Merge branch 'master' into qt

Author: siriak

DIRECTORY.md

@@ -0,0 +1,43 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * This class contains a method to check if the binary representation of a number is a palindrome.
+ * <p>
+ *     A binary palindrome is a number whose binary representation is the same when read from left to right and right to left.
+ *     For example, the number 9 has a binary representation of 1001, which is a palindrome.
+ *     The number 10 has a binary representation of 1010, which is not a palindrome.
+ * </p>
+ *
+ * @author Hardvan
+ */
+public final class BinaryPalindromeCheck {
+    private BinaryPalindromeCheck() {
+    }
+
+    /**
+     * Checks if the binary representation of a number is a palindrome.
+     *
+     * @param x The number to check.
+     * @return True if the binary representation is a palindrome, otherwise false.
+     */
+    public static boolean isBinaryPalindrome(int x) {
+        int reversed = reverseBits(x);
+        return x == reversed;
+    }
+
+    /**
+     * Helper function to reverse all the bits of an integer.
+     *
+     * @param x The number to reverse the bits of.
+     * @return The number with reversed bits.
+     */
+    private static int reverseBits(int x) {
+        int result = 0;
+        while (x > 0) {
+            result <<= 1;
+            result |= (x & 1);
+            x >>= 1;
+        }
+        return result;
+    }
+}

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

@@ -0,0 +1,39 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * ClearLeftmostSetBit class contains a method to clear the leftmost set bit of a number.
+ * The leftmost set bit is the leftmost bit that is set to 1 in the binary representation of a number.
+ *
+ * Example:
+ * 26 (11010) -> 10 (01010)
+ * 1 (1) -> 0 (0)
+ * 7 (111) -> 3 (011)
+ * 6 (0110) -> 2 (0010)
+ *
+ * @author Hardvan
+ */
+public final class ClearLeftmostSetBit {
+    private ClearLeftmostSetBit() {
+    }
+
+    /**
+     * Clears the leftmost set bit (1) of a given number.
+     * Step 1: Find the position of the leftmost set bit
+     * Step 2: Create a mask with all bits set except for the leftmost set bit
+     * Step 3: Clear the leftmost set bit using AND with the mask
+     *
+     * @param num The input number.
+     * @return The number after clearing the leftmost set bit.
+     */
+    public static int clearLeftmostSetBit(int num) {
+        int pos = 0;
+        int temp = num;
+        while (temp > 0) {
+            temp >>= 1;
+            pos++;
+        }
+
+        int mask = ~(1 << (pos - 1));
+        return num & mask;
+    }
+}

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

@@ -0,0 +1,39 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * CountLeadingZeros class contains a method to count the number of leading zeros in the binary representation of a number.
+ * The number of leading zeros is the number of zeros before the leftmost 1 bit.
+ * For example, the number 5 has 29 leading zeros in its 32-bit binary representation.
+ * The number 0 has 32 leading zeros.
+ * The number 1 has 31 leading zeros.
+ * The number -1 has no leading zeros.
+ *
+ * @author Hardvan
+ */
+public final class CountLeadingZeros {
+    private CountLeadingZeros() {
+    }
+
+    /**
+     * Counts the number of leading zeros in the binary representation of a number.
+     * Method: Keep shifting the mask to the right until the leftmost bit is 1.
+     * The number of shifts is the number of leading zeros.
+     *
+     * @param num The input number.
+     * @return The number of leading zeros.
+     */
+    public static int countLeadingZeros(int num) {
+        if (num == 0) {
+            return 32;
+        }
+
+        int count = 0;
+        int mask = 1 << 31;
+        while ((mask & num) == 0) {
+            count++;
+            mask >>>= 1;
+        }
+
+        return count;
+    }
+}

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

@@ -0,0 +1,44 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * Gray code is a binary numeral system where two successive values differ in only one bit.
+ * This is a simple conversion between binary and Gray code.
+ * Example:
+ * 7 -> 0111 -> 0100 -> 4
+ * 4 -> 0100 -> 0111 -> 7
+ * 0 -> 0000 -> 0000 -> 0
+ * 1 -> 0001 -> 0000 -> 0
+ * 2 -> 0010 -> 0011 -> 3
+ * 3 -> 0011 -> 0010 -> 2
+ *
+ * @author Hardvan
+ */
+public final class GrayCodeConversion {
+    private GrayCodeConversion() {
+    }
+
+    /**
+     * Converts a binary number to Gray code.
+     *
+     * @param num The binary number.
+     * @return The corresponding Gray code.
+     */
+    public static int binaryToGray(int num) {
+        return num ^ (num >> 1);
+    }
+
+    /**
+     * Converts a Gray code number back to binary.
+     *
+     * @param gray The Gray code number.
+     * @return The corresponding binary number.
+     */
+    public static int grayToBinary(int gray) {
+        int binary = gray;
+        while (gray > 0) {
+            gray >>= 1;
+            binary ^= gray;
+        }
+        return binary;
+    }
+}

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

@@ -0,0 +1,29 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * The Hamming distance between two integers is the number of positions at which the corresponding bits are different.
+ * Given two integers x and y, calculate the Hamming distance.
+ * Example:
+ * Input: x = 1, y = 4
+ * Output: 2
+ * Explanation: 1 (0001) and 4 (0100) have 2 differing bits.
+ *
+ * @author Hardvan
+ */
+public final class HammingDistance {
+    private HammingDistance() {
+    }
+
+    /**
+     * Calculates the Hamming distance between two integers.
+     * The Hamming distance is the number of differing bits between the two integers.
+     *
+     * @param x The first integer.
+     * @param y The second integer.
+     * @return The Hamming distance (number of differing bits).
+     */
+    public static int hammingDistance(int x, int y) {
+        int xor = x ^ y;
+        return Integer.bitCount(xor);
+    }
+}

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

@@ -0,0 +1,54 @@
+package com.thealgorithms.bitmanipulation;
+
+/**
+ * HigherLowerPowerOfTwo class has two methods to find the next higher and lower power of two.
+ * <p>
+ *     nextHigherPowerOfTwo method finds the next higher power of two.
+ *     nextLowerPowerOfTwo method finds the next lower power of two.
+ *     Both methods take an integer as input and return the next higher or lower power of two.
+ *     If the input is less than 1, the next higher power of two is 1.
+ *     If the input is less than or equal to 1, the next lower power of two is 0.
+ *     nextHigherPowerOfTwo method uses bitwise operations to find the next higher power of two.
+ *     nextLowerPowerOfTwo method uses Integer.highestOneBit method to find the next lower power of two.
+ *     The time complexity of both methods is O(1).
+ *     The space complexity of both methods is O(1).
+ * </p>
+ *
+ * @author Hardvan
+ */
+public final class HigherLowerPowerOfTwo {
+    private HigherLowerPowerOfTwo() {
+    }
+
+    /**
+     * Finds the next higher power of two.
+     *
+     * @param x The given number.
+     * @return The next higher power of two.
+     */
+    public static int nextHigherPowerOfTwo(int x) {
+        if (x < 1) {
+            return 1;
+        }
+        x--;
+        x |= x >> 1;
+        x |= x >> 2;
+        x |= x >> 4;
+        x |= x >> 8;
+        x |= x >> 16;
+        return x + 1;
+    }
+
+    /**
+     * Finds the next lower power of two.
+     *
+     * @param x The given number.
+     * @return The next lower power of two.
+     */
+    public static int nextLowerPowerOfTwo(int x) {
+        if (x < 1) {
+            return 0;
+        }
+        return Integer.highestOneBit(x);
+    }
+}

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

@@ -1,5 +1,7 @@
 package com.thealgorithms.dynamicprogramming;
 
+import java.util.Arrays;
+
 /**
  * Recursive Solution for 0-1 knapsack with memoization
  * This method is basically an extension to the recursive approach so that we
@@ -15,10 +17,8 @@ int knapSack(int capacity, int[] weights, int[] profits, int numOfItems) {
         int[][] dpTable = new int[numOfItems + 1][capacity + 1];
 
         // Loop to initially fill the table with -1
-        for (int i = 0; i < numOfItems + 1; i++) {
-            for (int j = 0; j < capacity + 1; j++) {
-                dpTable[i][j] = -1;
-            }
+        for (int[] table : dpTable) {
+            Arrays.fill(table, -1);
         }
 
         return solveKnapsackRecursive(capacity, weights, profits, numOfItems, dpTable);
@@ -38,7 +38,6 @@ int solveKnapsackRecursive(int capacity, int[] weights, int[] profits, int numOf
         if (weights[numOfItems - 1] > capacity) {
             // Store the value of function call stack in table
             dpTable[numOfItems][capacity] = solveKnapsackRecursive(capacity, weights, profits, numOfItems - 1, dpTable);
-            return dpTable[numOfItems][capacity];
         } else {
             // case 1. include the item, if it is less than the capacity
             final int includeCurrentItem = profits[numOfItems - 1] + solveKnapsackRecursive(capacity - weights[numOfItems - 1], weights, profits, numOfItems - 1, dpTable);
@@ -48,7 +47,7 @@ int solveKnapsackRecursive(int capacity, int[] weights, int[] profits, int numOf
 
             // Store the value of function call stack in table and return
             dpTable[numOfItems][capacity] = Math.max(includeCurrentItem, excludeCurrentItem);
-            return dpTable[numOfItems][capacity];
         }
+        return dpTable[numOfItems][capacity];
     }
 }

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

@@ -1,15 +1,31 @@
 package com.thealgorithms.dynamicprogramming;
 
-// Matrix-chain Multiplication
-// Problem Statement
-// we have given a chain A1,A2,...,Ani of n matrices, where for i = 1,2,...,n,
-// matrix Ai has dimension pi−1 ×pi
-// , fully parenthesize the product A1A2 ···An in a way that
-// minimizes the number of scalar multiplications.
+/**
+ * The MatrixChainRecursiveTopDownMemoisation class implements the matrix-chain
+ * multiplication problem using a top-down recursive approach with memoization.
+ *
+ * <p>Given a chain of matrices A1, A2, ..., An, where matrix Ai has dimensions
+ * pi-1 × pi, this algorithm finds the optimal way to fully parenthesize the
+ * product A1A2...An in a way that minimizes the total number of scalar
+ * multiplications required.</p>
+ *
+ * <p>This implementation uses a memoization technique to store the results of
+ * subproblems, which significantly reduces the number of recursive calls and
+ * improves performance compared to a naive recursive approach.</p>
+ */
 public final class MatrixChainRecursiveTopDownMemoisation {
     private MatrixChainRecursiveTopDownMemoisation() {
     }
 
+    /**
+     * Calculates the minimum number of scalar multiplications needed to multiply
+     * a chain of matrices.
+     *
+     * @param p an array of integers representing the dimensions of the matrices.
+     *          The length of the array is n + 1, where n is the number of matrices.
+     * @return the minimum number of multiplications required to multiply the chain
+     *         of matrices.
+     */
     static int memoizedMatrixChain(int[] p) {
         int n = p.length;
         int[][] m = new int[n][n];
@@ -21,6 +37,17 @@ static int memoizedMatrixChain(int[] p) {
         return lookupChain(m, p, 1, n - 1);
     }
 
+    /**
+     * A recursive helper method to lookup the minimum number of multiplications
+     * for multiplying matrices from index i to index j.
+     *
+     * @param m the memoization table storing the results of subproblems.
+     * @param p an array of integers representing the dimensions of the matrices.
+     * @param i the starting index of the matrix chain.
+     * @param j the ending index of the matrix chain.
+     * @return the minimum number of multiplications needed to multiply matrices
+     *         from i to j.
+     */
     static int lookupChain(int[][] m, int[] p, int i, int j) {
         if (i == j) {
             m[i][j] = 0;
@@ -38,11 +65,4 @@ static int lookupChain(int[][] m, int[] p, int i, int j) {
         }
         return m[i][j];
     }
-
-    // in this code we are taking the example of 4 matrixes whose orders are 1x2,2x3,3x4,4x5
-    // respectively output should be  Minimum number of multiplications is 38
-    public static void main(String[] args) {
-        int[] arr = {1, 2, 3, 4, 5};
-        System.out.println("Minimum number of multiplications is " + memoizedMatrixChain(arr));
-    }
 }