diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/LevenshteinDistance.java b/src/main/java/com/thealgorithms/dynamicprogramming/LevenshteinDistance.java index c4c9bbee9a78..119d65dfe365 100644 --- a/src/main/java/com/thealgorithms/dynamicprogramming/LevenshteinDistance.java +++ b/src/main/java/com/thealgorithms/dynamicprogramming/LevenshteinDistance.java @@ -1,49 +1,84 @@ package com.thealgorithms.dynamicprogramming; +import java.util.stream.IntStream; + /** - * @author Kshitij VERMA (github.com/kv19971) LEVENSHTEIN DISTANCE dyamic - * programming implementation to show the difference between two strings - * (https://en.wikipedia.org/wiki/Levenshtein_distance) + * Provides functions to calculate the Levenshtein distance between two strings. + * + * The Levenshtein distance is a measure of the similarity between two strings by calculating the minimum number of single-character + * edits (insertions, deletions, or substitutions) required to change one string into the other. */ -public class LevenshteinDistance { - - private static int minimum(int a, int b, int c) { - if (a < b && a < c) { - return a; - } else if (b < a && b < c) { - return b; - } else { - return c; - } +public final class LevenshteinDistance { + private LevenshteinDistance() { } - public static int calculateLevenshteinDistance(String str1, String str2) { - int len1 = str1.length() + 1; - int len2 = str2.length() + 1; - int[][] distanceMat = new int[len1][len2]; - for (int i = 0; i < len1; i++) { - distanceMat[i][0] = i; - } - for (int j = 0; j < len2; j++) { - distanceMat[0][j] = j; + /** + * Calculates the Levenshtein distance between two strings using a naive dynamic programming approach. + * + * This function computes the Levenshtein distance by constructing a dynamic programming matrix and iteratively filling it in. + * It follows the standard top-to-bottom, left-to-right approach for filling in the matrix. + * + * @param string1 The first string. + * @param string2 The second string. + * @return The Levenshtein distance between the two input strings. + * + * Time complexity: O(nm), + * Space complexity: O(nm), + * + * where n and m are lengths of `string1` and `string2`. + * + * Note that this implementation uses a straightforward dynamic programming approach without any space optimization. + * It may consume more memory for larger input strings compared to the optimized version. + */ + public static int naiveLevenshteinDistance(final String string1, final String string2) { + int[][] distanceMatrix = IntStream.rangeClosed(0, string1.length()).mapToObj(i -> IntStream.rangeClosed(0, string2.length()).map(j -> (i == 0) ? j : (j == 0) ? i : 0).toArray()).toArray(int[][] ::new); + + IntStream.range(1, string1.length() + 1).forEach(i -> IntStream.range(1, string2.length() + 1).forEach(j -> { + final int cost = (string1.charAt(i - 1) == string2.charAt(j - 1)) ? 0 : 1; + distanceMatrix[i][j] = Math.min(distanceMatrix[i - 1][j - 1] + cost, Math.min(distanceMatrix[i][j - 1] + 1, distanceMatrix[i - 1][j] + 1)); + })); + + return distanceMatrix[string1.length()][string2.length()]; + } + + /** + * Calculates the Levenshtein distance between two strings using an optimized dynamic programming approach. + * + * This edit distance is defined as 1 point per insertion, substitution, or deletion required to make the strings equal. + * + * @param string1 The first string. + * @param string2 The second string. + * @return The Levenshtein distance between the two input strings. + * + * Time complexity: O(nm), + * Space complexity: O(n), + * + * where n and m are lengths of `string1` and `string2`. + * + * Note that this implementation utilizes an optimized dynamic programming approach, significantly reducing the space complexity from O(nm) to O(n), where n and m are the lengths of `string1` and `string2`. + * + * Additionally, it minimizes space usage by leveraging the shortest string horizontally and the longest string vertically in the computation matrix. + */ + public static int optimizedLevenshteinDistance(final String string1, final String string2) { + if (string1.isEmpty()) { + return string2.length(); } - for (int i = 1; i < len1; i++) { - for (int j = 1; j < len2; j++) { - if (str1.charAt(i - 1) == str2.charAt(j - 1)) { - distanceMat[i][j] = distanceMat[i - 1][j - 1]; - } else { - distanceMat[i][j] = 1 + minimum(distanceMat[i - 1][j], distanceMat[i - 1][j - 1], distanceMat[i][j - 1]); - } + + int[] previousDistance = IntStream.rangeClosed(0, string1.length()).toArray(); + + for (int j = 1; j <= string2.length(); j++) { + int prevSubstitutionCost = previousDistance[0]; + previousDistance[0] = j; + + for (int i = 1; i <= string1.length(); i++) { + final int deletionCost = previousDistance[i] + 1; + final int insertionCost = previousDistance[i - 1] + 1; + final int substitutionCost = (string1.charAt(i - 1) == string2.charAt(j - 1)) ? prevSubstitutionCost : prevSubstitutionCost + 1; + prevSubstitutionCost = previousDistance[i]; + previousDistance[i] = Math.min(deletionCost, Math.min(insertionCost, substitutionCost)); } } - return distanceMat[len1 - 1][len2 - 1]; - } - - public static void main(String[] args) { - String str1 = ""; // enter your string here - String str2 = ""; // enter your string here - System.out.print("Levenshtein distance between " + str1 + " and " + str2 + " is: "); - System.out.println(calculateLevenshteinDistance(str1, str2)); + return previousDistance[string1.length()]; } } diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/LevenshteinDistanceTests.java b/src/test/java/com/thealgorithms/dynamicprogramming/LevenshteinDistanceTests.java index a22bf3fea30c..ad4c4c7c53e0 100644 --- a/src/test/java/com/thealgorithms/dynamicprogramming/LevenshteinDistanceTests.java +++ b/src/test/java/com/thealgorithms/dynamicprogramming/LevenshteinDistanceTests.java @@ -2,15 +2,44 @@ import static org.junit.jupiter.api.Assertions.assertEquals; +import java.util.Arrays; +import java.util.List; +import java.util.function.ToIntBiFunction; +import java.util.stream.Stream; import org.junit.jupiter.params.ParameterizedTest; -import org.junit.jupiter.params.provider.CsvSource; +import org.junit.jupiter.params.provider.Arguments; +import org.junit.jupiter.params.provider.MethodSource; public class LevenshteinDistanceTests { @ParameterizedTest - @CsvSource({"dog,cat,3", "sunday,saturday,3", "cat,cats,1", "rain,train,1"}) - void levenshteinDistanceTest(String str1, String str2, int distance) { - int result = LevenshteinDistance.calculateLevenshteinDistance(str1, str2); - assertEquals(distance, result); + @MethodSource("testCases") + public void testLevenshteinDistance(final int expected, final String str1, final String str2, final ToIntBiFunction dist) { + assertEquals(expected, dist.applyAsInt(str1, str2)); + assertEquals(expected, dist.applyAsInt(str2, str1)); + assertEquals(0, dist.applyAsInt(str1, str1)); + assertEquals(0, dist.applyAsInt(str2, str2)); + } + + private static Stream testCases() { + final Object[][] testData = { + {0, "", ""}, + {0, "Hello, World!", "Hello, World!"}, + {4, "", "Rust"}, + {3, "horse", "ros"}, + {6, "tan", "elephant"}, + {8, "execute", "intention"}, + {1, "a", "b"}, + {1, "a", "aa"}, + {1, "a", ""}, + {1, "a", "ab"}, + {1, "a", "ba"}, + {2, "a", "bc"}, + {2, "a", "cb"}, + }; + + final List> methods = Arrays.asList(LevenshteinDistance::naiveLevenshteinDistance, LevenshteinDistance::optimizedLevenshteinDistance); + + return Stream.of(testData).flatMap(input -> methods.stream().map(method -> Arguments.of(input[0], input[1], input[2], method))); } }