private final int id;
private final Map edges;
private Node slink;
public Node(final int id) {
this.id = id;
this.edges = new HashMap<>();
}
public void setSlink(final Node slink) {
this.slink = slink;
}
public Map getEdges() {
return this.edges;
}
public Node getSlink() {
return this.slink;
}
public String toString(final String word) {
return new StringBuilder()
.append("{")
.append("\"id\"")
.append(":")
.append(this.id)
.append(",")
.append("\"slink\"")
.append(":")
.append(this.slink != null ? this.slink.id : null)
.append(",")
.append("\"edges\"")
.append(":")
.append(edgesToString(word))
.append("}")
.toString();
}
private StringBuilder edgesToString(final String word) {
final StringBuilder edgesStringBuilder = new StringBuilder();
edgesStringBuilder.append("{");
for(final Map.Entry entry : this.edges.entrySet()) {
edgesStringBuilder.append("\"")
.append(entry.getKey())
.append("\"")
.append(":")
.append(entry.getValue().toString(word))
.append(",");
}
if(!this.edges.isEmpty()) {
edgesStringBuilder.deleteCharAt(edgesStringBuilder.length() - 1);
}
edgesStringBuilder.append("}");
return edgesStringBuilder;
}
public boolean contains(final String word, final String suffix) {
return !suffix.isEmpty()
&& this.edges.containsKey(suffix.charAt(0))
&& this.edges.get(suffix.charAt(0)).contains(word, suffix);
}
}
public class Edge {
private final int from;
private final int to;
private final Node next;
public Edge(final int from, final int to, final Node next) {
this.from = from;
this.to = to;
this.next = next;
}
public int getFrom() {
return this.from;
}
public int getTo() {
return this.to;
}
public Node getNext() {
return this.next;
}
public int getLength() {
return this.to - this.from;
}
public String toString(final String word) {
return new StringBuilder()
.append("{")
.append("\"content\"")
.append(":")
.append("\"")
.append(word.substring(this.from, this.to))
.append("\"")
.append(",")
.append("\"next\"")
.append(":")
.append(this.next != null ? this.next.toString(word) : null)
.append("}")
.toString();
}
public boolean contains(final String word, final String suffix) {
if(this.next == null) {
return word.substring(this.from, this.to).equals(suffix);
}
return suffix.startsWith(word.substring(this.from,
this.to)) && this.next.contains(word, suffix.substring(this.to - this.from));
}
}
public class ActivePoint {
private final Node activeNode;
private final Character activeEdgeFirstCharacter;
private final int activeLength;
public ActivePoint(final Node activeNode,
final Character activeEdgeFirstCharacter,
final int activeLength) {
this.activeNode = activeNode;
this.activeEdgeFirstCharacter = activeEdgeFirstCharacter;
this.activeLength = activeLength;
}
private Edge getActiveEdge() {
return this.activeNode.getEdges().get(this.activeEdgeFirstCharacter);
}
public boolean pointsToActiveNode() {
return this.activeLength == 0;
}
public boolean activeNodeIs(final Node node) {
return this.activeNode == node;
}
public boolean activeNodeHasEdgeStartingWith(final char character) {
return this.activeNode.getEdges().containsKey(character);
}
public boolean activeNodeHasSlink() {
return this.activeNode.getSlink() != null;
}
public boolean pointsToOnActiveEdge(final String word, final char character) {
return word.charAt(this.getActiveEdge().getFrom() + this.activeLength) == character;
}
public boolean pointsToTheEndOfActiveEdge() {
return this.getActiveEdge().getLength() == this.activeLength;
}
public boolean pointsAfterTheEndOfActiveEdge() {
return this.getActiveEdge().getLength() < this.activeLength;
}
public ActivePoint moveToEdgeStartingWithAndByOne(final char character) {
return new ActivePoint(this.activeNode, character, 1);
}
public ActivePoint moveToNextNodeOfActiveEdge() {
return new ActivePoint(this.getActiveEdge().getNext(), null, 0);
}
public ActivePoint moveToSlink() {
return new ActivePoint(this.activeNode.getSlink(),
this.activeEdgeFirstCharacter,
this.activeLength);
}
public ActivePoint moveTo(final Node node) {
return new ActivePoint(node, this.activeEdgeFirstCharacter, this.activeLength);
}
public ActivePoint moveByOneCharacter() {
return new ActivePoint(this.activeNode,
this.activeEdgeFirstCharacter,
this.activeLength + 1);
}
public ActivePoint moveToEdgeStartingWithAndByActiveLengthMinusOne(final Node node,
final char character) {
return new ActivePoint(node, character, this.activeLength - 1);
}
public ActivePoint moveToNextNodeOfActiveEdge(final String word, final int index) {
return new ActivePoint(this.getActiveEdge().getNext(),
word.charAt(index - this.activeLength + this.getActiveEdge().getLength()),
this.activeLength - this.getActiveEdge().getLength());
}
public void addEdgeToActiveNode(final char character, final Edge edge) {
this.activeNode.getEdges().put(character, edge);
}
public void splitActiveEdge(final String word,
final Node nodeToAdd,
final int index,
final char character) {
final Edge activeEdgeToSplit = this.getActiveEdge();
final Edge splittedEdge = new Edge(activeEdgeToSplit.getFrom(),
activeEdgeToSplit.getFrom() + this.activeLength,
nodeToAdd);
nodeToAdd.getEdges().put(word.charAt(activeEdgeToSplit.getFrom() + this.activeLength),
new Edge(activeEdgeToSplit.getFrom() + this.activeLength,
activeEdgeToSplit.getTo(),
activeEdgeToSplit.getNext()));
nodeToAdd.getEdges().put(character, new Edge(index, word.length(), null));
this.activeNode.getEdges().put(this.activeEdgeFirstCharacter, splittedEdge);
}
public Node setSlinkTo(final Node previouslyAddedNodeOrAddedEdgeNode,
final Node node) {
if(previouslyAddedNodeOrAddedEdgeNode != null) {
previouslyAddedNodeOrAddedEdgeNode.setSlink(node);
}
return node;
}
public Node setSlinkToActiveNode(final Node previouslyAddedNodeOrAddedEdgeNode) {
return setSlinkTo(previouslyAddedNodeOrAddedEdgeNode, this.activeNode);
}
}
private static int idGenerator;
private final String word;
private final Node root;
private ActivePoint activePoint;
private int remainder;
public ST(final String word) {
this.word = word;
this.root = new Node(idGenerator++);
this.activePoint = new ActivePoint(this.root, null, 0);
this.remainder = 0;
build();
}
private void build() {
for(int i = 0; i < this.word.length(); i++) {
add(i, this.word.charAt(i));
}
}
private void add(final int index, final char character) {
this.remainder++;
boolean characterFoundInTheTree = false;
Node previouslyAddedNodeOrAddedEdgeNode = null;
while(!characterFoundInTheTree && this.remainder > 0) {
if(this.activePoint.pointsToActiveNode()) {
if(this.activePoint.activeNodeHasEdgeStartingWith(character)) {
activeNodeHasEdgeStartingWithCharacter(character, previouslyAddedNodeOrAddedEdgeNode);
characterFoundInTheTree = true;
}
else {
if(this.activePoint.activeNodeIs(this.root)) {
rootNodeHasNotEdgeStartingWithCharacter(index, character);
}
else {
previouslyAddedNodeOrAddedEdgeNode = internalNodeHasNotEdgeStartingWithCharacter(index,
character, previouslyAddedNodeOrAddedEdgeNode);
}
}
}
else {
if(this.activePoint.pointsToOnActiveEdge(this.word, character)) {
activeEdgeHasCharacter();
characterFoundInTheTree = true;
}
else {
if(this.activePoint.activeNodeIs(this.root)) {
previouslyAddedNodeOrAddedEdgeNode = edgeFromRootNodeHasNotCharacter(index,
character,
previouslyAddedNodeOrAddedEdgeNode);
}
else {
previouslyAddedNodeOrAddedEdgeNode = edgeFromInternalNodeHasNotCharacter(index,
character,
previouslyAddedNodeOrAddedEdgeNode);
}
}
}
}
}
private void activeNodeHasEdgeStartingWithCharacter(final char character,
final Node previouslyAddedNodeOrAddedEdgeNode) {
this.activePoint.setSlinkToActiveNode(previouslyAddedNodeOrAddedEdgeNode);
this.activePoint = this.activePoint.moveToEdgeStartingWithAndByOne(character);
if(this.activePoint.pointsToTheEndOfActiveEdge()) {
this.activePoint = this.activePoint.moveToNextNodeOfActiveEdge();
}
}
private void rootNodeHasNotEdgeStartingWithCharacter(final int index, final char character) {
this.activePoint.addEdgeToActiveNode(character, new Edge(index, this.word.length(), null));
this.activePoint = this.activePoint.moveTo(this.root);
this.remainder--;
assert this.remainder == 0;
}
private Node internalNodeHasNotEdgeStartingWithCharacter(final int index,
final char character,
Node previouslyAddedNodeOrAddedEdgeNode) {
this.activePoint.addEdgeToActiveNode(character, new Edge(index, this.word.length(), null));
previouslyAddedNodeOrAddedEdgeNode = this.activePoint.setSlinkToActiveNode(previouslyAddedNodeOrAddedEdgeNode);
if(this.activePoint.activeNodeHasSlink()) {
this.activePoint = this.activePoint.moveToSlink();
}
else {
this.activePoint = this.activePoint.moveTo(this.root);
}
this.remainder--;
return previouslyAddedNodeOrAddedEdgeNode;
}
private void activeEdgeHasCharacter() {
this.activePoint = this.activePoint.moveByOneCharacter();
if(this.activePoint.pointsToTheEndOfActiveEdge()) {
this.activePoint = this.activePoint.moveToNextNodeOfActiveEdge();
}
}
private Node edgeFromRootNodeHasNotCharacter(final int index,
final char character,
Node previouslyAddedNodeOrAddedEdgeNode) {
final Node newNode = new Node(idGenerator++);
this.activePoint.splitActiveEdge(this.word, newNode, index, character);
previouslyAddedNodeOrAddedEdgeNode = this.activePoint.setSlinkTo(previouslyAddedNodeOrAddedEdgeNode, newNode);
this.activePoint = this.activePoint.moveToEdgeStartingWithAndByActiveLengthMinusOne(this.root,
this.word.charAt(index - this.remainder + 2));
this.activePoint = walkDown(index);
this.remainder--;
return previouslyAddedNodeOrAddedEdgeNode;
}
private Node edgeFromInternalNodeHasNotCharacter(final int index,
final char character,
Node previouslyAddedNodeOrAddedEdgeNode) {
final Node newNode = new Node(idGenerator++);
this.activePoint.splitActiveEdge(this.word, newNode, index, character);
previouslyAddedNodeOrAddedEdgeNode = this.activePoint.setSlinkTo(previouslyAddedNodeOrAddedEdgeNode, newNode);
if(this.activePoint.activeNodeHasSlink()) {
this.activePoint = this.activePoint.moveToSlink();
}
else {
this.activePoint = this.activePoint.moveTo(this.root);
}
this.activePoint = walkDown(index);
this.remainder--;
return previouslyAddedNodeOrAddedEdgeNode;
}
private ActivePoint walkDown(final int index) {
while(!this.activePoint.pointsToActiveNode()
&& (this.activePoint.pointsToTheEndOfActiveEdge() || this.activePoint.pointsAfterTheEndOfActiveEdge())) {
if(this.activePoint.pointsAfterTheEndOfActiveEdge()) {
this.activePoint = this.activePoint.moveToNextNodeOfActiveEdge(this.word, index);
}
else {
this.activePoint = this.activePoint.moveToNextNodeOfActiveEdge();
}
}
return this.activePoint;
}
public String toString(final String word) {
return this.root.toString(word);
}
public boolean contains(final String suffix) {
return this.root.contains(this.word, suffix);
}
public static void main(final String[] args) {
final String[] words = {
"abcabcabc$",
"abc$",
"abcabxabcd$",
"abcabxabda$",
"abcabxad$",
"aabaaabb$",
"aababcabcd$",
"ababcabcd$",
"abccba$",
"mississipi$",
"abacabadabacabae$",
"abcabcd$",
"00132220$"
};
Arrays.stream(words).forEach(word -> {
System.out.println("Building suffix tree for word: " + word);
final ST suffixTree = new ST(word);
System.out.println("Suffix tree: " + suffixTree.toString(word));
for(int i = 0; i < word.length() - 1; i++) {
assert suffixTree.contains(word.substring(i)) : word.substring(i);
}
});
}
}
加载中...