Merge branch 'master' into master

Author: rajucreate

pom.xml

@@ -112,14 +112,14 @@
                     <dependency>
                     <groupId>com.puppycrawl.tools</groupId>
                     <artifactId>checkstyle</artifactId>
-                    <version>12.0.1</version>
+                    <version>12.1.0</version>
                     </dependency>
                 </dependencies>
             </plugin>
             <plugin>
                 <groupId>com.github.spotbugs</groupId>
                 <artifactId>spotbugs-maven-plugin</artifactId>
-                <version>4.9.7.0</version>
+                <version>4.9.8.1</version>
                 <configuration>
                     <excludeFilterFile>spotbugs-exclude.xml</excludeFilterFile>
                     <includeTests>true</includeTests>

src/main/java/com/thealgorithms/compression/ArithmeticCoding.java

@@ -0,0 +1,157 @@
+package com.thealgorithms.compression;
+
+import java.math.BigDecimal;
+import java.math.MathContext;
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.List;
+import java.util.Map;
+
+/**
+ * An implementation of the Arithmetic Coding algorithm.
+ *
+ * <p>
+ * Arithmetic coding is a form of entropy encoding used in lossless data
+ * compression. It encodes an entire message into a single number, a fraction n
+ * where (0.0 <= n < 1.0). Unlike Huffman coding, which assigns a specific
+ * bit sequence to each symbol, arithmetic coding represents the message as a
+ * sub-interval of the [0, 1) interval.
+ * </p>
+ *
+ * <p>
+ * This implementation uses BigDecimal for precision to handle the shrinking
+ * intervals, making it suitable for educational purposes to demonstrate the
+ * core logic.
+ * </p>
+ *
+ * <p>
+ * Time Complexity: O(n*m) for compression and decompression where n is the
+ * length of the input and m is the number of unique symbols, due to the need
+ * to calculate symbol probabilities.
+ * </p>
+ *
+ * <p>
+ * References:
+ * <ul>
+ * <li><a href="https://en.wikipedia.org/wiki/Arithmetic_coding">Wikipedia:
+ * Arithmetic coding</a></li>
+ * </ul>
+ * </p>
+ */
+public final class ArithmeticCoding {
+
+    private ArithmeticCoding() {
+    }
+
+    /**
+     * Compresses a string using the Arithmetic Coding algorithm.
+     *
+     * @param uncompressed The string to be compressed.
+     * @return The compressed representation as a BigDecimal number.
+     * @throws IllegalArgumentException if the input string is null or empty.
+     */
+    public static BigDecimal compress(String uncompressed) {
+        if (uncompressed == null || uncompressed.isEmpty()) {
+            throw new IllegalArgumentException("Input string cannot be null or empty.");
+        }
+
+        Map<Character, Symbol> probabilityTable = calculateProbabilities(uncompressed);
+
+        BigDecimal low = BigDecimal.ZERO;
+        BigDecimal high = BigDecimal.ONE;
+
+        for (char symbol : uncompressed.toCharArray()) {
+            BigDecimal range = high.subtract(low);
+            Symbol sym = probabilityTable.get(symbol);
+
+            high = low.add(range.multiply(sym.high()));
+            low = low.add(range.multiply(sym.low()));
+        }
+
+        return low; // Return the lower bound of the final interval
+    }
+
+    /**
+     * Decompresses a BigDecimal number back into the original string.
+     *
+     * @param compressed       The compressed BigDecimal number.
+     * @param length           The length of the original uncompressed string.
+     * @param probabilityTable The probability table used during compression.
+     * @return The original, uncompressed string.
+     */
+    public static String decompress(BigDecimal compressed, int length, Map<Character, Symbol> probabilityTable) {
+        StringBuilder decompressed = new StringBuilder();
+
+        // Create a sorted list of symbols for deterministic decompression, matching the
+        // order used in calculateProbabilities
+        List<Map.Entry<Character, Symbol>> sortedSymbols = new ArrayList<>(probabilityTable.entrySet());
+        sortedSymbols.sort(Map.Entry.comparingByKey());
+
+        BigDecimal low = BigDecimal.ZERO;
+        BigDecimal high = BigDecimal.ONE;
+
+        for (int i = 0; i < length; i++) {
+            BigDecimal range = high.subtract(low);
+
+            // Find which symbol the compressed value falls into
+            for (Map.Entry<Character, Symbol> entry : sortedSymbols) {
+                Symbol sym = entry.getValue();
+
+                // Calculate the actual range for this symbol in the current interval
+                BigDecimal symLow = low.add(range.multiply(sym.low()));
+                BigDecimal symHigh = low.add(range.multiply(sym.high()));
+
+                // Check if the compressed value falls within this symbol's range
+                if (compressed.compareTo(symLow) >= 0 && compressed.compareTo(symHigh) < 0) {
+                    decompressed.append(entry.getKey());
+
+                    // Update the interval for the next iteration
+                    low = symLow;
+                    high = symHigh;
+                    break;
+                }
+            }
+        }
+
+        return decompressed.toString();
+    }
+
+    /**
+     * Calculates the frequency and probability range for each character in the
+     * input string in a deterministic order.
+     *
+     * @param text The input string.
+     * @return A map from each character to a Symbol object containing its
+     * probability range.
+     */
+    public static Map<Character, Symbol> calculateProbabilities(String text) {
+        Map<Character, Integer> frequencies = new HashMap<>();
+        for (char c : text.toCharArray()) {
+            frequencies.put(c, frequencies.getOrDefault(c, 0) + 1);
+        }
+
+        // Sort the characters to ensure a deterministic order for the probability table
+        List<Character> sortedKeys = new ArrayList<>(frequencies.keySet());
+        Collections.sort(sortedKeys);
+
+        Map<Character, Symbol> probabilityTable = new HashMap<>();
+        BigDecimal currentLow = BigDecimal.ZERO;
+        int total = text.length();
+
+        for (char symbol : sortedKeys) {
+            BigDecimal probability = BigDecimal.valueOf(frequencies.get(symbol)).divide(BigDecimal.valueOf(total), MathContext.DECIMAL128);
+            BigDecimal high = currentLow.add(probability);
+            probabilityTable.put(symbol, new Symbol(currentLow, high));
+            currentLow = high;
+        }
+
+        return probabilityTable;
+    }
+
+    /**
+     * Helper class to store the probability range [low, high) for a symbol.
+     */
+    public record Symbol(BigDecimal low, BigDecimal high) {
+    }
+}

src/main/java/com/thealgorithms/compression/BurrowsWheelerTransform.java

@@ -0,0 +1,220 @@
+package com.thealgorithms.compression;
+
+import java.util.Arrays;
+import java.util.HashMap;
+import java.util.Map;
+
+/**
+ * Implementation of the Burrows-Wheeler Transform (BWT) and its inverse.
+ * <p>
+ * BWT is a reversible data transformation algorithm that rearranges a string into runs of
+ * similar characters. While not a compression algorithm itself, it significantly improves
+ * the compressibility of data for subsequent algorithms like Move-to-Front encoding and
+ * Run-Length Encoding.
+ * </p>
+ *
+ * <p>The transform works by:
+ * <ol>
+ *   <li>Generating all rotations of the input string</li>
+ *   <li>Sorting these rotations lexicographically</li>
+ *   <li>Taking the last column of the sorted matrix as output</li>
+ *   <li>Recording the index of the original string in the sorted matrix</li>
+ * </ol>
+ * </p>
+ *
+ * <p><b>Important:</b> The input string should end with a unique end-of-string marker
+ * (typically '$') that:
+ * <ul>
+ *   <li>Does not appear anywhere else in the text</li>
+ *   <li>Is lexicographically smaller than all other characters</li>
+ *   <li>Ensures unique rotations and enables correct inverse transformation</li>
+ * </ul>
+ * Without this marker, the inverse transform may not correctly reconstruct the original string.
+ * </p>
+ *
+ * <p><b>Time Complexity:</b>
+ * <ul>
+ *   <li>Forward transform: O(n² log n) where n is the string length</li>
+ *   <li>Inverse transform: O(n) using the LF-mapping technique</li>
+ * </ul>
+ * </p>
+ *
+ * <p><b>Example:</b></p>
+ * <pre>
+ * Input:  "banana$"
+ * Output: BWTResult("annb$aa", 4)
+ *         - "annb$aa" is the transformed string (groups similar characters)
+ *         - 4 is the index of the original string in the sorted rotations
+ * </pre>
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Burrows%E2%80%93Wheeler_transform">Burrows–Wheeler transform (Wikipedia)</a>
+ */
+public final class BurrowsWheelerTransform {
+
+    private BurrowsWheelerTransform() {
+    }
+
+    /**
+     * A container for the result of the forward BWT.
+     * <p>
+     * Contains the transformed string and the index of the original string
+     * in the sorted rotations matrix, both of which are required for the
+     * inverse transformation.
+     * </p>
+     */
+    public static class BWTResult {
+        /** The transformed string (last column of the sorted rotation matrix) */
+        public final String transformed;
+
+        /** The index of the original string in the sorted rotations matrix */
+        public final int originalIndex;
+
+        /**
+         * Constructs a BWTResult with the transformed string and original index.
+         *
+         * @param transformed the transformed string (L-column)
+         * @param originalIndex the index of the original string in sorted rotations
+         */
+        public BWTResult(String transformed, int originalIndex) {
+            this.transformed = transformed;
+            this.originalIndex = originalIndex;
+        }
+
+        @Override
+        public boolean equals(Object obj) {
+            if (this == obj) {
+                return true;
+            }
+            if (obj == null || getClass() != obj.getClass()) {
+                return false;
+            }
+            BWTResult bwtResult = (BWTResult) obj;
+            return originalIndex == bwtResult.originalIndex && transformed.equals(bwtResult.transformed);
+        }
+
+        @Override
+        public int hashCode() {
+            return 31 * transformed.hashCode() + originalIndex;
+        }
+
+        @Override
+        public String toString() {
+            return "BWTResult[transformed=" + transformed + ", originalIndex=" + originalIndex + "]";
+        }
+    }
+
+    /**
+     * Performs the forward Burrows-Wheeler Transform on the input string.
+     * <p>
+     * The algorithm generates all cyclic rotations of the input, sorts them
+     * lexicographically, and returns the last column of this sorted matrix
+     * along with the position of the original string.
+     * </p>
+     *
+     * <p><b>Note:</b> It is strongly recommended that the input string ends with
+     * a unique end-of-string marker (e.g., '$') that is lexicographically smaller
+     * than any other character in the string. This ensures correct inversion.</p>
+     *
+     * @param text the input string to transform; must not be {@code null}
+     * @return a {@link BWTResult} object containing the transformed string (L-column)
+     *         and the index of the original string in the sorted rotations matrix;
+     *         returns {@code BWTResult("", -1)} for empty input
+     * @throws NullPointerException if {@code text} is {@code null}
+     */
+    public static BWTResult transform(String text) {
+        if (text == null || text.isEmpty()) {
+            return new BWTResult("", -1);
+        }
+
+        int n = text.length();
+
+        // Generate all rotations of the input string
+        String[] rotations = new String[n];
+        for (int i = 0; i < n; i++) {
+            rotations[i] = text.substring(i) + text.substring(0, i);
+        }
+
+        // Sort rotations lexicographically
+        Arrays.sort(rotations);
+        int originalIndex = Arrays.binarySearch(rotations, text);
+        StringBuilder lastColumn = new StringBuilder(n);
+        for (int i = 0; i < n; i++) {
+            lastColumn.append(rotations[i].charAt(n - 1));
+        }
+
+        return new BWTResult(lastColumn.toString(), originalIndex);
+    }
+
+    /**
+     * Performs the inverse Burrows-Wheeler Transform using the LF-mapping technique.
+     * <p>
+     * The LF-mapping (Last-First mapping) is an efficient method to reconstruct
+     * the original string from the BWT output without explicitly reconstructing
+     * the entire sorted rotations matrix.
+     * </p>
+     *
+     * <p>The algorithm works by:
+     * <ol>
+     *   <li>Creating the first column by sorting the BWT string</li>
+     *   <li>Building a mapping from first column indices to last column indices</li>
+     *   <li>Following this mapping starting from the original index to reconstruct the string</li>
+     * </ol>
+     * </p>
+     *
+     * @param bwtString the transformed string (L-column) from the forward transform; must not be {@code null}
+     * @param originalIndex the index of the original string row from the forward transform;
+     *                      use -1 for empty strings
+     * @return the original, untransformed string; returns empty string if input is empty or {@code originalIndex} is -1
+     * @throws NullPointerException if {@code bwtString} is {@code null}
+     * @throws IllegalArgumentException if {@code originalIndex} is out of valid range (except -1)
+     */
+    public static String inverseTransform(String bwtString, int originalIndex) {
+        if (bwtString == null || bwtString.isEmpty() || originalIndex == -1) {
+            return "";
+        }
+
+        int n = bwtString.length();
+        if (originalIndex < 0 || originalIndex >= n) {
+            throw new IllegalArgumentException("Original index must be between 0 and " + (n - 1) + ", got: " + originalIndex);
+        }
+
+        char[] lastColumn = bwtString.toCharArray();
+        char[] firstColumn = bwtString.toCharArray();
+        Arrays.sort(firstColumn);
+
+        // Create the "next" array for LF-mapping.
+        // next[i] stores the row index in the last column that corresponds to firstColumn[i]
+        int[] next = new int[n];
+
+        // Track the count of each character seen so far in the last column
+        Map<Character, Integer> countMap = new HashMap<>();
+
+        // Store the first occurrence index of each character in the first column
+        Map<Character, Integer> firstOccurrence = new HashMap<>();
+
+        for (int i = 0; i < n; i++) {
+            if (!firstOccurrence.containsKey(firstColumn[i])) {
+                firstOccurrence.put(firstColumn[i], i);
+            }
+        }
+
+        // Build the LF-mapping
+        for (int i = 0; i < n; i++) {
+            char c = lastColumn[i];
+            int count = countMap.getOrDefault(c, 0);
+            int firstIndex = firstOccurrence.get(c);
+            next[firstIndex + count] = i;
+            countMap.put(c, count + 1);
+        }
+
+        // Reconstruct the original string by following the LF-mapping
+        StringBuilder originalString = new StringBuilder(n);
+        int currentRow = originalIndex;
+        for (int i = 0; i < n; i++) {
+            originalString.append(firstColumn[currentRow]);
+            currentRow = next[currentRow];
+        }
+
+        return originalString.toString();
+    }
+}