Given two variables, x and y, swap two variables without using a third variable.

**Method 1 (Using Arithmetic Operators)**

The idea is to get sum in one of the two given numbers. The numbers can then be swapped using the sum and subtraction from sum.

#include <stdio.h> int main() { int x = 10, y = 5; // Code to swap 'x' and 'y' x = x + y; // x now becomes 15 y = x - y; // y becomes 10 x = x - y; // x becomes 5 printf("After Swapping: x = %d, y = %d", x, y); return 0; }

Output:

After Swapping: x = 5, y = 10

Multiplication and division can also be used for swapping.

#include <stdio.h> int main() { int x = 10, y = 5; // Code to swap 'x' and 'y' x = x * y; // x now becomes 50 y = x / y; // y becomes 10 x = x / y; // x becomes 5 printf("After Swapping: x = %d, y = %d", x, y); return 0; }

Output:

After Swapping: x = 5, y = 10

**Method 2 (Using Bitwise XOR)**

The bitwise XOR operator can be used to swap two variables. The XOR of two numbers x and y returns a number which has all the bits as 1 wherever bits of x and y differ. For example XOR of 10 (In Binary 1010) and 5 (In Binary 0101) is 1111 and XOR of 7 (0111) and 5 (0101) is (0010).

#include <stdio.h> int main() { int x = 10, y = 5; // Code to swap 'x' (1010) and 'y' (0101) x = x ^ y; // x now becomes 15 (1111) y = x ^ y; // y becomes 10 (1010) x = x ^ y; // x becomes 5 (0101) printf("After Swapping: x = %d, y = %d", x, y); return 0; }

Output:

After Swapping: x = 5, y = 10

**Problems with above methods**

**1)** The multiplication and division based approach doesn’ work if one of the numbers is 0 as the product becomes 0 irrespective of the other number.

**2)** Both Arithmetic solutions may cause arithmetic overflow. If x and y are too large, addition and multiplication may go out of integer range.

**3)** When we use pointers to variable and make a function swap, all of the above methods fail when both pointers point to the same variable. Let’s take a look what will happen in this case if both are pointing to the same variable.

// Bitwise XOR based method

x = x ^ x; // x becomes 0

x = x ^ x; // x remains 0

x = x ^ x; // x remains 0

// Arithmetic based method

x = x + x; // x becomes 2x

x = x – x; // x becomes 0

x = x – x; // x remains 0

Let us see the following program.

#include <stdio.h> void swap(int *xp, int *yp) { *xp = *xp ^ *yp; *yp = *xp ^ *yp; *xp = *xp ^ *yp; } int main() { int x = 10; swap(&x, &x); printf("After swap(&x, &x): x = %d", x); return 0; }

Output:

After swap(&x, &x): x = 0

Swapping a variable with itself may needed in many standard algorithms. For example see this implementation of QuickSort where we may swap a variable with itself. The above problem can be avoided by putting a condition before the swapping.

#include <stdio.h> void swap(int *xp, int *yp) { if (xp == yp) // Check if the two addresses are same return; *xp = *xp + *yp; *yp = *xp - *yp; *xp = *xp - *yp; } int main() { int x = 10; swap(&x, &x); printf("After swap(&x, &x): x = %d", x); return 0; }

Output:

After swap(&x, &x): x = 10

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above