Merge branch 'master' into dependabot/maven/org.apache.maven.plugins-maven-checkstyle-plugin-3.6.0

Author: siriak

DIRECTORY.md

@@ -1,6 +1,7 @@
 package com.thealgorithms.backtracking;
 
 import java.util.Arrays;
+import java.util.Collections;
 import java.util.LinkedList;
 import java.util.List;
 import java.util.TreeSet;
@@ -13,8 +14,6 @@ public final class Combination {
     private Combination() {
     }
 
-    private static int length;
-
     /**
      * Find all combinations of given array using backtracking
      * @param arr the array.
@@ -23,39 +22,45 @@ private Combination() {
      * @return a list of all combinations of length n. If n == 0, return null.
      */
     public static <T> List<TreeSet<T>> combination(T[] arr, int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("The combination length cannot be negative.");
+        }
+
         if (n == 0) {
-            return null;
+            return Collections.emptyList();
         }
-        length = n;
         T[] array = arr.clone();
         Arrays.sort(array);
+
         List<TreeSet<T>> result = new LinkedList<>();
-        backtracking(array, 0, new TreeSet<T>(), result);
+        backtracking(array, n, 0, new TreeSet<T>(), result);
         return result;
     }
 
     /**
      * Backtrack all possible combinations of a given array
      * @param arr the array.
+     * @param n length of the combination
      * @param index the starting index.
      * @param currSet set that tracks current combination
      * @param result the list contains all combination.
      * @param <T> the type of elements in the array.
      */
-    private static <T> void backtracking(T[] arr, int index, TreeSet<T> currSet, List<TreeSet<T>> result) {
-        if (index + length - currSet.size() > arr.length) {
+    private static <T> void backtracking(T[] arr, int n, int index, TreeSet<T> currSet, List<TreeSet<T>> result) {
+        if (index + n - currSet.size() > arr.length) {
             return;
         }
-        if (length - 1 == currSet.size()) {
+        if (currSet.size() == n - 1) {
             for (int i = index; i < arr.length; i++) {
                 currSet.add(arr[i]);
-                result.add((TreeSet<T>) currSet.clone());
+                result.add(new TreeSet<>(currSet));
                 currSet.remove(arr[i]);
             }
+            return;
         }
         for (int i = index; i < arr.length; i++) {
             currSet.add(arr[i]);
-            backtracking(arr, i + 1, currSet, result);
+            backtracking(arr, n, i + 1, currSet, result);
             currSet.remove(arr[i]);
         }
     }

src/main/java/com/thealgorithms/backtracking/Combination.java

@@ -0,0 +1,33 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * This class provides a method to find the first differing bit
+ * between two integers.
+ *
+ * Example:
+ *  x = 10 (1010 in binary)
+ *  y = 12 (1100 in binary)
+ *  The first differing bit is at index 1 (0-based)
+ *  So, the output will be 1
+ *
+ * @author Hardvan
+ */
+public final class FirstDifferentBit {
+    private FirstDifferentBit() {
+    }
+
+    /**
+     * Identifies the index of the first differing bit between two integers.
+     * Steps:
+     * 1. XOR the two integers to get the differing bits
+     * 2. Find the index of the first set bit in XOR result
+     *
+     * @param x the first integer
+     * @param y the second integer
+     * @return the index of the first differing bit (0-based)
+     */
+    public static int firstDifferentBit(int x, int y) {
+        int diff = x ^ y;
+        return Integer.numberOfTrailingZeros(diff);
+    }
+}

src/main/java/com/thealgorithms/bitmanipulation/FirstDifferentBit.java

@@ -0,0 +1,44 @@
+package com.thealgorithms.bitmanipulation;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * This class provides a method to generate all subsets (power set)
+ * of a given set using bit manipulation.
+ *
+ * @author Hardvan
+ */
+public final class GenerateSubsets {
+    private GenerateSubsets() {
+    }
+
+    /**
+     * Generates all subsets of a given set using bit manipulation.
+     * Steps:
+     * 1. Iterate over all numbers from 0 to 2^n - 1.
+     * 2. For each number, iterate over all bits from 0 to n - 1.
+     * 3. If the i-th bit of the number is set, add the i-th element of the set to the current subset.
+     * 4. Add the current subset to the list of subsets.
+     * 5. Return the list of subsets.
+     *
+     * @param set the input set of integers
+     * @return a list of all subsets represented as lists of integers
+     */
+    public static List<List<Integer>> generateSubsets(int[] set) {
+        int n = set.length;
+        List<List<Integer>> subsets = new ArrayList<>();
+
+        for (int mask = 0; mask < (1 << n); mask++) {
+            List<Integer> subset = new ArrayList<>();
+            for (int i = 0; i < n; i++) {
+                if ((mask & (1 << i)) != 0) {
+                    subset.add(set[i]);
+                }
+            }
+            subsets.add(subset);
+        }
+
+        return subsets;
+    }
+}

src/main/java/com/thealgorithms/bitmanipulation/GenerateSubsets.java

@@ -1,13 +1,27 @@
 package com.thealgorithms.bitmanipulation;
 
 /**
- * Is number power of 2
+ * Utility class for checking if a number is a power of two.
+ * A power of two is a number that can be expressed as 2^n where n is a non-negative integer.
+ * This class provides a method to determine if a given integer is a power of two using bit manipulation.
+ *
  * @author Bama Charan Chhandogi (https://github.com/BamaCharanChhandogi)
  */
-
 public final class IsPowerTwo {
     private IsPowerTwo() {
     }
+
+    /**
+     * Checks if the given integer is a power of two.
+     *
+     * A number is considered a power of two if it is greater than zero and
+     * has exactly one '1' bit in its binary representation. This method
+     * uses the property that for any power of two (n), the expression
+     * (n & (n - 1)) will be zero.
+     *
+     * @param number the integer to check
+     * @return true if the number is a power of two, false otherwise
+     */
     public static boolean isPowerTwo(int number) {
         if (number <= 0) {
             return false;

src/main/java/com/thealgorithms/bitmanipulation/IsPowerTwo.java

@@ -0,0 +1,28 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * This class provides a method to compute the remainder
+ * of a number when divided by a power of two (2^n)
+ * without using division or modulo operations.
+ *
+ * @author Hardvan
+ */
+public final class ModuloPowerOfTwo {
+    private ModuloPowerOfTwo() {
+    }
+
+    /**
+     * Computes the remainder of a given integer when divided by 2^n.
+     *
+     * @param x the input number
+     * @param n the exponent (power of two)
+     * @return the remainder of x divided by 2^n
+     */
+    public static int moduloPowerOfTwo(int x, int n) {
+        if (n <= 0) {
+            throw new IllegalArgumentException("The exponent must be positive");
+        }
+
+        return x & ((1 << n) - 1);
+    }
+}

src/main/java/com/thealgorithms/bitmanipulation/ModuloPowerOfTwo.java

@@ -0,0 +1,30 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * This class provides a method to find the next higher number
+ * with the same number of set bits as the given number.
+ *
+ * @author Hardvan
+ */
+public final class NextHigherSameBitCount {
+    private NextHigherSameBitCount() {
+    }
+
+    /**
+     * Finds the next higher integer with the same number of set bits.
+     * Steps:
+     * 1. Find {@code c}, the rightmost set bit of {@code n}.
+     * 2. Find {@code r}, the rightmost set bit of {@code n + c}.
+     * 3. Swap the bits of {@code r} and {@code n} to the right of {@code c}.
+     * 4. Shift the bits of {@code r} and {@code n} to the right of {@code c} to the rightmost.
+     * 5. Combine the results of steps 3 and 4.
+     *
+     * @param n the input number
+     * @return the next higher integer with the same set bit count
+     */
+    public static int nextHigherSameBitCount(int n) {
+        int c = n & -n;
+        int r = n + c;
+        return (((r ^ n) >> 2) / c) | r;
+    }
+}

src/main/java/com/thealgorithms/bitmanipulation/NextHigherSameBitCount.java

@@ -1,14 +1,30 @@
 package com.thealgorithms.bitmanipulation;
 
 /**
- * Find Non Repeating Number
+ * A utility class to find the non-repeating number in an array where every other number repeats.
+ * This class contains a method to identify the single unique number using bit manipulation.
+ *
+ * The solution leverages the properties of the XOR operation, which states that:
+ * - x ^ x = 0 for any integer x (a number XORed with itself is zero)
+ * - x ^ 0 = x for any integer x (a number XORed with zero is the number itself)
+ *
+ * Using these properties, we can find the non-repeating number in linear time with constant space.
+ *
+ * Example:
+ * Given the input array [2, 3, 5, 2, 3], the output will be 5 since it does not repeat.
+ *
  * @author Bama Charan Chhandogi (https://github.com/BamaCharanChhandogi)
  */
-
 public final class NonRepeatingNumberFinder {
     private NonRepeatingNumberFinder() {
     }
 
+    /**
+     * Finds the non-repeating number in the given array.
+     *
+     * @param arr an array of integers where every number except one appears twice
+     * @return the integer that appears only once in the array or 0 if the array is empty
+     */
     public static int findNonRepeatingNumber(int[] arr) {
         int result = 0;
         for (int num : arr) {

src/main/java/com/thealgorithms/bitmanipulation/NonRepeatingNumberFinder.java

@@ -1,21 +1,41 @@
 package com.thealgorithms.bitmanipulation;
 
 /**
- * Find the Number Appearing Odd Times in an array
+ * This class provides a method to find the element that appears an
+ * odd number of times in an array. All other elements in the array
+ * must appear an even number of times for the logic to work.
+ *
+ * The solution uses the XOR operation, which has the following properties:
+ * - a ^ a = 0 (XOR-ing the same numbers cancels them out)
+ * - a ^ 0 = a
+ * - XOR is commutative and associative.
+ *
+ * Time Complexity: O(n), where n is the size of the array.
+ * Space Complexity: O(1), as no extra space is used.
+ *
+ * Usage Example:
+ * int result = NumberAppearingOddTimes.findOddOccurrence(new int[]{1, 2, 1, 2, 3});
+ * // result will be 3
+ *
  * @author Lakshyajeet Singh Goyal (https://github.com/DarkMatter-999)
  */
 
 public final class NumberAppearingOddTimes {
     private NumberAppearingOddTimes() {
     }
+
+    /**
+     * Finds the element in the array that appears an odd number of times.
+     *
+     * @param arr the input array containing integers, where all elements
+     *            except one appear an even number of times.
+     * @return the integer that appears an odd number of times.
+     */
     public static int findOddOccurrence(int[] arr) {
         int result = 0;
-
-        // XOR all elements in the array
         for (int num : arr) {
             result ^= num;
         }
-
         return result;
     }
 }

src/main/java/com/thealgorithms/bitmanipulation/NumberAppearingOddTimes.java

@@ -1,14 +1,29 @@
 package com.thealgorithms.bitmanipulation;
 
 /**
- * Numbers Different Signs
+ * This class provides a method to determine whether two integers have
+ * different signs. It utilizes the XOR operation on the two numbers:
+ *
+ * - If two numbers have different signs, their most significant bits
+ *   (sign bits) will differ, resulting in a negative XOR result.
+ * - If two numbers have the same sign, the XOR result will be non-negative.
+ *
+ * Time Complexity: O(1) - Constant time operation.
+ * Space Complexity: O(1) - No extra space used.
+ *
  * @author Bama Charan Chhandogi
  */
-
 public final class NumbersDifferentSigns {
     private NumbersDifferentSigns() {
     }
 
+    /**
+     * Determines if two integers have different signs using bitwise XOR.
+     *
+     * @param num1 the first integer
+     * @param num2 the second integer
+     * @return true if the two numbers have different signs, false otherwise
+     */
     public static boolean differentSigns(int num1, int num2) {
         return (num1 ^ num2) < 0;
     }

src/main/java/com/thealgorithms/bitmanipulation/NumbersDifferentSigns.java

@@ -0,0 +1,32 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * This class provides a method to detect if two integers
+ * differ by exactly one bit flip.
+ *
+ * Example:
+ * 1 (0001) and 2 (0010) differ by exactly one bit flip.
+ * 7 (0111) and 3 (0011) differ by exactly one bit flip.
+ *
+ * @author Hardvan
+ */
+public final class OneBitDifference {
+    private OneBitDifference() {
+    }
+
+    /**
+     * Checks if two integers differ by exactly one bit.
+     *
+     * @param x the first integer
+     * @param y the second integer
+     * @return true if x and y differ by exactly one bit, false otherwise
+     */
+    public static boolean differByOneBit(int x, int y) {
+        if (x == y) {
+            return false;
+        }
+
+        int xor = x ^ y;
+        return (xor & (xor - 1)) == 0;
+    }
+}