Question

Consider the following function: int mystery(int x, double y, char ch) { if (x == 0 && ch > 'A') return(static_cast(pow(y, 2)) + static_cast(ch)); else if (x > 0) return(x + static_cast(sqrt(y)) - static_cast(ch)); else return(2 * x + static_cast(y) - static_cast(ch)); } What is the output of the following C++ statements? a. cout << mystery(0, 6.5, 'K') << endl; b. cout << mystery(4, 16.0, '#') << endl; c. cout << 2 * mystery(-11, 13.8, '8') << endl;

Short answer

a. 117, b. -27, c. -130

Step-by-step solution

Evaluate Function for Part (a)

We are given a call to mystery function as `mystery(0, 6.5, 'K')`. Here, `x` is 0, `y` is 6.5, and `ch` is 'K'. The first `if` condition checks if `x` is 0 and `ch` > 'A'. This is true since 'K' is greater than 'A'. Thus, the return value is calculated using `pow(y, 2)` which is `6.5^2 = 42.25`. We then cast this to an integer to get 42. For the character 'K', we cast it to its ASCII value which is 75. Therefore, the function returns `42 + 75 = 117`.

Evaluate Function for Part (b)

We are given a call to mystery function as `mystery(4, 16.0, '#')`. Here, `x` is 4, `y` is 16.0, and `ch` is '#'. The first `if` condition `x == 0 && ch > 'A'` fails because `x` is 4. Checking the second condition `x > 0`, it is true. Therefore, the return value is calculated as `x + static_cast(sqrt(16.0)) - static_cast('#')`. `sqrt(16.0)` is 4.0 and casting it to an integer gives 4. '#' has an ASCII value of 35. Therefore, the function returns `4 + 4 - 35 = -27`.

Evaluate Function for Part (c)

We are given a call to mystery function as `mystery(-11, 13.8, '8')`. Here, `x` is -11, `y` is 13.8, and `ch` is '8'. Both previous conditions for `x == 0 && ch > 'A'` and `x > 0` fail since `x` is negative. Thus, the function evaluates the else clause. The return value is `2 * x + static_cast(y) - static_cast('8')`. This computes as `2 * (-11) + 13 - 56`, where the ASCII value of '8' is 56. The outcome is `-22 + 13 - 56 = -65`. However, the call in the statement is `2 * mystery(-11, 13.8, '8')` thus the output is `2 * -65 = -130`.

Key concepts

Type Casting in C++

In C++, type casting allows you to convert a variable from one data type to another. This is particularly useful in situations where you need to perform operations between different data types.
C++ supports two primary forms of casting: implicit and explicit. Implicit casting is automatic and occurs when converting a smaller data type to a larger one, such as `int` to `double`. However, explicit casting, also known as type casting, is performed manually by the programmer. This involves using casting operators to convert data types.

• Static cast: `static_cast(expression)` is the most common and safest form of casting, used when converting from one data type to another compatible type, as shown when converting the result of `pow(y, 2)` and `sqrt(y)` to integers in the function.
• Dynamic cast: Primarily used for safely downcasting pointers and references in class hierarchies.
• Reinterpret cast: Treats the value as a different type without altering the bit pattern.
• Const cast: Casts away the `const-ness` of variables.

ASCII Values

ASCII stands for American Standard Code for Information Interchange. It is a character encoding standard that assigns a numeric value to each character, including letters, digits, and symbols.
Understanding ASCII values is crucial when dealing with characters in programming languages like C++. Each character is represented by an integer value, which can be obtained using a character's ASCII code.

• The conversion of a character to its ASCII integer value can be easily done using type casting. For example, casting `'K'` to an integer yields the ASCII value `75`.
• Arithmetic operations can be performed using ASCII values, as illustrated in the exercise, where character values are added and subtracted from integers.

Knowing ASCII values allows you to manipulate texts at a more granular level, making it easier to manage and transform text-based data.

Conditional Statements

Conditional statements, often known as decision-making statements, allow you to perform different actions based on different conditions. This is essential in programming to make decisions and execute particular blocks of code.

• If statement: Executes a block of code only if a specified condition is true.
• If-else statement: Provides two paths to choose from; if the condition is true, the first block is executed, otherwise, the second block runs.
• If-else if-else ladder: Used when multiple conditions need to be checked, executing one block of code when the first true condition is found.

In the given function, conditional statements determine which block of code executes: - The first condition checks if `x` is 0 and `ch` is greater than `'A'`. If true, a specific block runs. - If not, but `x` is greater than 0, another block executes. - If neither condition is met, the code moves to the `else` clause, running a different block. This structure helps optimize and control program flow, thus efficiently solving problems.

Mathematical Functions in C++

C++ provides a wide array of mathematical functions through its standard library, including `cmath`, which contains functions for basic arithmetic operations, trigonometry, logarithms, and exponential functions.

• Power function (`pow`): Calculates the power of a number, such as `y^2`, and is used in the exercise to square a number.
• Square Root function (`sqrt`): Computes the square root, such as `sqrt(16.0)`, and converts it to an integer representation.

These mathematical functions are efficient and can handle complex calculations easily, often requiring type casting when used alongside integer arithmetic to ensure appropriate operations and results.
Accurate mathematical computations are vital in many applications, making these functions indispensable for C++ developers.