1. Swapping Two Numbers Using XOR

Problem Statement

Given two numbers a and b, swap their values without using a temporary variable.

Solution Explanation

• Use the XOR (^) operator, leveraging its properties:
  • XOR of a number with itself is 0 (x ^ x = 0).
  • XOR of a number with 0 is the number itself (x ^ 0 = x).
• Steps:
  1. a = a ^ b
  2. b = a ^ b (substitutes to (a ^ b) ^ b = a)
  3. a = a ^ b (substitutes to (a ^ b) ^ a = b)

Example

• Input: a = 5 (binary: 101), b = 6 (binary: 110)
• Step 1: a = 5 ^ 6 = 3 (binary: 011)
• Step 2: b = 3 ^ 6 = 5 (binary: 101)
• Step 3: a = 3 ^ 5 = 6 (binary: 110)
• Output: a = 6, b = 5

Java Code

public class SwapNumbers {
    public static void main(String[] args) {
        int a = 5;
        int b = 6;
        System.out.println("Before swap: a = " + a + ", b = " + b);
        a = a ^ b;
        b = a ^ b;
        a = a ^ b;
        System.out.println("After swap: a = " + a + ", b = " + b);
    }
}

2. Check if the i-th Bit is Set

Problem Statement

Given a number n and an index i (counting from the right, starting at 0), determine if the i-th bit is set (1) in n’s binary representation.

Solution Explanation

• Create a mask by left-shifting 1 by i positions (1 << i), which sets only the i-th bit to 1.