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Implementation of various string similarity and distance algorithms: Levenshtein, Jaro-winkler, n-Gram, Q-Gram, Jaccard index, Longest Common Subsequence edit distance, cosine similarity...
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/*
 * The MIT License
 *
 * Copyright 2015 Thibault Debatty.
 *
 * 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.
 */
package info.debatty.java.stringsimilarity;

import info.debatty.java.stringsimilarity.interfaces.MetricStringDistance;
import java.util.HashMap;
import net.jcip.annotations.Immutable;

/**
 * Implementation of Damerau-Levenshtein distance with transposition (also
 * sometimes calls unrestricted Damerau-Levenshtein distance).
 * It is the minimum number of operations needed to transform one string into
 * the other, where an operation is defined as an insertion, deletion, or
 * substitution of a single character, or a transposition of two adjacent
 * characters.
 * It does respect triangle inequality, and is thus a metric distance.
 *
 * This is not to be confused with the optimal string alignment distance, which
 * is an extension where no substring can be edited more than once.
 *
 * @author Thibault Debatty
 */
@Immutable
public class Damerau implements MetricStringDistance {

    /**
     * Compute the distance between strings: the minimum number of operations
     * needed to transform one string into the other (insertion, deletion,
     * substitution of a single character, or a transposition of two adjacent
     * characters).
     * @param s1
     * @param s2
     * @return
     */
    public final double distance(final String s1, final String s2) {

        // INFinite distance is the max possible distance
        int inf = s1.length() + s2.length();

        // Create and initialize the character array indices
        HashMap da = new HashMap();

        for (int d = 0; d < s1.length(); d++) {
            if (!da.containsKey(s1.charAt(d))) {
                da.put(s1.charAt(d), 0);
            }
        }

        for (int d = 0; d < s2.length(); d++) {
            if (!da.containsKey(s2.charAt(d))) {
                da.put(s2.charAt(d), 0);
            }
        }

        // Create the distance matrix H[0 .. s1.length+1][0 .. s2.length+1]
        int[][] h = new int[s1.length() + 2][s2.length() + 2];

        // initialize the left and top edges of H
        for (int i = 0; i <= s1.length(); i++) {
            h[i + 1][0] = inf;
            h[i + 1][1] = i;
        }

        for (int j = 0; j <= s2.length(); j++) {
            h[0][j + 1] = inf;
            h[1][j + 1] = j;

        }

        // fill in the distance matrix H
        // look at each character in s1
        for (int i = 1; i <= s1.length(); i++) {
            int db = 0;

            // look at each character in b
            for (int j = 1; j <= s2.length(); j++) {
                int i1 = da.get(s2.charAt(j - 1));
                int j1 = db;

                int cost = 1;
                if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
                    cost = 0;
                    db = j;
                }

                h[i + 1][j + 1] = min(
                        h[i][j] + cost, // substitution
                        h[i + 1][j] + 1, // insertion
                        h[i][j + 1] + 1, // deletion
                        h[i1][j1] + (i - i1 - 1) + 1 + (j - j1 - 1));
            }

            da.put(s1.charAt(i - 1), i);
        }

        return h[s1.length() + 1][s2.length() + 1];
    }

    private static int min(
            final int a, final int b, final int c, final int d) {
        return Math.min(a, Math.min(b, Math.min(c, d)));
    }

}