Question

Swap the values of two integers without a temporary variable.

Short answer

Swap values using A=A+B, B=A-B, A=A-B.

Step-by-step solution

Determine the Initial Values

Let the two integers be represented as variables, say variable A and variable B. For example, let A = 5 and B = 3.

Perform the First Addition

Add the value of B to A and store the result in A. Now A will contain the sum of the initial values of A and B. For instance, A = A + B => A = 5 + 3 => A = 8.

Calculate the New Value of B

Subtract the new value of A (which is the sum of A and B) by the initial value of B to get the initial value of A. This is then stored in B. B = A - B => B = 8 - 3 => B = 5.

Calculate the New Value of A

Subtract the new value of B (which is the initial value of A) from the current value of A (which is the sum of initial A and B) to get the initial value of B. This is then stored in A. A = A - B => A = 8 - 5 => A = 3.

Check the Results

Now the values have been swapped: A (originally 5) is now 3 and B (originally 3) is now 5.

Key concepts

Variable Swapping

Swapping the values of two variables means exchanging their values. Imagine you have two containers, one with apples and one with oranges. Swapping is like transferring the apples to the orange container and oranges to the apple container. Normally, we use a temporary third container to make this exchange. However, it's possible to swap without a third container using arithmetic operations. This method ensures memory efficiency and showcases a clever use of mathematical operations. Instead of directly using a third variable, we perform a series of additions and subtractions, which internally handle the value exchange.

Arithmetic Operations

The arithmetic operations involved in swapping values without a temporary variable rely on basic operations like addition and subtraction. These operations manipulate the values held within the variables to achieve the swap.

Here's how it works:

• The sum of both values is stored temporarily in one of the variables.
• Subtraction then isolates the original values into the other variables.

Consider two integers A and B:

• Step 1: Summing up the values: A = A + B
• Step 2: Deducting the original second value to find the first: B = A - B
• Step 3: Deducting the first value to find the second: A = A - B

This approach ensures that the original values are temporarily merged and successfully separated again using these basic arithmetic operations.

Integer Manipulation

Manipulating integers involves understanding how operations change their values. When swapping integers without a temporary variable, we're effectively using their summed values to reorganize them.

Consider an example:
Let A = 5 and B = 3:

• First, A becomes 8 (since 5 + 3 = 8).
• Then, subtracting B’s original value from this sum gives us A's original value: B = 8 - 3 = 5.
• Lastly, subtracting the new B from our sum retrieves B's original value: A = 8 - 5 = 3.

This method manipulates the integers directly, ensuring that no external storage is required. This is powerful in programming, especially in memory-constrained environments. It forces the programmer to deeply understand number properties and dependencies.