Question

Consider the following C++ function: int mystery(int num) { int y = 1; if (num == 0) return 1; else if (num < 0) return -1; else for (int count = 1; count < num; count++) y = y * (num - count); return y; } What is the output of the following statements? a. cout << mystery(6) << endl; b. cout << mystery(0) << endl; c. cout << mystery(-5) << endl; d. cout << mystery(10) << endl;

Short answer

a. 120, b. 1, c. -1, d. 362880

Step-by-step solution

Understand the Function

The `mystery` function takes an integer `num` as its argument. It returns 1 if `num` is 0, returns -1 if `num` is negative, and calculates a product if `num` is positive.

Initialize and Check Base Cases

For `num` equal to 0, the function returns 1 immediately. For negative values of `num`, the function returns -1 as the output.

Evaluate Loop for Positive `num`

If `num` is positive, the function initializes `y` to 1 and enters a loop from `count = 1` to `count < num`. Inside the loop, it multiplies `y` by `(num - count)`. The initial value of `y` and loop calculations determine the final output.

Compute Output for `mystery(6)`

`y` starts at 1 and the loop modifies `y` as follows: `y = 1 * 5`, `y = 5 * 4`, `y = 20 * 3`, `y = 60 * 2`, `y = 120 * 1`. The loop ends when `count` is 5. Therefore, `mystery(6)` returns 120.

Compute Output for `mystery(0)`

Since `num` is 0, the function immediately returns 1.

Compute Output for `mystery(-5)`

Because `num` is negative, the function directly returns -1.

Compute Output for `mystery(10)`

`y` starts at 1 and the loop modifies `y` as follows: `y = 1 * 9`, `y = 9 * 8`, `y = 72 * 7`, `y = 504 * 6`, `y = 3024 * 5`, `y = 15120 * 4`, `y = 60480 * 3`, `y = 181440 * 2`, `y = 362880 * 1`. Therefore, `mystery(10)` returns 362880.

Key concepts

Loop Structures

In C++, loop structures allow us to execute a block of code multiple times. They are foundational in programming for tasks that need repetition. The `mystery` function uses a `for` loop to perform calculations based on the input value `num`. Each iteration of the loop adjusts the variable `y` by multiplying it with (num - count). This setup helps in calculating factorial-like values, minus the full range from the original number down to 1.

A loop typically consists of:

• An initialization clause, which sets up the loop variable (e.g., `int count = 1`).
• A condition that determines whether the loop will continue (e.g., `count < num`).
• An iteration expression that modifies the loop variable, moving towards the loop termination (e.g., `count++`).

The `mystery` function loop is crucial because it handles the multiplication logic when `num` is positive, determining how many times it iterates. It stops once `count` matches `num`, ensuring that the loop does not mistakenly execute for an unintended range.

Conditional Statements

Conditional statements in C++ are used to perform different actions based on specific conditions. These conditions allow your code to make decisions and respond dynamically. The `mystery` function utilizes `if`, `else if`, and `else` blocks to control the flow based on the provided integer `num`.

Within the `mystery` function:

• The `if` statement checks `if (num == 0)` and returns `1`. This condition is a direct decision path for the function.
• The `else if (num < 0)` checks for negative numbers and returns `-1`. This caters to a scenario where the function shouldn't proceed with calculations.
• The `else` block runs a loop structure for positive numbers, indicating a continuation of the function's process.

This use of conditional statements ensures that the function can quickly respond to different input values, optimizing execution by bypassing unnecessary computations under specific conditions.

Function Output

In C++, functions often provide results via output mechanisms. These outputs represent the final results of a function's internal calculations or logic. The `mystery` function returns an integer based on different input criteria and conditions.

Here's how the output works:

• If the input `num` is `0`, it outputs `1` immediately without further calculations. This is straightforward since the condition is checked first in the function.
• For negative inputs, it outputs `-1`. This quickly concludes the function's process for those values, as computation isn't useful in this context.
• Positive numbers will result in a calculation process through the loop, generating a factorial-like output. After all iterations, the function outputs the computed value of `y`.

This function's output system efficiently uses return statements at different execution points to handle distinct scenarios.

Return Values

Return values in C++ functions are pivotal as they convey the function's result back to its caller. The return values are determined by the conditions and logic within the function, like those in the `mystery` function.

In `mystery`, the return value relies on:

• A simple return of `1` or `-1` immediately through conditional checks when `num` is `0` or negative, respectively.
• An iterative calculation process for positive `num`, where the loop modifies `y` to eventually convey the result, outputting the final value at the end of the function.

Using return values effectively allows functions to serve their purpose of processing data or performing operations while offering a clear output result. This concept is fundamental in C++ as it simplifies the task of performing complex calculations while informing other parts of the program of its outcomes.