Problem

You have two integer variables, i and j. How can you swap their values without using any extra storage, i.e., no temporary variable?

Solution Using Arithmetic

You can swap i and j in-place using arithmetic operations:

i = i + j
j = i - j
i = i - j

Example:

Suppose initially i = 3 and j = 5:

  • Step 1: i = 3 + 5 = 8
  • Step 2: j = 8 - 5 = 3 (original i)
  • Step 3: i = 8 - 3 = 5 (original j)

Now i = 5, j = 3 — swap complete!

Note: This method works reliably for integers as long as there’s no overflow in the arithmetic operations.

Alternative: Bitwise XOR Method

You can also use the XOR bitwise operation (which is common in low-level programming):

i = i ^ j
j = i ^ j
i = i ^ j

Explanation:

  • XOR is reversible: \( a \oplus b \oplus b = a \)

This version avoids potential overflow, making it safer for bounded integer types in systems languages like C.

Conclusion

There are two common in-place swap techniques:

  • Arithmetic swap: i = i + j; j = i - j; i = i - j
  • Bitwise XOR swap: i = i ^ j; j = i ^ j; i = i ^ j

Both accomplish the swap without any temporary storage.

Reference