Question

I have a string that is about a thousand characters long composed of L’s, T’s, and A’s. I’m pretty sure there is a simple pattern in it and I’m wondering if there is any quick and easy way of going about finding it. This string changes so that this is not just a one off.

The pattern I’m looking for is for example if the string was

LLLLLLLLAATAALLLLALLLLLLAATAALLLATLLLLLAATAALLAALLLLLAATAALL

The substring LLLLLAATAALL repeats 4 times in this string. I want to search for substrings like this but I don’t know where they start, end, how many there are, and how long they are in the main string.

If there are any tools in Java for looking for this kind of thing any advice would be much appreciated.

nt

Answer 1

Ok, so I took the code from here and adapted it to keep track of and print the longest repeated substring. Just run it using JUnit.

/* Copyright (c) 2010 the authors listed at the following URL, and/or
 the authors of referenced articles or incorporated external code:
 http://en.literateprograms.org/Suffix_tree_(Java)?action=history&offset=20100123220137

 Permission is hereby granted, free of charge, to any person obtaining
 a copy of this software and associated documentation files (the
 "Software"), to deal in the Software without restriction, including
 without limitation the rights to use, copy, modify, merge, publish,
 distribute, sublicense, and/or sell copies of the Software, and to
 permit persons to whom the Software is furnished to do so, subject to
 the following conditions:

 The above copyright notice and this permission notice shall be
 included in all copies or substantial portions of the Software.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
 CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

 Retrieved from: http://en.literateprograms.org/Suffix_tree_(Java)?oldid=16641
 */

import java.util.ArrayList;
import java.util.Collection;
import java.util.List;
import org.junit.Test;

public class SuffixTree {
    @Test
    public void sampleUsage() {

        AbstractSuffixTree tree = new SimpleSuffixTree(
                "LLLLLLLLAATAALLLLALLLLLLAATAALLLATLLLLLAATAALLAALLLLLAATAALL");
        System.out.println("Longest repeating substring "
                + tree.best.printResult() + " repetitions=" + tree.best.visits
                + " length=" + tree.best.stringDepth);
    }
}

abstract class AbstractSuffixTree {

    SuffixTreeNode best;
    String text = null;
    SuffixTreeNode root = null;
    int inputAlphabetSize = -1;

    AbstractSuffixTree(String text) {
        if (text.length() > 0 && text.charAt(text.length() - 1) == '$') {
            this.text = text;
        } else {
            this.text = text + "$";
        }
    }

}

class SimpleSuffixTree extends AbstractSuffixTree {

    public SimpleSuffixTree(String text) {
        super(text);
        constructTree();
    }

    private void constructTree() {
        super.root = new SuffixTreeNode(this);
        best = root;
        char[] s = super.text.toCharArray();
        for (int i = 0; i < s.length; i++) {
            List<String> suffixList = new ArrayList<String>();
            for (int k = i; k < s.length; k++) {
                suffixList.add(s[k] + "");
            }
            super.root.addSuffix(suffixList, i + 1);
        }
    }

}

class CompactSuffixTree extends AbstractSuffixTree {

    public CompactSuffixTree(SimpleSuffixTree simpleSuffixTree) {
        super(simpleSuffixTree.text);
        super.root = compactNodes(simpleSuffixTree.root, 0);
        super.best = simpleSuffixTree.best;
    }

    private SuffixTreeNode compactNodes(SuffixTreeNode node, int nodeDepth) {
        node.nodeDepth = nodeDepth;
        for (SuffixTreeNode child : node.children) {
            while (child.children.size() == 1) {
                SuffixTreeNode grandchild = child.children.iterator().next();
                child.incomingEdge.label += ", "
                        + grandchild.incomingEdge.label;
                child.stringDepth += grandchild.incomingEdge.label.length();
                child.children = grandchild.children;
                // for (SuffixTreeNode grandchild : child.children)
                grandchild.parent = node;
            }
            child = compactNodes(child, nodeDepth + 1);
        }
        return node;
    }

}

class SuffixTreeNode {

    AbstractSuffixTree tree;
    SuffixTreeEdge incomingEdge = null;
    int nodeDepth = -1;
    int label = -1;
    Collection<SuffixTreeNode> children = null;
    SuffixTreeNode parent = null;
    int stringDepth;
    int id = 0;
    public static int c;
    public int visits = 1;

    public SuffixTreeNode(AbstractSuffixTree tree, SuffixTreeNode parent,
            String incomingLabel, int depth, int label, int id) {
        children = new ArrayList<SuffixTreeNode>();
        incomingEdge = new SuffixTreeEdge(incomingLabel, label);
        nodeDepth = depth;
        this.label = label;
        this.parent = parent;
        stringDepth = parent.stringDepth + incomingLabel.length();
        this.id = id;
        this.tree = tree;
    }

    public SuffixTreeNode(AbstractSuffixTree tree) {
        children = new ArrayList<SuffixTreeNode>();
        nodeDepth = 0;
        label = 0;
        this.tree = tree;
    }

    public void addSuffix(List<String> suffix, int pathIndex) {
        SuffixTreeNode insertAt = this;
        insertAt = search(this, suffix);
        insert(insertAt, suffix, pathIndex);
    }

    private SuffixTreeNode search(SuffixTreeNode startNode, List<String> suffix) {
        if (suffix.isEmpty()) {
            throw new IllegalArgumentException(
                    "Empty suffix. Probably no valid simple suffix tree exists for the input.");
        }
        Collection<SuffixTreeNode> children = startNode.children;
        for (SuffixTreeNode child : children) {
            if (child.incomingEdge.label.equals(suffix.get(0))) {
                suffix.remove(0);
                child.visits++;
                if (child.visits > 1
                        && child.stringDepth > tree.best.stringDepth) {
                    tree.best = child;
                }
                if (suffix.isEmpty()) {
                    return child;
                }
                return search(child, suffix);
            }
        }
        return startNode;
    }

    private void insert(SuffixTreeNode insertAt, List<String> suffix,
            int pathIndex) {
        for (String x : suffix) {
            SuffixTreeNode child = new SuffixTreeNode(tree, insertAt, x,
                    insertAt.nodeDepth + 1, pathIndex, id);
            insertAt.children.add(child);
            insertAt = child;
        }
    }

    public String toString() {
        StringBuilder result = new StringBuilder();
        String incomingLabel = this.isRoot() ? "" : this.incomingEdge.label;
        for (int i = 1; i <= this.nodeDepth; i++)
            result.append("\t");
        if (this.isRoot()) {
            c = 1;
            this.id = 1;
        } else {
            this.id = c;
            result.append(this.parent.id + " -> ");
            result.append(this.id + "[label=\"" + incomingLabel + "\"]" + "("
                    + visits + "," + (stringDepth) + ")" + ";\n");
        }
        for (SuffixTreeNode child : children) {
            c++;
            child.id = c;
            result.append(child.toString());
        }
        return result.toString();
    }

    public String printResult() {
        if (parent == null) {
            return "";
        } else {
            return this.parent.printResult() + this.incomingEdge.label;
        }
    }

    public boolean isRoot() {
        return this.parent == null;
    }

    public boolean isLeaf() {
        return children.size() == 0;
    }

}

class SuffixTreeEdge {

    String label = null;
    @SuppressWarnings("unused")
    private int branchIndex = -1;

    public SuffixTreeEdge(String label, int branchIndex) {
        this.label = label;
        this.branchIndex = branchIndex;
    }

}

Output:

Longest repeating substring
LLLLLLAATAALLL repetitions=2 length=14

EDIT: response to your comments.

Currently I simply keep track of the longest repeating SuffixTreeNode (it’s a field in AbstractSuffixTree). You could modify this so it keeps track of a SortedQueue of nodes, ordered by their stringDepth.