Question

Suppose list is an array of six components of type int. What is stored in 1 ist after the following \(\mathrm{C}++\) code executes? list[0] = 5; for (int i = 1; i < 6; i++) { list[i] = i * i + 5; if (i > 2) list[i] = 2 * list[i] - list[i - 1]; }

Short answer

The array list stores the values [5, 6, 9, 19, 23, 37] after execution.

Step-by-step solution

Initial Setup

We begin by initializing the array `list` with six elements, where initially all values are set to zero. The given program starts with `list[0] = 5`.

First Iteration (i = 1)

In the first iteration of the loop, for `i = 1`, calculate `list[1]` as follows: \[ list[1] = 1 \times 1 + 5 = 6 \] Since `i` is not greater than 2, the condition `if (i > 2)` is false and this part of the loop does not execute.

Second Iteration (i = 2)

For `i = 2`, compute `list[2]` as: \[ list[2] = 2 \times 2 + 5 = 9 \] Again, since `i` is not greater than 2, the additional condition does not apply.

Third Iteration (i = 3)

With `i = 3`, find `list[3]` initially as: \[ list[3] = 3 \times 3 + 5 = 14 \] Now `i > 2` is true, so update using the conditional statement: \[ list[3] = 2 \times 14 - 9 = 19 \]

Fourth Iteration (i = 4)

For `i = 4`, calculate the initial `list[4]` value: \[ list[4] = 4 \times 4 + 5 = 21 \] Apply the conditional update: \[ list[4] = 2 \times 21 - 19 = 23 \]

Fifth Iteration (i = 5)

Finally, for `i = 5`, compute the initial `list[5]` as: \[ list[5] = 5 \times 5 + 5 = 30 \] Then update with the conditional statement: \[ list[5] = 2 \times 30 - 23 = 37 \]

Final Array Values

After completing the loop, the values stored in the array `list` are: `list[0] = 5`, `list[1] = 6`, `list[2] = 9`, `list[3] = 19`, `list[4] = 23`, `list[5] = 37`. The final state of `list` is: `[5, 6, 9, 19, 23, 37]`.

Key concepts

C++ Loops

Loops are a fundamental concept in C++ programming which allow us to execute a block of code multiple times, based on specific conditions. The primary types of loops in C++ are `for`, `while`, and `do-while` loops. This article focuses on `for` loops, as seen in the provided exercise.

A **`for` loop** has three parts in its head: initialization, condition check, and increment or decrement operation:

• **Initialization**: Sets a starting value and executes only once.
• **Condition**: Evaluated before each loop iteration. If true, the loop continues; if false, the loop terminates.
• **Increment/Decrement**: Updates the loop variable after each iteration.

In the example above, the loop initializes `i = 1` and continues while `i` is less than 6, incrementing `i` by 1 after each iteration. Inside the loop, each element `list[i]` is calculated, demonstrating loop usage to automate repetitive tasks. This is key in manipulating arrays, making C++ programming both efficient and intuitive.

Loops greatly enhance the capability to handle repetitive structures, which is particularly useful with arrays. Once you grasp the structure of a loop, you can control complex operations within your program effortlessly.

Conditional Statements in C++

Conditional statements are the backbone of decision-making in C++ programming. They direct the flow of execution based on evaluated conditions, determining which code block is executed. The most common conditional statements are `if`, `else-if`, and `else`.

In the context of the provided exercise, there is an **`if` statement** checking whether `i` is greater than 2.

• **`if` statement**: Allows the execution of a block of code if the stated condition is true.

The `if` condition `if (i > 2)` modifies the values of `list[i]` by executing a unique calculation. Prior to `i > 2`, values are computed normally using the formula `i * i + 5`. However, once `i` exceeds 2, the conditional statement alters the behavior, ensuring advanced customization of element values.

This conditional execution is crucial in C++ programming as it dynamically changes program behavior in real-time. Ultimately, understanding these statements provides the programmer with control over how data is manipulated and processed within loops.

C++ Programming

C++ is a powerful and versatile programming language known for its efficiency and performance. It supports both high-level and low-level programming, making it a favorite for creating system software, games, and real-time simulations.

Key features of C++ include:

• **Object-Oriented Programming (OOP)**: Allows for the creation of objects, encapsulating data and functions, promoting code reuse and modularity.
• **Rich Library Supports**: Offers many built-in functions and classes that simplify complex operations.
• **Flexibility with Pointers**: Allows direct memory access, a feature not found in many high-level languages, perfect for resource-constrained applications.

The exercise illustrates basic concepts of C++ programming such as arrays, iteration, and conditionals. The manipulation of the `list` array through loops and conditions exemplifies the language's efficiency.

By understanding these core concepts, programmers can build robust applications, taking full advantage of C++'s capabilities to handle complex computations and data manipulation. With practice and experience, mastering C++ opens the door to advanced programming techniques and designs.