Swap using XOR

#include <iostream>
using namespace std;

void swapXOR(int& a, int& b) {
    a = a ^ b;
    b = a ^ b;  // b = (a^b) ^ b = a
    a = a ^ b;  // a = (a^b) ^ a = b
}

int main() {
    int a = 10, b = 20;
    
    cout << "Before swap: a = " << a << ", b = " << b << endl;
    
    swapXOR(a, b);
    
    cout << "After swap: a = " << a << ", b = " << b << endl;
    
    // Multiple swaps
    cout << "\nMultiple swaps:" << endl;
    int x = 5, y = 15, z = 25;
    
    cout << "Before: x = " << x << ", y = " << y << ", z = " << z << endl;
    
    swapXOR(x, y);
    swapXOR(y, z);
    
    cout << "After: x = " << x << ", y = " << y << ", z = " << z << endl;
    
    // XOR properties demonstration
    cout << "\nXOR properties:" << endl;
    int num1 = 12, num2 = 25;
    cout << "num1 = " << num1 << ", num2 = " << num2 << endl;
    cout << "num1 ^ num2 = " << (num1 ^ num2) << endl;
    cout << "(num1 ^ num2) ^ num2 = " << ((num1 ^ num2) ^ num2) << " (back to num1)" << endl;
    cout << "(num1 ^ num2) ^ num1 = " << ((num1 ^ num2) ^ num1) << " (back to num2)" << endl;
    
    return 0;
}

Before swap: a = 10, b = 20
After swap: a = 20, b = 10

Multiple swaps:
Before: x = 5, y = 15, z = 25
After: x = 15, y = 25, z = 5

XOR properties:
num1 = 12, num2 = 25
num1 ^ num2 = 21
(num1 ^ num2) ^ num2 = 12 (back to num1)
(num1 ^ num2) ^ num1 = 25 (back to num2)

This program teaches you how to Swap Two Numbers using XOR in C++. The XOR swap algorithm is an elegant bit manipulation technique that swaps two values without using a temporary variable. It demonstrates the unique properties of the XOR operation.

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1. What This Program Does

The program demonstrates XOR swap algorithm:

• Swapping two numbers without temporary variable
• Using XOR properties
• Multiple swaps demonstration
• XOR properties explanation

XOR swap is a clever bit manipulation technique.

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2. Header Files Used

1. #include <iostream>
   • Provides cout and cin for input/output operations.

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3. Understanding XOR Swap

XOR Properties:

• a ^ a = 0 (XOR with itself is zero)
• a ^ 0 = a (XOR with zero is identity)
• (a ^ b) ^ b = a (XOR is reversible)
• Commutative: a ^ b = b ^ a

Swap Algorithm:

• Uses XOR properties
• No temporary variable needed
• Three XOR operations
• Elegant solution

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4. XOR Swap Algorithm

Three Steps:

1. a = a ^ b
2. b = a ^ b // b = (a^b) ^ b = a
3. a = a ^ b // a = (a^b) ^ a = b

How it works:

• Step 1: Store XOR in a
• Step 2: Recover original a in b
• Step 3: Recover original b in a
• Swaps values using XOR properties

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5. Why It Works

Mathematical Proof:

• After step 1: a = a^b, b = b
• After step 2: a = a^b, b = (a^b)^b = a
• After step 3: a = (a^b)^a = b, b = a
• Result: a and b are swapped

XOR Reversibility:

• (a ^ b) ^ b = a (recover a)
• (a ^ b) ^ a = b (recover b)
• XOR is its own inverse

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6. Important Limitation

Same Memory Location:

• Don't use if variables are same
• a ^ a = 0 (would zero the value)
• Always check if different
• Use temporary for safety

Example Problem:

• swapXOR(x, x) would set x to 0
• Must ensure different variables
• Check before swapping

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7. When to Use XOR Swap

Best For:

• Embedded systems (limited memory)
• Educational purposes
• Demonstrating XOR properties
• Memory-constrained environments

Not Recommended For:

• Modern systems (compiler optimizes)
• Readability concerns
• Same variable risk
• Production code (usually)

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8. Modern Compilers

Compiler Optimization:

• Modern compilers optimize swaps
• Temporary variable optimized away
• XOR swap may be slower
• Use standard swap for clarity

Recommendation:

• Use std::swap() in production
• XOR swap for learning
• Understand the concept
• Prefer readability

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9. XOR Properties Demonstration

Reversibility:

• (a ^ b) ^ b = a
• (a ^ b) ^ a = b
• XOR can recover original values
• Foundation of XOR swap

Understanding:

• Helps understand algorithm
• Demonstrates XOR power
• Educational value
• Foundation for other algorithms

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10. return 0;

This ends the program successfully.

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Summary

• XOR swap: swaps two numbers without temporary variable using XOR properties.
• Algorithm: a = a^b, b = a^b (recover a), a = a^b (recover b).
• Works because: (a^b)^b = a and (a^b)^a = b (XOR reversibility).
• Important: don't use if variables point to same memory location.
• Understanding XOR swap demonstrates XOR properties and bit manipulation.
• Useful in embedded systems, though modern compilers optimize standard swaps.

This program is fundamental for learning XOR properties, understanding bit manipulation techniques, and preparing for advanced bit manipulation algorithms in C++ programs.