[TEXT-235] Add Damerau-Levenshtein distance (#687)

* [TEXT-235] Implement Damerau-Levenshtein distance

* Fix comment formatting

* Fix style and spotbugs

---------

Co-authored-by: Eirik Lorgen Tanberg <[email protected]>

Author: LorgeN

src/main/java/org/apache/commons/text/similarity/DamerauLevenshteinDistance.java

@@ -0,0 +1,326 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      https://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.text.similarity;
+
+/**
+ * An algorithm for measuring the difference between two character sequences using the
+ * <a href="https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance">Damerau-Levenshtein Distance</a>.
+ *
+ * <p>
+ * This is the number of changes needed to change one sequence into another, where each change is a single character
+ * modification (deletion, insertion, substitution, or transposition of two adjacent characters).
+ * </p>
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance">Damerau-Levenshtein Distance on Wikipedia</a>
+ * @since 1.15.0
+ */
+public class DamerauLevenshteinDistance implements EditDistance<Integer> {
+
+    /**
+     * Utility function to ensure distance is valid according to threshold.
+     *
+     * @param distance  The distance value
+     * @param threshold The threshold value
+     * @return The distance value, or {@code -1} if distance is greater than threshold
+     */
+    private static int clampDistance(final int distance, final int threshold) {
+        return distance > threshold ? -1 : distance;
+    }
+
+    /**
+     * Finds the Damerau-Levenshtein distance between two CharSequences if it's less than or equal to a given threshold.
+     *
+     * @param left      the first SimilarityInput, must not be null.
+     * @param right     the second SimilarityInput, must not be null.
+     * @param threshold the target threshold, must not be negative.
+     * @return result distance, or -1 if distance exceeds threshold
+     */
+    private static <E> int limitedCompare(SimilarityInput<E> left, SimilarityInput<E> right, final int threshold) {
+        if (left == null || right == null) {
+            throw new IllegalArgumentException("Left/right inputs must not be null");
+        }
+
+        if (threshold < 0) {
+            throw new IllegalArgumentException("Threshold can not be negative");
+        }
+
+        // Implementation based on https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance#Optimal_string_alignment_distance
+
+        int leftLength = left.length();
+        int rightLength = right.length();
+
+        if (leftLength == 0) {
+            return clampDistance(rightLength, threshold);
+        }
+
+        if (rightLength == 0) {
+            return clampDistance(leftLength, threshold);
+        }
+
+        // Inspired by LevenshteinDistance impl; swap the input strings to consume less memory
+        if (rightLength > leftLength) {
+            final SimilarityInput<E> tmp = left;
+            left = right;
+            right = tmp;
+            leftLength = rightLength;
+            rightLength = right.length();
+        }
+
+        // If the difference between the lengths of the strings is greater than the threshold, we must at least do
+        // threshold operations so we can return early
+        if (leftLength - rightLength > threshold) {
+            return -1;
+        }
+
+        // Use three arrays of minimum possible size to reduce memory usage. This avoids having to create a 2D
+        // array of size leftLength * rightLength
+        int[] curr = new int[rightLength + 1];
+        int[] prev = new int[rightLength + 1];
+        int[] prevPrev = new int[rightLength + 1];
+        int[] temp; // Temp variable use to shuffle arrays at the end of each iteration
+
+        int rightIndex, leftIndex, cost, minCost;
+
+        // Changing empty sequence to [0..i] requires i insertions
+        for (rightIndex = 0; rightIndex <= rightLength; rightIndex++) {
+            prev[rightIndex] = rightIndex;
+        }
+
+        // Calculate how many operations it takes to change right[0..rightIndex] into left[0..leftIndex]
+        // For each iteration
+        //  - curr[i] contains the cost of changing right[0..i] into left[0..leftIndex]
+        //          (computed in current iteration)
+        //  - prev[i] contains the cost of changing right[0..i] into left[0..leftIndex - 1]
+        //          (computed in previous iteration)
+        //  - prevPrev[i] contains the cost of changing right[0..i] into left[0..leftIndex - 2]
+        //          (computed in iteration before previous)
+        for (leftIndex = 1; leftIndex <= leftLength; leftIndex++) {
+            // For right[0..0] we must insert leftIndex characters, which means the cost is always leftIndex
+            curr[0] = leftIndex;
+
+            minCost = Integer.MAX_VALUE;
+
+            for (rightIndex = 1; rightIndex <= rightLength; rightIndex++) {
+                cost = (left.at(leftIndex - 1) == right.at(rightIndex - 1)) ? 0 : 1;
+
+                // Select cheapest operation
+                curr[rightIndex] = Math.min(
+                        Math.min(
+                                prev[rightIndex] + 1, // Delete current character
+                                curr[rightIndex - 1] + 1 // Insert current character
+                        ),
+                        prev[rightIndex - 1] + cost // Replace (or no cost if same character)
+                );
+
+                // Check if adjacent characters are the same -> transpose if cheaper
+                if (leftIndex > 1
+                        && rightIndex > 1
+                        && left.at(leftIndex - 1) == right.at(rightIndex - 2)
+                        && left.at(leftIndex - 2) == right.at(rightIndex - 1)) {
+                    // Use cost here, to properly handle two subsequent equal letters
+                    curr[rightIndex] = Math.min(curr[rightIndex], prevPrev[rightIndex - 2] + cost);
+                }
+
+                minCost = Math.min(curr[rightIndex], minCost);
+            }
+
+            // If there was no total cost for this entire iteration to transform right to left[0..leftIndex], there
+            // can not be a way to do it below threshold. This is because we have no way to reduce the overall cost
+            // in later operations.
+            if (minCost > threshold) {
+                return -1;
+            }
+
+            // Rotate arrays for next iteration
+            temp = prevPrev;
+            prevPrev = prev;
+            prev = curr;
+            curr = temp;
+        }
+
+        // Prev contains the value computed in the latest iteration
+        return clampDistance(prev[rightLength], threshold);
+    }
+
+    /**
+     * Finds the Damerau-Levenshtein distance between two inputs using optimal string alignment.
+     *
+     * @param left  the first CharSequence, must not be null.
+     * @param right the second CharSequence, must not be null.
+     * @return result distance.
+     * @throws IllegalArgumentException if either CharSequence input is {@code null}.
+     */
+    private static <E> int unlimitedCompare(SimilarityInput<E> left, SimilarityInput<E> right) {
+        if (left == null || right == null) {
+            throw new IllegalArgumentException("Left/right inputs must not be null");
+        }
+
+        /*
+         * Implementation based on https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance#Optimal_string_alignment_distance
+         */
+
+        int leftLength = left.length();
+        int rightLength = right.length();
+
+        if (leftLength == 0) {
+            return rightLength;
+        }
+
+        if (rightLength == 0) {
+            return leftLength;
+        }
+
+        // Inspired by LevenshteinDistance impl; swap the input strings to consume less memory
+        if (rightLength > leftLength) {
+            final SimilarityInput<E> tmp = left;
+            left = right;
+            right = tmp;
+            leftLength = rightLength;
+            rightLength = right.length();
+        }
+
+        // Use three arrays of minimum possible size to reduce memory usage. This avoids having to create a 2D
+        // array of size leftLength * rightLength
+        int[] curr = new int[rightLength + 1];
+        int[] prev = new int[rightLength + 1];
+        int[] prevPrev = new int[rightLength + 1];
+        int[] temp; // Temp variable use to shuffle arrays at the end of each iteration
+
+        int rightIndex, leftIndex, cost;
+
+        // Changing empty sequence to [0..i] requires i insertions
+        for (rightIndex = 0; rightIndex <= rightLength; rightIndex++) {
+            prev[rightIndex] = rightIndex;
+        }
+
+        // Calculate how many operations it takes to change right[0..rightIndex] into left[0..leftIndex]
+        // For each iteration
+        //  - curr[i] contains the cost of changing right[0..i] into left[0..leftIndex]
+        //          (computed in current iteration)
+        //  - prev[i] contains the cost of changing right[0..i] into left[0..leftIndex - 1]
+        //          (computed in previous iteration)
+        //  - prevPrev[i] contains the cost of changing right[0..i] into left[0..leftIndex - 2]
+        //          (computed in iteration before previous)
+        for (leftIndex = 1; leftIndex <= leftLength; leftIndex++) {
+            // For right[0..0] we must insert leftIndex characters, which means the cost is always leftIndex
+            curr[0] = leftIndex;
+
+            for (rightIndex = 1; rightIndex <= rightLength; rightIndex++) {
+                cost = (left.at(leftIndex - 1) == right.at(rightIndex - 1)) ? 0 : 1;
+
+                // Select cheapest operation
+                curr[rightIndex] = Math.min(
+                        Math.min(
+                                prev[rightIndex] + 1, // Delete current character
+                                curr[rightIndex - 1] + 1 // Insert current character
+                        ),
+                        prev[rightIndex - 1] + cost // Replace (or no cost if same character)
+                );
+
+                // Check if adjacent characters are the same -> transpose if cheaper
+                if (leftIndex > 1
+                        && rightIndex > 1
+                        && left.at(leftIndex - 1) == right.at(rightIndex - 2)
+                        && left.at(leftIndex - 2) == right.at(rightIndex - 1)) {
+                    // Use cost here, to properly handle two subsequent equal letters
+                    curr[rightIndex] = Math.min(curr[rightIndex], prevPrev[rightIndex - 2] + cost);
+                }
+            }
+
+            // Rotate arrays for next iteration
+            temp = prevPrev;
+            prevPrev = prev;
+            prev = curr;
+            curr = temp;
+        }
+
+        // Prev contains the value computed in the latest iteration
+        return prev[rightLength];
+    }
+
+    /**
+     * Threshold.
+     */
+    private final Integer threshold;
+
+    /**
+     * Constructs a default instance that uses a version of the algorithm that does not use a threshold parameter.
+     */
+    public DamerauLevenshteinDistance() {
+        this(null);
+    }
+
+    /**
+     * Constructs a new instance. If the threshold is not null, distance calculations will be limited to a maximum length.
+     * If the threshold is null, the unlimited version of the algorithm will be used.
+     *
+     * @param threshold If this is null then distances calculations will not be limited. This may not be negative.
+     */
+    public DamerauLevenshteinDistance(final Integer threshold) {
+        if (threshold != null && threshold < 0) {
+            throw new IllegalArgumentException("Threshold must not be negative");
+        }
+        this.threshold = threshold;
+    }
+
+    /**
+     * Computes the Damerau-Levenshtein distance between two Strings.
+     *
+     * <p>
+     * A higher score indicates a greater distance.
+     * </p>
+     *
+     * @param left  the first input, must not be null.
+     * @param right the second input, must not be null.
+     * @return result distance, or -1 if threshold is exceeded.
+     * @throws IllegalArgumentException if either String input {@code null}.
+     */
+    @Override
+    public Integer apply(final CharSequence left, final CharSequence right) {
+        return apply(SimilarityInput.input(left), SimilarityInput.input(right));
+    }
+
+    /**
+     * Computes the Damerau-Levenshtein distance between two inputs.
+     *
+     * <p>
+     * A higher score indicates a greater distance.
+     * </p>
+     *
+     * @param <E>   The type of similarity score unit.
+     * @param left  the first input, must not be null.
+     * @param right the second input, must not be null.
+     * @return result distance, or -1 if threshold is exceeded.
+     * @throws IllegalArgumentException if either String input {@code null}.
+     * @since 1.13.0
+     */
+    public <E> Integer apply(final SimilarityInput<E> left, final SimilarityInput<E> right) {
+        if (threshold != null) {
+            return limitedCompare(left, right, threshold);
+        }
+        return unlimitedCompare(left, right);
+    }
+
+    /**
+     * Gets the distance threshold.
+     *
+     * @return The distance threshold.
+     */
+    public Integer getThreshold() {
+        return threshold;
+    }
+}