Answer: Java Programs — Number Swapping & Recursive Factorial

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Part (a): Swap Two Numbers Without Using a Third Variable

1. Algorithm & Logic

We can swap two numbers without a temporary variable using arithmetic addition/subtraction or bitwise XOR operations:

• Step 1: $a = a + b$ (Holds sum of both)
• Step 2: $b = a - b$ (Original value of $a$)
• Step 3: $a = a - b$ (Original value of $b$)

2. Java Code:

import java.util.Scanner;

public class SwapWithoutThirdVariable {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        System.out.print("Enter first number (a): ");
        int a = sc.nextInt();
        System.out.print("Enter second number (b): ");
        int b = sc.nextInt();
        
        System.out.println("
--- Before Swapping ---");
        System.out.println("a = " + a + ", b = " + b);
        
        // Swapping logic using arithmetic operators
        a = a + b;
        b = a - b;
        a = a - b;
        
        System.out.println("
--- After Swapping ---");
        System.out.println("a = " + a + ", b = " + b);
        
        sc.close();
    }
}

3. Dry Run:

• Initial: $a = 15, b = 25$
• Line 1 ($a = a + b$): $a = 15 + 25 = 40$
• Line 2 ($b = a - b$): $b = 40 - 25 = 15$ ($b$ now holds original $a$)
• Line 3 ($a = a - b$): $a = 40 - 15 = 25$ ($a$ now holds original $b$)
• Result: $a = 25, b = 15$ (Swapped successfully!)

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Part (b): Factorial of a Number Using Recursion

1. Mathematical Principle & Base Case

$$\text{Factorial}(n) = \begin{cases} 1 & \text{if } n = 0 \text{ or } n = 1 \quad \text{(Base Case)} \\ n \times \text{Factorial}(n - 1) & \text{if } n > 1 \quad \text{(Recursive Step)} \end{cases}$$

2. Java Code:

import java.util.Scanner;

public class RecursiveFactorial {
    // Recursive function to calculate factorial
    public static long calculateFactorial(int n) {
        // Base Condition
        if (n <= 1) {
            return 1;
        }
        // Recursive Call
        return n * calculateFactorial(n - 1);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        System.out.print("Enter a non-negative integer: ");
        int number = sc.nextInt();
        
        if (number < 0) {
            System.out.println("Factorial is not defined for negative numbers.");
        } else {
            long result = calculateFactorial(number);
            System.out.println("Factorial of " + number + " (" + number + "!) = " + result);
        }
        
        sc.close();
    }
}

3. Recursive Call Stack Trace (For $n = 4$):

calculateFactorial(4)
  = 4 * calculateFactorial(3)
        = 3 * calculateFactorial(2)
              = 2 * calculateFactorial(1)
                    = 1 (Base case reached)
              = 2 * 1 = 2
        = 3 * 2 = 6
  = 4 * 6 = 24
Output: 24

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Complete Unified Program

import java.util.Scanner;

public class CombinedExamDemo {
    public static void swap(int a, int b) {
        System.out.println("Before Swap: a = " + a + ", b = " + b);
        a = a ^ b; // Bitwise XOR swapping
        b = a ^ b;
        a = a ^ b;
        System.out.println("After Swap:  a = " + a + ", b = " + b);
    }

    public static long factorial(int n) {
        if (n <= 1) return 1;
        return n * factorial(n - 1);
    }

    public static void main(String[] args) {
        // Test (a)
        swap(10, 20);

        // Test (b)
        int num = 5;
        System.out.println("Factorial of " + num + " = " + factorial(num));
    }
}