Question

Write a recursive void function that takes a single int argument \(n\) and writes integers \(n, n-1, \ldots, 3,2,1 .\) Hint: Notice that you can get from the code for Self-Test Exercise 4 to that for Self-Test Exercise 5 (or vice versa) by an exchange of as little as two lines.

Short answer

A) When n is a negative number B) When n equals 1 C) When n equals 0 D) When n is an even number

Step-by-step solution

Understanding the problem

In this problem, we want to write a function that prints integers from \(n\) down to 1, where \(n\) is the given integer. We need to create a recursive void function to achieve this.

Identify the base case

A base case is needed in every recursive function to stop the recursion when a certain condition is met. In this case, since we want to print integers down to 1, our base case will stop the recursion when we reached 1.

Create the recursive step

The recursive step must contain the main logic that will lead to the base case. In this scenario, with each recursive call, our function will print the current integer and call the next function with the integer one less than the current integer till the base case is reached.

Implement the recursive function

Let's implement the function "printNumbers" using the base case and recursive step discussed in the previous steps. ```cpp #include void printNumbers(int n) { if (n == 1) { // Base case std::cout << n << " "; } else { std::cout << n << " "; // Print current number printNumbers(n - 1); // Call function with the next smaller integer } } ```

Test the function

Test the function by calling it with some test cases to make sure it works as expected. ```cpp int main() { printNumbers(5); // Output: 5 4 3 2 1 printNumbers(3); // Output: 3 2 1 return 0; } ``` The written function correctly solves the problem and prints the integers from the given integer down to 1 using recursion.

Key concepts

Recursion

Recursion is a programming technique where a function calls itself in its definition. This strategy is often used to break down complicated problems into simpler ones by performing the same operation multiple times with different inputs. In C++, a recursive function continues to call itself with adjusted parameters until it reaches a condition known as the base case.

Using recursion in the exercise, we create a flow where each function call represents a level in a hierarchy, progressively working towards a termination point. For instance, to print integers down to 1, the function begins at a specified integer and recursively invokes itself with the next lower integer. This continues until the base case, which stops further recursive calls.

Void Function

In C++, a void function is a function that does not return a value. It is often used for performing an action, such as printing to the console, modifying global variables, or altering the state of objects, rather than calculating and passing back data. In the context of the exercise, our recursive function is a void function because its main goal is to print out a sequence of integers. It executes a task without the need for returning a value to the calling function.

The use of a void function is appropriate in situations like this one, where the output is not meant to be used in further computations but displayed or used to affect the program's state in some way.

Base Case in Recursion

The base case in recursion acts as the exit condition, preventing infinite cycles of function calls. It's a scenario where the function can return a result without needing to call itself. It is critical to have a well-defined base case; otherwise, the recursion may lead to a stack overflow error as it eats up the system's call stack.

In the example from the exercise, the base case occurs when the integer argument, n, becomes 1. Here the function simply prints the number 1 and ceases to call itself, thus halting the recursion. Identifying and implementing a sound base case is crucial to the proper operation and termination of a recursive function.

Print Integers

Printing integers in a specific order or pattern is a common exercise in programming, designed to familiarize students with control structures such as loops and recursion. In our exercise, we are using recursion to print integers from a starting number down to 1.

Implementing a function to correctly display the integers on the screen is a straightforward process, but it requires attention to the flow of function calls and the structure of the program's output. Always ensure that the format of the output matches the expectations, with correct spacing or line breaks as required.