Swap Two Numbers

Problem Statement:

• Example:

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✅ Solution: Bit Manipulation (XOR Swap)

class Solution {
  public:
    void swapNumbers(int &a, int &b) {
        if (a != b) {
            a = a ^ b;  // Step 1
            b = a ^ b;  // Step 2 (a ^ b) ^ b = a
            a = a ^ b;  // Step 3 (a ^ b) ^ a = b
        }
    }
};

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📝 How It Works

• This method uses XOR to swap two variables without using a temporary variable.
• Step-by-step:
  1. a = a ^ b — Now a holds (a ⊕ b)
  2. b = a ^ b — Now b becomes (a ⊕ b) ⊕ b = a
  3. a = a ^ b — Now a becomes (a ⊕ b) ⊕ a = b
• After the three XOR operations, a and b are swapped.

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🧩 Key Formula

a = a ^ b;
b = a ^ b;
a = a ^ b;

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⏱️ Time & Space Complexity

Metric	Value
Time	O(1)
Space	O(1)

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⚠️ Edge Cases

• Must check a != b. If both refer to the same memory address, result will become zero.
• Doesn’t work safely for pointers to the same variable.

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💡 Other Approaches

Method	Extra Space	Temp Var Used?
Temp variable	O(1)	Yes
Arithmetic method	O(1)	No
Bit manipulation ✅	O(1)	No

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🔁 Related Problems

• Swap values in an array without using extra space
• XOR properties in finding missing number
• Bitwise tricks in interview puzzles

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