Merge branch 'master' into needlemanwunsch

Author: alxkm

src/main/java/com/thealgorithms/dynamicprogramming/DamerauLevenshteinDistance.java

@@ -0,0 +1,185 @@
+package com.thealgorithms.dynamicprogramming;
+
+import java.util.HashMap;
+import java.util.Map;
+
+/**
+ * Implementation of the full Damerau–Levenshtein distance algorithm.
+ *
+ * This algorithm calculates the minimum number of operations required
+ * to transform one string into another. Supported operations are:
+ * insertion, deletion, substitution, and transposition of adjacent characters.
+ *
+ * Unlike the restricted version (OSA), this implementation allows multiple
+ * edits on the same substring, computing the true edit distance.
+ *
+ * Time Complexity: O(n * m * max(n, m))
+ * Space Complexity: O(n * m)
+ */
+public final class DamerauLevenshteinDistance {
+
+    private DamerauLevenshteinDistance() {
+        // Utility class
+    }
+
+    /**
+     * Computes the full Damerau–Levenshtein distance between two strings.
+     *
+     * @param s1 the first string
+     * @param s2 the second string
+     * @return the minimum edit distance between the two strings
+     * @throws IllegalArgumentException if either input string is null
+     */
+    public static int distance(String s1, String s2) {
+        validateInputs(s1, s2);
+
+        int n = s1.length();
+        int m = s2.length();
+
+        Map<Character, Integer> charLastPosition = buildCharacterMap(s1, s2);
+        int[][] dp = initializeTable(n, m);
+
+        fillTable(s1, s2, dp, charLastPosition);
+
+        return dp[n + 1][m + 1];
+    }
+
+    /**
+     * Validates that both input strings are not null.
+     *
+     * @param s1 the first string to validate
+     * @param s2 the second string to validate
+     * @throws IllegalArgumentException if either string is null
+     */
+    private static void validateInputs(String s1, String s2) {
+        if (s1 == null || s2 == null) {
+            throw new IllegalArgumentException("Input strings must not be null.");
+        }
+    }
+
+    /**
+     * Builds a character map containing all unique characters from both strings.
+     * Each character is initialized with a position value of 0.
+     *
+     * This map is used to track the last occurrence position of each character
+     * during the distance computation, which is essential for handling transpositions.
+     *
+     * @param s1 the first string
+     * @param s2 the second string
+     * @return a map containing all unique characters from both strings, initialized to 0
+     */
+    private static Map<Character, Integer> buildCharacterMap(String s1, String s2) {
+        Map<Character, Integer> charMap = new HashMap<>();
+        for (char c : s1.toCharArray()) {
+            charMap.putIfAbsent(c, 0);
+        }
+        for (char c : s2.toCharArray()) {
+            charMap.putIfAbsent(c, 0);
+        }
+        return charMap;
+    }
+
+    /**
+     * Initializes the dynamic programming table for the algorithm.
+     *
+     * The table has dimensions (n+2) x (m+2) where n and m are the lengths
+     * of the input strings. The extra rows and columns are used to handle
+     * the transposition operation correctly.
+     *
+     * The first row and column are initialized with the maximum possible distance,
+     * while the second row and column represent the base case of transforming
+     * from an empty string.
+     *
+     * @param n the length of the first string
+     * @param m the length of the second string
+     * @return an initialized DP table ready for computation
+     */
+    private static int[][] initializeTable(int n, int m) {
+        int maxDist = n + m;
+        int[][] dp = new int[n + 2][m + 2];
+
+        dp[0][0] = maxDist;
+
+        for (int i = 0; i <= n; i++) {
+            dp[i + 1][0] = maxDist;
+            dp[i + 1][1] = i;
+        }
+
+        for (int j = 0; j <= m; j++) {
+            dp[0][j + 1] = maxDist;
+            dp[1][j + 1] = j;
+        }
+
+        return dp;
+    }
+
+    /**
+     * Fills the dynamic programming table by computing the minimum edit distance
+     * for each substring pair.
+     *
+     * This method implements the core algorithm logic, iterating through both strings
+     * and computing the minimum cost of transforming substrings. It considers all
+     * four operations: insertion, deletion, substitution, and transposition.
+     *
+     * The character position map is updated as we progress through the first string
+     * to enable efficient transposition cost calculation.
+     *
+     * @param s1 the first string
+     * @param s2 the second string
+     * @param dp the dynamic programming table to fill
+     * @param charLastPosition map tracking the last position of each character in s1
+     */
+    private static void fillTable(String s1, String s2, int[][] dp, Map<Character, Integer> charLastPosition) {
+        int n = s1.length();
+        int m = s2.length();
+
+        for (int i = 1; i <= n; i++) {
+            int lastMatchCol = 0;
+
+            for (int j = 1; j <= m; j++) {
+                char char1 = s1.charAt(i - 1);
+                char char2 = s2.charAt(j - 1);
+
+                int lastMatchRow = charLastPosition.get(char2);
+                int cost = (char1 == char2) ? 0 : 1;
+
+                if (char1 == char2) {
+                    lastMatchCol = j;
+                }
+
+                dp[i + 1][j + 1] = computeMinimumCost(dp, i, j, lastMatchRow, lastMatchCol, cost);
+            }
+
+            charLastPosition.put(s1.charAt(i - 1), i);
+        }
+    }
+
+    /**
+     * Computes the minimum cost among all possible operations at the current position.
+     *
+     * This method evaluates four possible operations:
+     * 1. Substitution: replace character at position i with character at position j
+     * 2. Insertion: insert character from s2 at position j
+     * 3. Deletion: delete character from s1 at position i
+     * 4. Transposition: swap characters that have been seen before
+     *
+     * The transposition cost accounts for the gap between the current position
+     * and the last position where matching characters were found.
+     *
+     * @param dp the dynamic programming table
+     * @param i the current position in the first string (1-indexed in the DP table)
+     * @param j the current position in the second string (1-indexed in the DP table)
+     * @param lastMatchRow the row index where the current character of s2 last appeared in s1
+     * @param lastMatchCol the column index where the current character of s1 last matched in s2
+     * @param cost the substitution cost (0 if characters match, 1 otherwise)
+     * @return the minimum cost among all operations
+     */
+    private static int computeMinimumCost(int[][] dp, int i, int j, int lastMatchRow, int lastMatchCol, int cost) {
+        int substitution = dp[i][j] + cost;
+        int insertion = dp[i + 1][j] + 1;
+        int deletion = dp[i][j + 1] + 1;
+        int transposition = dp[lastMatchRow][lastMatchCol] + i - lastMatchRow - 1 + 1 + j - lastMatchCol - 1;
+
+        return Math.min(Math.min(substitution, insertion), Math.min(deletion, transposition));
+    }
+}

src/main/java/com/thealgorithms/dynamicprogramming/SmithWaterman.java

@@ -0,0 +1,56 @@
+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * Smith–Waterman algorithm for local sequence alignment.
+ * Finds the highest scoring local alignment between substrings of two sequences.
+ *
+ * Time Complexity: O(n * m)
+ * Space Complexity: O(n * m)
+ */
+public final class SmithWaterman {
+
+    private SmithWaterman() {
+        // Utility Class
+    }
+
+    /**
+     * Computes the Smith–Waterman local alignment score between two strings.
+     *
+     * @param s1 first string
+     * @param s2 second string
+     * @param matchScore score for a match
+     * @param mismatchPenalty penalty for mismatch (negative)
+     * @param gapPenalty penalty for insertion/deletion (negative)
+     * @return the maximum local alignment score
+     */
+    public static int align(String s1, String s2, int matchScore, int mismatchPenalty, int gapPenalty) {
+        if (s1 == null || s2 == null) {
+            throw new IllegalArgumentException("Input strings must not be null.");
+        }
+
+        int n = s1.length();
+        int m = s2.length();
+        int maxScore = 0;
+
+        int[][] dp = new int[n + 1][m + 1];
+
+        for (int i = 1; i <= n; i++) {
+            for (int j = 1; j <= m; j++) {
+                int matchOrMismatch = (s1.charAt(i - 1) == s2.charAt(j - 1)) ? matchScore : mismatchPenalty;
+
+                dp[i][j] = Math.max(0,
+                    Math.max(Math.max(dp[i - 1][j - 1] + matchOrMismatch, // match/mismatch
+                                 dp[i - 1][j] + gapPenalty // deletion
+                                 ),
+                        dp[i][j - 1] + gapPenalty // insertion
+                        ));
+
+                if (dp[i][j] > maxScore) {
+                    maxScore = dp[i][j];
+                }
+            }
+        }
+
+        return maxScore;
+    }
+}

src/main/java/com/thealgorithms/maths/SieveOfAtkin.java

@@ -0,0 +1,143 @@
+package com.thealgorithms.maths;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Implementation of the Sieve of Atkin, an optimized algorithm to generate
+ * all prime numbers up to a given limit.
+ *
+ * The Sieve of Atkin uses quadratic forms and modular arithmetic to identify
+ * prime candidates, then eliminates multiples of squares. It is more efficient
+ * than the Sieve of Eratosthenes for large limits.
+ */
+public final class SieveOfAtkin {
+
+    private SieveOfAtkin() {
+        // Utlity class; prevent instantiation
+    }
+
+    /**
+     * Generates a list of all prime numbers up to the specified limit
+     * using the Sieve of Atkin algorithm.
+     *
+     * @param limit the upper bound up to which primes are generated; must be zero or positive
+     * @return a list of prime numbers up to the limit; empty if the limit is less than 2
+     */
+    public static List<Integer> generatePrimes(int limit) {
+        if (limit < 1) {
+            return List.of();
+        }
+
+        boolean[] sieve = new boolean[limit + 1];
+        int sqrtLimit = (int) Math.sqrt(limit);
+
+        markQuadraticResidues(limit, sqrtLimit, sieve);
+        eliminateMultiplesOfSquares(limit, sqrtLimit, sieve);
+
+        List<Integer> primes = new ArrayList<>();
+        if (limit >= 2) {
+            primes.add(2);
+        }
+        if (limit >= 3) {
+            primes.add(3);
+        }
+
+        for (int i = 5; i <= limit; i++) {
+            if (sieve[i]) {
+                primes.add(i);
+            }
+        }
+
+        return primes;
+    }
+
+    /**
+     * Marks numbers in the sieve as prime candidates based on quadratic residues.
+     *
+     * This method iterates over all x and y up to sqrt(limit) and applies
+     * the three quadratic forms used in the Sieve of Atkin. Numbers satisfying
+     * the modulo conditions are toggled in the sieve array.
+     *
+     * @param limit the upper bound for primes
+     * @param sqrtLimit square root of the limit
+     * @param sieve boolean array representing potential primes
+     */
+    private static void markQuadraticResidues(int limit, int sqrtLimit, boolean[] sieve) {
+        for (int x = 1; x <= sqrtLimit; x++) {
+            for (int y = 1; y <= sqrtLimit; y++) {
+                applyQuadraticForm(4 * x * x + y * y, limit, sieve, 1, 5);
+                applyQuadraticForm(3 * x * x + y * y, limit, sieve, 7);
+                applyQuadraticForm(3 * x * x - y * y, limit, sieve, 11, x > y);
+            }
+        }
+    }
+
+    /**
+     * Toggles the sieve entry for a number if it satisfies one modulo condition.
+     *
+     * @param n the number to check
+     * @param limit upper bound of primes
+     * @param sieve boolean array representing potential primes
+     * @param modulo the modulo condition number to check
+     */
+    private static void applyQuadraticForm(int n, int limit, boolean[] sieve, int modulo) {
+        if (n <= limit && n % 12 == modulo) {
+            sieve[n] ^= true;
+        }
+    }
+
+    /**
+     * Toggles the sieve entry for a number if it satisfies either of two modulo conditions.
+     *
+     * @param n the number to check
+     * @param limit upper bound of primes
+     * @param sieve boolean array representing potential primes
+     * @param modulo1 first modulo condition number to check
+     * @param modulo2 second modulo condition number to check
+     */
+    private static void applyQuadraticForm(int n, int limit, boolean[] sieve, int modulo1, int modulo2) {
+        if (n <= limit && (n % 12 == modulo1 || n % 12 == modulo2)) {
+            sieve[n] ^= true;
+        }
+    }
+
+    /**
+     * Toggles the sieve entry for a number if it satisfies the modulo condition and an additional boolean condition.
+     *
+     * This version is used for the quadratic form 3*x*x - y*y, which requires x > y.
+     *
+     * @param n the number to check
+     * @param limit upper bound of primes
+     * @param sieve boolean array representing potential primes
+     * @param modulo the modulo condition number to check
+     * @param condition an additional boolean condition that must be true
+     */
+    private static void applyQuadraticForm(int n, int limit, boolean[] sieve, int modulo, boolean condition) {
+        if (condition && n <= limit && n % 12 == modulo) {
+            sieve[n] ^= true;
+        }
+    }
+
+    /**
+     * Eliminates numbers that are multiples of squares from the sieve.
+     *
+     * All numbers that are multiples of i*i (where i is marked as prime) are
+     * marked non-prime to finalize the sieve. This ensures only actual primes remain.
+     *
+     * @param limit the upper bound for primes
+     * @param sqrtLimit square root of the limit
+     * @param sieve boolean array representing potential primes
+     */
+    private static void eliminateMultiplesOfSquares(int limit, int sqrtLimit, boolean[] sieve) {
+        for (int i = 5; i <= sqrtLimit; i++) {
+            if (!sieve[i]) {
+                continue;
+            }
+            int square = i * i;
+            for (int j = square; j <= limit; j += square) {
+                sieve[j] = false;
+            }
+        }
+    }
+}