Question

What is stored in list after the following C++ code executes? int list[10]; list[0] = 2; list[1] = 3; for (int i = 2; i < 10; i++) { list[i] = list[i - 1] + list[i - 2]; if (i > 7) list[i] = 2 * list[i] - list[i - 2]; }

Short answer

The list will store: 2, 3, 5, 8, 13, 21, 34, 55, 144, 343.

Step-by-step solution

Initialize the List

The given C++ code initializes an array `list` of size 10, with all its positions uninitialized. The code then explicitly assigns values to the first two elements: - `list[0]` is set to `2`. - `list[1]` is set to `3`.

Calculate Initial Values in the Loop (i = 2 to 7)

The loop runs starting from `i = 2` up to `i = 9`. For `2 ≤ i ≤ 7`, the code computes each `list[i]` as the sum of the two previous elements: - For `i = 2`: `list[2] = list[1] + list[0] = 3 + 2 = 5`. - For `i = 3`: `list[3] = list[2] + list[1] = 5 + 3 = 8`. - For `i = 4`: `list[4] = list[3] + list[2] = 8 + 5 = 13`. - For `i = 5`: `list[5] = list[4] + list[3] = 13 + 8 = 21`. - For `i = 6`: `list[6] = list[5] + list[4] = 21 + 13 = 34`. - For `i = 7`: `list[7] = list[6] + list[5] = 34 + 21 = 55`.

Adjust Values in the Loop (i = 8 to 9)

For `i > 7`, a modified formula is applied: - For `i = 8`: Compute `list[8]` as normal first, `list[8] = list[7] + list[6] = 55 + 34 = 89`. Then adjust it: `list[8] = 2 * list[8] - list[6] = 2 * 89 - 34 = 178 - 34 = 144`. - For `i = 9`: Compute `list[9]` as normal first, `list[9] = list[8] + list[7] = 144 + 55 = 199`. Then adjust it: `list[9] = 2 * list[9] - list[7] = 2 * 199 - 55 = 398 - 55 = 343`.

Conclude the Stored List

The concluding list after all iterations in the loop is complete will be: - `list[0] = 2` - `list[1] = 3` - `list[2] = 5` - `list[3] = 8` - `list[4] = 13` - `list[5] = 21` - `list[6] = 34` - `list[7] = 55` - `list[8] = 144` - `list[9] = 343`.

Key concepts

Array Initialization

When you start working with arrays in C++, the first step is array initialization, which is critical to ensure the array is ready to use. In the provided code, the array `list` is declared with a size of 10 using `int list[10];`. This declaration tells the compiler to allocate memory for 10 integers. Initially, these elements are uninitialized, meaning they contain garbage values until they're explicitly assigned.

The importance of initialization lies in providing known starting values. In the code example, the first two elements are initialized like so:

• `list[0] = 2`
• `list[1] = 3`

By specifying these values, the code sets a foundation for later calculations. Initializing an array is a fundamental practice to avoid unpredictable behaviors caused by random, uninitialized data.

Loop Structures

Loops are a foundational element in C++ programming, allowing repetitive tasks to be reduced to a few lines of code. In the example, a `for` loop is used to iterate through the array elements starting from `i=2` to `i=9`. The syntax `for (int i = 2; i < 10; i++)` initializes the loop variable `i`, checks a condition `i < 10` to continue execution, and updates `i` in each iteration with `i++`.

This loop efficiently processes each element in the array from the third position onwards. By adjusting its parameters, loops can customize the start and end points, making them versatile for varied range iterations. The loop here is crucial for processing multiple elements in sequence using just a handful of lines, thereby enhancing coding efficiency and readability.

Array Manipulation

Array manipulation involves performing operations on array elements, such as updating their values based on specific criteria. In the exercise, list elements are computed in two parts. For `i` from 2 to 7, each element is the sum of the prior two elements:

• `list[2] = list[1] + list[0] = 5`
• `list[3] = list[2] + list[1] = 8`

These computations build upon the previous elements, showcasing how arrays can hold and dynamically update values.

For `i` greater than 7, array manipulation becomes a bit more complex. After initial computation, additional changes are made using a different formula, doubling the current value and subtracting an earlier element. For example, `list[8]` is adjusted as `2 * list[8] - list[6]`. This alteration allows for more intricate transformations within the array. Understanding and applying these manipulation techniques is key to harnessing the full potential of arrays in C++.

Control Flow in C++

Control flow dictates the execution path of a program. In this exercise, flow control is demonstrated through a combination of loops and conditional statements. Once inside a loop, conditional logic like `if (i > 7)` detects when an index exceeds 7. When true, the code inside the `if` block executes, introducing a modified operation for specific elements.

This demonstrates how control flow can introduce different behaviors based on conditions, adding flexibility to the code. Control structures, such as loops and conditionals, make C++ powerful and adaptable, able to handle various scenarios and decisions in a program. They're indispensable tools for building complex logic without hardcoding every possible step.