Question

Consider the following function: int secret (int one) \\{ \\[ \begin{array}{l} \text { int i; } \\ \text { int prod = 1 } \\ \text { for }(i=1 ; i<=3 ; i++) \\ \text { prod = prod * one; } \end{array} \\] return prod;} a. What is the output of the following C++ statements? i. cout \(<<\) secret \((5)<<\) endl ii. cout \(<<2 *\) secret \((6)<<\) endl b. What does the function secret do?

Short answer

i. 125; ii. 432; The function computes the cube of the input integer.

Step-by-step solution

Analyzing the Function

The function `secret(int one)` calculates the cube of the input integer `one`. This is achieved by initializing `prod` to 1 and then multiplying it by `one` three times in the loop, effectively computing \(one \times one \times one\). Then, it returns `prod`, which is \(one^3\).

Calculating Output for Part i

For `cout << secret(5) << endl;`, we substitute `one` with 5 in the function. The calculation inside the function will be: - Iteration 1: `prod = 1 * 5 = 5` - Iteration 2: `prod = 5 * 5 = 25` - Iteration 3: `prod = 25 * 5 = 125` Thus, the function returns 125. The output is `125`.

Calculating Output for Part ii

For `cout << 2 * secret(6) << endl;`, first evaluate `secret(6)`. Substitute `one` with 6 in the function and run the loop: - Iteration 1: `prod = 1 * 6 = 6` - Iteration 2: `prod = 6 * 6 = 36` - Iteration 3: `prod = 36 * 6 = 216` The function returns 216. The expression `2 * secret(6)` becomes `2 * 216 = 432`. The output is `432`.

Explaining the Function Behavior

The function `secret` computes the cube of the given integer `one`. It uses a loop to multiply the integer by itself three times, which is equivalent to raising `one` to the power of 3.

Key concepts

Integer Operations

Understanding integer operations is fundamental in programming with C++. In the `secret` function, integer multiplication is used to calculate the cube of a number. Multiplication is a basic arithmetic operation that multiplies values to produce a product. In C++, multiplication is denoted by the `*` symbol.

In our function, the initial value of `prod` is set to 1, and through each iteration of the loop, `prod` is multiplied by the input integer `one`. This repeated multiplication over three iterations results in the value being cubed:

• Iteration 1: Multiply `prod` by `one`.
• Iteration 2: Multiply the new `prod` by `one` again.
• Iteration 3: Perform the multiplication one last time.

This sequence of operations illustrates the compound operation of exponentiation specifically tailored for computing cubes, achieved by repeating basic integer multiplication.

Loops in C++

Loops are a powerful feature in C++ that allow for the repetition of code blocks based on specified conditions. In the `secret` function, the `for` loop is used to repeat multiplication three times to achieve the goal of cubing the number.

The `for` loop syntax comprises three parts: initialization, condition, and increment/decrement. Here's how it's structured in our function:

• Initialization: `int i=1` sets the starting point for the loop counter `i`.
• Condition: `i<=3` checks if the loop should continue running.
• Increment: `i++` increases the loop counter after each iteration.

This loop effectively runs three times, applying the same operation of multiplication in each cycle. Loops like this allow for repetitive processing tasks efficiently, minimizing manual repetition in code.

Function Analysis

Understanding and analyzing the behavior of a function is critical to ensure it performs as expected. The `secret` function is a simple demonstration of a function that encapsulates both operations and logic to compute a result.

Inside the function:

• Function Declaration: `int secret (int one)` declares a function that takes an integer input and returns an integer output.
• Variable Initialization: `int prod = 1;` ensures a starting value for multiplication.
• Logic: The loop multiplies the base value by the input integer `one` three times, effectively computing the cube.
• Return Statement: `return prod;` outputs the resultant cube value to the calling scope.

Through function analysis, we understand that `secret` compresses the repetitive operation of cubing into a reusable block of code. This promotes code reusability and abstraction, letting complex operations be handled by simpler high-level statements in main program flows.