import java.util.*; public class Main { public static void main(String args[]) { Scanner scn = new Scanner(System.in); String s = scn.next(); SuffixTree st = new SuffixTree(s.toCharArray()); st.build(); // Write code here } } class SuffixTree { ///////////////////////////////////////////////////////////////// Code starts here ///////////////////////////////////////////////////////////////// Code ends here public SuffixNode root; private Active active; private int remainingSuffixCount; private End end; private char input[]; private static char UNIQUE_CHAR = ''$''; SuffixTree(char input[]) { this.input = new char[input.length + 1]; for (int i = 0; i < input.length; i++) { this.input[i] = input[i]; } this.input[input.length] = UNIQUE_CHAR; } public void build() { root = SuffixNode.createNode(1, new End(0)); root.index = -1; active = new Active(root); this.end = new End(-1); //loop through string to start new phase for (int i = 0; i < input.length; i++) { startPhase(i); } if (remainingSuffixCount != 0) { System.out.print("Something wrong happened"); } //finally walk the tree again and set up the index. setIndexUsingDfs(root, 0, input.length); } private void startPhase(int i) { //set lastCreatedInternalNode to null before start of every phase. SuffixNode lastCreatedInternalNode = null; //global end for leaf. Does rule 1 extension as per trick 3 by incrementing end. end.end++; //these many suffixes need to be created. remainingSuffixCount++; while (remainingSuffixCount > 0) { //if active length is 0 then look for current character from root. if (active.activeLength == 0) { //if current character from root is not null then increase active length by 1 //and break out of while loop. This is rule 3 extension and trick 2 (show stopper) if (selectNode(i) != null) { active.activeEdge = selectNode(i).start; active.activeLength++; break; } //create a new leaf node with current character from leaf. This is rule 2 extension. else { root.child[input[i]] = SuffixNode.createNode(i, end); remainingSuffixCount--; } } else { //if active length is not 0 means we are traversing somewhere in middle. So check if next character is same as //current character. try { char ch = nextChar(i); //if next character is same as current character then do a walk down. This is again a rule 3 extension and //trick 2 (show stopper). if (ch == input[i]) { //if lastCreatedInternalNode is not null means rule 2 extension happened before this. Point suffix link of that node //to selected node using active point. //TODO - Could be wrong here. Do we only do this if when walk down goes past a node or we do it every time. if (lastCreatedInternalNode != null) { lastCreatedInternalNode.suffixLink = selectNode(); } //walk down and update active node if required as per rules of active node update for rule 3 extension. walkDown(i); break; } else { //next character is not same as current character so create a new internal node as per //rule 2 extension. SuffixNode node = selectNode(); int oldStart = node.start; node.start = node.start + active.activeLength; //create new internal node SuffixNode newInternalNode = SuffixNode.createNode(oldStart, new End(oldStart + active.activeLength - 1)); //create new leaf node SuffixNode newLeafNode = SuffixNode.createNode(i, this.end); //set internal nodes child as old node and new leaf node. newInternalNode.child[input[newInternalNode.start + active.activeLength]] = node; newInternalNode.child[input[i]] = newLeafNode; newInternalNode.index = -1; active.activeNode.child[input[newInternalNode.start]] = newInternalNode; //if another internal node was created in last extension of this phase then suffix link of that //node will be this node. if (lastCreatedInternalNode != null) { lastCreatedInternalNode.suffixLink = newInternalNode; } //set this guy as lastCreatedInternalNode and if new internalNode is created in next extension of this phase //then point suffix of this node to that node. Meanwhile set suffix of this node to root. lastCreatedInternalNode = newInternalNode; newInternalNode.suffixLink = root; //if active node is not root then follow suffix link if (active.activeNode != root) { active.activeNode = active.activeNode.suffixLink; } //if active node is root then increase active index by one and decrease active length by 1 else { active.activeEdge = active.activeEdge + 1; active.activeLength--; } remainingSuffixCount--; } } catch (EndOfPathException e) { //this happens when we are looking for new character from end of current path edge. Here we already have internal node so //we don''t have to create new internal node. Just create a leaf node from here and move to suffix new link. SuffixNode node = selectNode(); node.child[input[i]] = SuffixNode.createNode(i, end); if (lastCreatedInternalNode != null) { lastCreatedInternalNode.suffixLink = node; } lastCreatedInternalNode = node; //if active node is not root then follow suffix link if (active.activeNode != root) { active.activeNode = active.activeNode.suffixLink; } //if active node is root then increase active index by one and decrease active length by 1 else { active.activeEdge = active.activeEdge + 1; active.activeLength--; } remainingSuffixCount--; } } } } private void walkDown(int index) { SuffixNode node = selectNode(); //active length is greater than path edge length. //walk past current node so change active point. //This is as per rules of walk down for rule 3 extension. if (diff(node) < active.activeLength) { active.activeNode = node; active.activeLength = active.activeLength - diff(node); active.activeEdge = node.child[input[index]].start; } else { active.activeLength++; } } //find next character to be compared to current phase character. private char nextChar(int i) throws EndOfPathException{ SuffixNode node = selectNode(); if (diff(node) >= active.activeLength) { return input[active.activeNode.child[input[active.activeEdge]].start + active.activeLength]; } if (diff(node) + 1 == active.activeLength ) { if (node.child[input[i]] != null) { return input[i]; } } else { active.activeNode = node; active.activeLength = active.activeLength - diff(node) - 1; active.activeEdge = active.activeEdge + diff(node) + 1; return nextChar(i); } throw new EndOfPathException(); } private static class EndOfPathException extends Exception { } private SuffixNode selectNode() { return active.activeNode.child[input[active.activeEdge]]; } private SuffixNode selectNode(int index) { return active.activeNode.child[input[index]]; } private int diff(SuffixNode node) { return node.end.end - node.start; } private void setIndexUsingDfs(SuffixNode root, int val, int size) { if (root == null) { return; } val += root.end.end - root.start + 1; if (root.index != -1) { root.index = size - val; return; } for (SuffixNode node : root.child) { setIndexUsingDfs(node, val, size); } } /** * Do a DFS traversal of the tree. */ public void dfsTraversal() { List result = new ArrayList<>(); for (SuffixNode node : root.child) { dfsTraversal(node, result); } } private void dfsTraversal(SuffixNode root, List result) { if (root == null) { return; } if (root.index != -1) { for (int i = root.start; i <= root.end.end; i++) { result.add(input[i]); } result.stream().forEach(System.out::print); System.out.println(" " + root.index); for (int i = root.start; i <= root.end.end; i++) { result.remove(result.size() - 1); } return; } for (int i = root.start; i <= root.end.end; i++) { result.add(input[i]); } for (SuffixNode node : root.child) { dfsTraversal(node, result); } for (int i = root.start; i <= root.end.end; i++) { result.remove(result.size() - 1); } } /** * Do validation of the tree by comparing all suffixes and their index at leaf node. */ private boolean validate(SuffixNode root, char[] input, int index, int curr) { if (root == null) { System.out.println("Failed at " + curr + " for index " + index); return false; } if (root.index != -1) { if (root.index != index) { System.out.println("Index not same. Failed at " + curr + " for index " + index); return false; } else { return true; } } if (curr >= input.length) { System.out.println("Index not same. Failed at " + curr + " for index " + index); return false; } SuffixNode node = root.child[input[curr]]; if (node == null) { System.out.println("Failed at " + curr + " for index " + index); return false; } int j = 0; for (int i = node.start ; i <= node.end.end; i++) { if (input[curr + j] != input[i] ) { System.out.println("Mismatch found " + input[curr + j] + " " + input[i]); return false; } j++; } curr += node.end.end - node.start + 1; return validate(node, input, index, curr); } public boolean validate() { for (int i = 0; i < this.input.length; i++) { if (!validate(this.root, this.input, i, i)) { System.out.println("Failed validation"); return false; } } return true; } } class SuffixNode { private SuffixNode() { } private static final int TOTAL = 256; SuffixNode[] child = new SuffixNode[TOTAL]; int start; End end; int index; SuffixNode suffixLink; public static SuffixNode createNode(int start, End end) { SuffixNode node = new SuffixNode(); node.start = start; node.end = end; return node; } @Override public String toString() { StringBuffer buffer = new StringBuffer(); int i = 0; for (SuffixNode node : child) { if (node != null) { buffer.append((char)i + " "); } i++; } return "SuffixNode [start=" + start + "]" + " " + buffer.toString(); } } class End { public End(int end) { this.end = end; } int end; } class Active { Active(SuffixNode node) { activeLength = 0; activeNode = node; activeEdge = -1; } @Override public String toString() { return "Active [activeNode=" + activeNode + ", activeIndex=" + activeEdge + ", activeLength=" + activeLength + "]"; } SuffixNode activeNode; int activeEdge; int activeLength; }

Suffix Tree - Application 2 - Longest Repeated Substrings

Input Format

Output Format

Constraints

Example

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