Question

Consider the following recursive function: void exercise(int x) { if (x > 0 && x < 10) { cout << x << " "; exercise(x + 1); } } What is the output of the following statements? a. exercise(0); b. exercise(5); c. exercise(10); d. exercise(-5);

Short answer

a. No output; b. '5 6 7 8 9 '; c. No output; d. No output.

Step-by-step solution

Understanding the Function

The function 'exercise' takes an integer \( x \) as input. It checks if \( x \) is greater than 0 and less than 10. If true, it prints \( x \), followed by a space, and then recursively calls itself with the argument \( x + 1 \). This recursion continues until \( x \) no longer satisfies the condition (when \( x \) is not between 0 and 10).

Analyzing the Call 'exercise(0)'

For the call `exercise(0)`, the input value \( x = 0 \) does not satisfy the condition \( x > 0 \). Therefore, the body of the if statement is not executed, and nothing is printed.

Analyzing the Call 'exercise(5)'

For `exercise(5)`, the input \( x = 5 \) satisfies the condition \( 5 > 0 \) and \( 5 < 10 \). Therefore, the sequence of numbers starting from 5 up to, but not including 10, is printed. The output is '5 6 7 8 9 '.

Analyzing the Call 'exercise(10)'

For `exercise(10)`, the input \( x = 10 \) does not satisfy the condition \( x < 10 \). Thus, the if statement's body is skipped, and nothing is printed.

Analyzing the Call 'exercise(-5)'

For `exercise(-5)`, the input \( x = -5 \) does not satisfy the condition \( x > 0 \), so the function body is not executed, and nothing is printed.

Conclusion on Outputs

Based on the analysis above, we identify that the calls yield different outputs: a. No output, b. '5 6 7 8 9 ', c. No output, d. No output.

Key concepts

Recursion

Recursion is a fundamental programming concept where a function calls itself to solve smaller instances of the same problem. It can be compared to the idea of peeling an onion layer by layer until reaching the core. In the provided function example, recursion is vividly demonstrated by the repeated invocation of the `exercise` function within itself. When the function is called with a value of `x` that satisfies the condition (greater than 0 and less than 10), it prints the current value and then calls itself with `x` incremented by one.

Key aspects of recursion include:

• Base Case: This is the condition that stops the recursion to prevent infinite calls. In the given example, the base case is when `x` no longer satisfies the condition (when `x` is zero or ten).
• Recursive Case: This is where the function continues to call itself with new values that eventually progress towards reaching the base case.

Each recursive call creates a new instance of the function, which is important for achieving the desired output and eventually stopping the recursion.

Conditional Statements

Conditional statements are a core part of controlling the flow of a program. They allow the program to decide between different actions based on certain conditions. In the `exercise` function, a conditional statement evaluates if `x` is both greater than 0 and less than 10.

Let's break down its components:

• Condition: The expression `(x > 0 && x < 10)` acts as the gatekeeper. Only if both conditions are true will the print statement and the recursive function call be executed.
• Logical Operator: The `&&` operator is crucial here, combining two checks that must both be true for the block of code to execute. This logical AND operator ensures a specifically narrow range where the function prints numbers.

Conditional statements allow for powerful decisions in programming, affecting how functions behave at runtime based on input values.

Function Output Analysis

Analyzing the output of functions, especially recursive ones, involves understanding the flow and conditions set within the function. The `exercise` function demonstrates this well. When evaluating function outputs, observe:

• Initial Input: Consider what value starts the function. This affects whether the output will be generated or if nothing will be printed.
• Condition Evaluation: Understand how the conditions affect each call. In our case, only `exercise(5)` produced an output because it satisfied the stipulated condition `(x > 0 && x < 10)` for several iterations.
• Output Format: The numbers printed by the function are followed by a space, yielding a neat sequence that halts before 10 due to the recursive nature and logical constraints.

Effectively analyzing function outputs facilitates troubleshooting and enhances understanding of the program's behavior. This comprehension is key when debugging or predicting how changes in input will affect output.