DamerauLevenshteinAlgorithm.java

package squidpony;

import squidpony.annotation.Beta;

import java.util.HashMap;
import java.util.Map;

/**
 * The Damerau-Levenshtein Algorithm is an extension to the Levenshtein
 * Algorithm which solves the edit distance problem between a source string and
 * a target string with the following operations:
 *
 * <ul>
 * <li>Character Insertion</li>
 * <li>Character Deletion</li>
 * <li>Character Replacement</li>
 * <li>Adjacent Character Swap</li>
 * </ul>
 *
 * Note that the adjacent character swap operation is an edit that may be
 * applied when two adjacent characters in the source string match two adjacent
 * characters in the target string, but in reverse order, rather than a general
 * allowance for adjacent character swaps.
 *
 * This implementation allows the client to specify the costs of the various
 * edit operations with the restriction that the cost of two swap operations
 * must not be less than the cost of a delete operation followed by an insert
 * operation. This restriction is required to preclude two swaps involving the
 * same character being required for optimality which, in turn, enables a fast
 * dynamic programming solution.
 *
 * The running time of the Damerau-Levenshtein algorithm is O(n*m) where n is
 * the length of the source string and m is the length of the target string.
 * This implementation consumes O(n*m) space.
 * 
* @author Kevin L. Stern
 */
@Beta
public class DamerauLevenshteinAlgorithm {

    private final int deleteCost, insertCost, replaceCost, swapCost;

    /**
     * Constructor.
     *     
* @param deleteCost the cost of deleting a character.
     * @param insertCost the cost of inserting a character.
     * @param replaceCost the cost of replacing a character.
     * @param swapCost the cost of swapping two adjacent characters.
     */
    public DamerauLevenshteinAlgorithm(int deleteCost, int insertCost, int replaceCost, int swapCost) {
        /*
         * Required to facilitate the premise to the algorithm that two swaps of
         * the same character are never required for optimality.
         */
        if (2 * swapCost < insertCost + deleteCost) {
            throw new IllegalArgumentException("Unsupported cost assignment");
        }
        this.deleteCost = deleteCost;
        this.insertCost = insertCost;
        this.replaceCost = replaceCost;
        this.swapCost = swapCost;
    }

    /**
     * Compute the Damerau-Levenshtein distance between the specified source
     * string and the specified target string.
     */
    public int execute(String source, String target) {
        if (source.length() == 0) {
            return target.length() * insertCost;
        }

        if (target.length() == 0) {
            return source.length() * deleteCost;
        }

        int[][] table = new int[source.length()][target.length()];
        Map<Character, Integer> sourceIndexByCharacter = new HashMap<>();

        if (source.charAt(0) != target.charAt(0)) {
            table[0][0] = Math.min(replaceCost, deleteCost + insertCost);
        }

        sourceIndexByCharacter.put(source.charAt(0), 0);

        for (int i = 1; i < source.length(); i++) {
            int deleteDistance = table[i - 1][0] + deleteCost;
            int insertDistance = (i + 1) * deleteCost + insertCost;
            int matchDistance = i * deleteCost
                    + (source.charAt(i) == target.charAt(0) ? 0 : replaceCost);
            table[i][0] = Math.min(Math.min(deleteDistance, insertDistance),
                    matchDistance);
        }

        for (int j = 1; j < target.length(); j++) {
            int deleteDistance = table[0][j - 1] + insertCost;
            int insertDistance = (j + 1) * insertCost + deleteCost;
            int matchDistance = j * insertCost
                    + (source.charAt(0) == target.charAt(j) ? 0 : replaceCost);
            table[0][j] = Math.min(Math.min(deleteDistance, insertDistance),
                    matchDistance);
        }

        for (int i = 1; i < source.length(); i++) {
            int maxSourceLetterMatchIndex = source.charAt(i) == target
                    .charAt(0) ? 0 : -1;
            for (int j = 1; j < target.length(); j++) {
                Integer candidateSwapIndex = sourceIndexByCharacter.get(target
                        .charAt(j));
                int jSwap = maxSourceLetterMatchIndex;
                int deleteDistance = table[i - 1][j] + deleteCost;
                int insertDistance = table[i][j - 1] + insertCost;
                int matchDistance = table[i - 1][j - 1];
                if (source.charAt(i) != target.charAt(j)) {
                    matchDistance += replaceCost;
                } else {
                    maxSourceLetterMatchIndex = j;
                }
                int swapDistance;
                if (candidateSwapIndex != null && jSwap != -1) {
                    int iSwap = candidateSwapIndex;
                    int preSwapCost;
                    if (iSwap == 0 && jSwap == 0) {
                        preSwapCost = 0;
                    } else {
                        preSwapCost = table[Math.max(0, iSwap - 1)][Math.max(0,
                                jSwap - 1)];
                    }
                    swapDistance = preSwapCost + (i - iSwap - 1) * deleteCost
                            + (j - jSwap - 1) * insertCost + swapCost;
                } else {
                    swapDistance = Integer.MAX_VALUE;
                }
                table[i][j] = Math.min(
                        Math.min(Math.min(deleteDistance, insertDistance),
                                matchDistance), swapDistance);
            }
            sourceIndexByCharacter.put(source.charAt(i), i);
        }
        return table[source.length() - 1][target.length() - 1];
    }
}