Question

Consider the following functions: int find(int num) { int first, second; first = num * num; second = first + num; if (second > 100) num = first / 10; else num = first / 20; return num + 2; } int discover(int one, int two) { int secret = 0; for (int i = one; i < two; i++) secret = secret + i * i; return secret; } What is the output of each of the following program segments? a. cout << find(15) << endl; b. cout << discover(3, 9) << endl; c. cout << find(10) << " " << discover(10, find(10)) << endl; d. x = 12; y = 8; cout << discover(y, x) << endl;

Short answer

a. 24 b. 199 c. 12 221 d. 366

Step-by-step solution

Evaluating find(15)

First, we substitute $num=15$ into the `find` function. We calculate $first=num\times num=15\times 15=225$. Then, $second=first+num=225+15=240$. The `if` condition $second>100$ is true, so we update $num=first/10=225/10=22$. Finally, the function returns $num+2=22+2=24$. Thus, `find(15)` outputs **24**.

Evaluating discover(3, 9)

For `discover(3, 9)`, start with $secret=0$. The loop iterates from $i=3$ to $i=8$ (since it goes up to, but does not include `two`). In each iteration, calculate $i\times i$ and add it to `secret`.- When $i=3$: `secret` = 0 + 9 = 9- When $i=4$: `secret` = 9 + 16 = 25- When $i=5$: `secret` = 25 + 25 = 50- When $i=6$: `secret` = 50 + 36 = 86- When $i=7$: `secret` = 86 + 49 = 135- When $i=8$: `secret` = 135 + 64 = 199Thus, `discover(3, 9)` outputs **199**.

Evaluating find(10)

Substituting $num=10$ into `find`, calculate $first=num\times num=10\times 10=100$. Then $second=first+num=100+10=110$. The `if` condition $second>100$ is true, so update $num=first/10=100/10=10$. The function returns $num+2=10+2=12$. Thus, `find(10)` outputs **12**.

Evaluating discover(10, 12)

From Step 3, we know that `find(10)` returns $12$. We then evaluate `discover(10, 12)`. Start with $secret=0$. The loop iterates from $i=10$ to $i=11$.- When $i=10$: `secret` = 0 + 100 = 100- When $i=11$: `secret` = 100 + 121 = 221Thus, `discover(10, 12)` outputs **221**.

Assembling output for find(10) and discover(10, find(10))

From Steps 3 and 4, `find(10)` yields **12** and `discover(10, 12)` yields **221**. Therefore, the output for `cout << find(10) << " " << discover(10, find(10)) << endl;` is **12 221**.

Evaluating discover(8, 12)

For `discover(y, x)` where $y=8$ and $x=12$, start with $secret=0$. The loop iterates from $i=8$ to $i=11$.- When $i=8$: `secret` = 0 + 64 = 64- When $i=9$: `secret` = 64 + 81 = 145- When $i=10$: `secret` = 145 + 100 = 245- When $i=11$: `secret` = 245 + 121 = 366Thus, `discover(8, 12)` outputs **366**.

Key concepts

Function Definition

In C++, a function is a block of code designed to perform a specific task. You're already familiar with the `main` function that executes the program; similarly, custom functions help organize and reuse code efficiently. Functions start with a declaration that specifies the return type, name, and parameters.

For example, consider the function definition:

• Return Type: This indicates what kind of value the function will return. For instance, `int` specifies that the function returns an integer.
• Function Name: The name you give your function, such as `find` or `discover`, should be descriptive of its task.
• Parameters: These are the values you pass to the function, which it uses when performing its task.

In the given exercise, both functions `find` and `discover` are defined to return an integer value. Defining functions correctly is crucial for code readability and reusability.

Control Structures

Control structures are essential for directing the flow of a C++ program. They help the program make decisions based on given conditions. The most common control structures are `if`, `else`, and `switch` statements.

In the `find` function provided, an `if` statement checks whether the `second` variable is greater than 100:

• `if (second > 100)`: This condition is true or false depending on the result of an expression.
• Depending on this condition, the program executes the appropriate block of code — dividing `first` by 10 or 20.

Such structures allow your program to take various paths based on data, adding flexibility and interactivity.

Loop Iteration

Loops are control structures that repeat a block of code multiple times. This repetition continues until a specific condition is met. The `for`, `while`, and `do-while` loops are common examples.

In the `discover` function, a `for` loop is used to iterate through numbers between `one` and `two`:

• `for (int i = one; i < two; i++)`: This loop runs from `one` to just before `two`.
• With each iteration, `i` is squared (`i * i`) and added to the `secret` variable.
• The loop stops when `i` equals `two`.

Loop iteration is incredibly powerful for processing multiple data elements or calculating cumulative results, like summing squares in the `discover` function.

Mathematical Operations

Mathematical operations in C++ allow you to compute numerical results. These operations include addition (+), subtraction (-), multiplication (*), division (/), and more complex tasks.

Both `find` and `discover` functions use these operations heavily:

• In `find`, `num * num` computes the square of `num`, while `first + num` adds values.
• Conditional logic then divides `first` by 10 or 20 based on a condition.
• In `discover`, multiplication and addition occur in the loop, as each `i` value is squared, accumulated into `secret`.

Understanding these operations is crucial, as they form the basis for handling numerical data and implementing logic within programs.