Write a Program to Swap Two Numbers Without Using a Third Variable in C

October 16, 2024

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Write a Program to Swap Two Numbers Without Using a Third Variable

Swapping two numbers is a common task in programming. Normally, you would use a third variable to temporarily hold one of the numbers during the swap. However, it’s also possible to swap two numbers without using a third variable, by using arithmetic or bitwise operations. In this blog post, we will show you how to write a C program to swap two numbers without a third variable and explain how the logic works.

Why Avoid a Third Variable?

Swapping two numbers without using a third variable is an efficient and elegant way of solving this problem. It reduces memory usage since we don't need an extra variable for swapping, which can be particularly useful when working with large-scale programs or memory-constrained environments. It also teaches you about fundamental operations like addition, subtraction, and bitwise XOR, and how they can be applied creatively.

1. Logic to Swap Two Numbers Without a Third Variable

There are two main methods to swap two numbers without a third variable:

Using arithmetic operations (addition and subtraction).
Using bitwise XOR operation.

Method 1: Using Arithmetic Operations

The idea behind this method is simple: we modify the values of the two variables in such a way that their sum and differences give the swapped values. Here’s how it works:

Add both numbers and assign the result to one of the variables.
Subtract the second number from the result, and assign the value to the second variable (this swaps the first variable's value into the second).
Now subtract the first variable (which holds the sum) by the new value of the second variable to get the original second number in the first variable.

2. Writing the Program

Now, let’s write the program in C using arithmetic operations to swap two numbers without a third variable.

Code Example: Swapping with Arithmetic Operations

#include <stdio.h>

int main() {
    int a, b;

    // Ask the user to enter two numbers
    printf("Enter two integers: ");
    scanf("%d %d", &a, &b);

    // Display the numbers before swapping
    printf("Before swapping: a = %d, b = %d\n", a, b);

    // Swap the numbers using addition and subtraction
    a = a + b;  // Step 1: Add both numbers
    b = a - b;  // Step 2: Subtract b from the new a to get original a in b
    a = a - b;  // Step 3: Subtract the new b from a to get original b in a

    // Display the numbers after swapping
    printf("After swapping: a = %d, b = %d\n", a, b);

    return 0;
}

Explanation of the Code

In this program:

We ask the user to input two integers.
We use arithmetic operations to swap the values of the variables without using a third variable. The steps are:
- Add the two numbers and store the result in a.
- Assign the difference (a - b) to b (this will now hold the original value of a).
- Subtract b from a to assign the original value of b to a.
We print the values before and after the swap to show that the variables have been swapped successfully.

3. Example Output

Here’s an example of how the program works:

Enter two integers: 5 10
Before swapping: a = 5, b = 10
After swapping: a = 10, b = 5

In this example, the values of a and b are swapped without using a third variable.

4. Swapping Using Bitwise XOR

The second method uses the bitwise XOR operator (^) to swap two numbers. This method is efficient and uses bit-level operations to achieve the swap. The XOR operation has the following properties:

If a ^ b, then it stores the result of XOR between a and b.
If we XOR the result with one of the original numbers, we get the other number back.

Code Example: Swapping with Bitwise XOR

#include <stdio.h>

int main() {
    int a, b;

    // Ask the user to enter two numbers
    printf("Enter two integers: ");
    scanf("%d %d", &a, &b);

    // Display the numbers before swapping
    printf("Before swapping: a = %d, b = %d\n", a, b);

    // Swap the numbers using XOR
    a = a ^ b;  // Step 1: a = a ^ b
    b = a ^ b;  // Step 2: b = a ^ b (original a is stored in b)
    a = a ^ b;  // Step 3: a = a ^ b (original b is stored in a)

    // Display the numbers after swapping
    printf("After swapping: a = %d, b = %d\n", a, b);

    return 0;
}

Explanation of the XOR Method

In this program:

We use the XOR bitwise operation to swap the two numbers without using a third variable.
The XOR operation is applied in three steps:
- First, a is XORed with b and stored in a.
- Next, a (which now holds the result of a ^ b) is XORed with b, giving the original value of a and storing it in b.
- Finally, a is XORed again with b, giving the original value of b and storing it in a.

5. Example Output (XOR Method)

Here’s an example of the output using the XOR method:

Enter two integers: 3 7
Before swapping: a = 3, b = 7
After swapping: a = 7, b = 3

6. Common Mistakes to Avoid

When swapping numbers without a third variable, here are some common mistakes to avoid:

Overflow: If you are using arithmetic operations, be mindful of potential integer overflow when adding very large numbers. This could cause incorrect results.
Misunderstanding XOR: Ensure that you understand how the XOR operation works. It’s a bitwise operation, so it manipulates the bits of the numbers directly.
Swapping Negative Numbers: Both methods work with negative numbers, but make sure you account for signed integer behavior, especially in edge cases.

7. Expanding the Program

Here are some ideas to expand on this program:

Modify the program to swap three or more numbers using different techniques.
Implement a function that performs the swap and call it in the main() function for better code organization.
Test the program with different types of numbers, such as floating-point numbers.

8. Conclusion

In this post, we’ve demonstrated two methods for swapping two numbers without using a third variable: using arithmetic operations and using bitwise XOR. Both approaches are efficient, and they eliminate the need for an extra variable. By understanding these methods, you can improve your understanding of basic programming operations, number manipulation, and memory optimization.

Now that you’ve learned how to swap numbers without a third variable, try applying these methods in more complex programming problems. Happy coding!