Swap using XOR in C++

Swap Two Numbers using XOR in C++.

IntermediateBitwise Operations ProgramsExample 4 of 5

swap-using-xor.cpp

1#include <iostream>
2using namespace std;
3
4void swapXOR(int& a, int& b) {
5    a = a ^ b;
6    b = a ^ b;  // b = (a^b) ^ b = a
7    a = a ^ b;  // a = (a^b) ^ a = b
8}
9
10int main() {
11    int a = 10, b = 20;
12    
13    cout << "Before swap: a = " << a << ", b = " << b << endl;
14    
15    swapXOR(a, b);
16    
17    cout << "After swap: a = " << a << ", b = " << b << endl;
18    
19    // Multiple swaps
20    cout << "\nMultiple swaps:" << endl;
21    int x = 5, y = 15, z = 25;
22    
23    cout << "Before: x = " << x << ", y = " << y << ", z = " << z << endl;
24    
25    swapXOR(x, y);
26    swapXOR(y, z);
27    
28    cout << "After: x = " << x << ", y = " << y << ", z = " << z << endl;
29    
30    // XOR properties demonstration
31    cout << "\nXOR properties:" << endl;
32    int num1 = 12, num2 = 25;
33    cout << "num1 = " << num1 << ", num2 = " << num2 << endl;
34    cout << "num1 ^ num2 = " << (num1 ^ num2) << endl;
35    cout << "(num1 ^ num2) ^ num2 = " << ((num1 ^ num2) ^ num2) << " (back to num1)" << endl;
36    cout << "(num1 ^ num2) ^ num1 = " << ((num1 ^ num2) ^ num1) << " (back to num2)" << endl;
37    
38    return 0;
39}

Output

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)

What's going on

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.

Header Files Used

1.#include <iostream>

Provides cout and cin for input/output operations.

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

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

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

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

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)

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

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

return 0;

This ends the program successfully.

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