Question

Write a recursive void function that has one parameter, which is a positive integer. When called, the function writes its argument to the screen backward. That is, if the argument is \(1234,\) it outputs the following to the screen: 4321

Short answer

Question: Write a short description of how a recursive function can be used to print the digits of a positive integer in reverse order. Answer: A recursive function can be used to print the digits of a positive integer in reverse order by defining a base case when the integer has only one digit, and printing it directly. If the integer has more than one digit, the function extracts the last digit and the remaining digits by performing modulus and integer division operations, respectively. Then, it calls itself recursively with the remaining digits and, after the recursive call, prints the last digit. This process continues until the base case is reached, resulting in the digits being printed in reverse order.

Step-by-step solution

1. Recursive Function Definition:

First, define a recursive void function called "print_reverse" with one parameter, "n", which is a positive integer. ```cpp void print_reverse(int n); ```

2. Base Case:

The base case is essential for the recursion to terminate. In this case, when the given integer "n" has only one digit, i.e., when it is less than 10, the function should print the digit to the screen. ```cpp if (n < 10) { cout << n; } ```

3. Recursive Call and Printing:

If the integer "n" has more than one digit, the function should print the last digit while finding the rest of the digits and provide it to the recursive call. To obtain the last digit, use the modulus operation: "n % 10". To get the remaining digits, perform an integer division by 10: "n / 10". After that, call the "print_reverse" function recursively with the remaining digits, and finally, print the last digit to the screen. ```cpp else { int last_digit = n % 10; int remaining_digits = n / 10; print_reverse(remaining_digits); cout << last_digit; } ```

4. Complete Function:

Combining all the steps above, the complete recursive void function to print the reverse of positive integer "n" is as follows: ```cpp void print_reverse(int n) { if (n < 10) { cout << n; } else { int last_digit = n % 10; int remaining_digits = n / 10; print_reverse(remaining_digits); cout << last_digit; } } ``` Now the function will work correctly and print the reverse of a given positive integer when called.

Key concepts

Base Case

In recursive functions, the base case serves as the crucial stopping condition. It determines when the recursion should cease. Without a base case, a recursive function might call itself indefinitely, leading to an overflow error.

In the context of the provided exercise, the base case is applied when the function processes a single-digit number. When the integer parameter "n" is less than 10, the function recognizes this as the simplest form to handle—printing the digit directly to the screen.

Here’s why that's essential:

• If there is only one digit in the number, there is no need for further breakdown or recursive function calls. This ensures that the function doesn't attempt to process further unnecessarily.
• Establishing this provides a clear exit point for the recursion, thereby preventing infinite loops and ensuring efficiency.

Modulus Operation

The modulus operation is a mathematical operation that helps in finding the remainder of a division of two numbers. It is represented by the symbol "%" in most programming languages, including C++.

When tasked with reversing a number, identifying each digit from the last is crucial. This is where the modulus operation comes into play. By applying "n % 10", you get the last digit of the given number "n".

For example:

• For the number 1234, performing 1234 % 10 yields 4.
• This operation is repeated recursively, extracting one digit at a time starting from the end.

With this, you can handle the digits individually and effectively reverse them during the recursive process.

Integer Division

Integer division is a division operation in which the fractional part or remainder of the division is discarded. It is used to break down complex numbers into simpler components by essentially truncating the results to a whole number.

In this exercise, after identifying the last digit of the number with the modulus operation, you need to work with the rest of the number. Integer division helps here. By dividing the number by 10 using the operation "n / 10", you eliminate the last digit, leaving the remaining part of the number.

For instance:

• When dividing 1234 by 10, the result is 123.
• This simplifies the number and prepares it for the next recursive call.

Repeated application of integer division allows the function to process every digit until all digits are printed in reverse order.

Void Function

In programming, a void function signifies that it does not return any value. Instead, it might perform actions or operations like printing values, modifying data passed by reference, etc. It’s essential when the goal is an action rather than getting a return value.

In the given problem, the function "print_reverse" is a void function because its primary purpose is to print the digits of the number in reverse order, not to return a transformed number or any other value.

Here are some benefits of using a void function in this context:

• The function can have parameters, enabling speech actions like displaying results directly on the screen.
• It remains efficient since it doesn't involve additional steps to process or store return values.

In summary, void functions are ideal for tasks focused on execution rather than computation, such as displaying outputs or executing iterations without altering the primary data returned.