Question

What is stored in list after the following C++ code executes? int list[10]; for (int i = 0; i < 5; i++) { list[i] = i * i - 5; if (i % 3 == 0) list[i] = list[i] + i; else list[i] = list[i] - i; }

Short answer

The first five elements of the list are \([-5, -5, -3, 7, 7\].

Step-by-step solution

Initialize List and Loop Conditions

The array `list` is initialized with 10 integer slots. However, the loop runs for `i` ranging from 0 to 4 (inclusive), modifying only the first 5 elements of `list`. The loop iterates exactly 5 times.

Iteration 0 (i = 0)

Calculate the initial value: $list[0]=0\ast 0-5=-5$. Since $0\mathrm{mod}3=0$, we apply the modification: $list[0]=-5+0=-5$. Thus, $list[0]=-5$.

Iteration 1 (i = 1)

Calculate the initial value: $list[1]=1\ast 1-5=-4$. Since $1\mathrm{mod}3eq0$, apply the subtraction: $list[1]=-4-1=-5$. Thus, $list[1]=-5$.

Iteration 2 (i = 2)

Calculate the initial value: $list[2]=2\ast 2-5=-1$. Since $2\mathrm{mod}3eq0$, apply the subtraction: $list[2]=-1-2=-3$. Thus, $list[2]=-3$.

Iteration 3 (i = 3)

Calculate the initial value: $list[3]=3\ast 3-5=4$. Since $3\mathrm{mod}3=0$, add $i$ to the list: $list[3]=4+3=7$. Thus, $list[3]=7$.

Iteration 4 (i = 4)

Calculate the initial value: $list[4]=4\ast 4-5=11$. Since $4\mathrm{mod}3eq0$, apply the subtraction: $list[4]=11-4=7$. Thus, $list[4]=7$.

Finalized List; Unmodified Elements

The first five elements of the list are: $[-5,-5,-3,7,7]$. The remaining elements $list[5]$ to $list[9]$ were not modified and retain their default initialization value, which is not specified here.

Key concepts

Understanding For Loops in C++

In C++, a "for loop" is a control flow statement that allows a block of code to be executed repeatedly based on a given boolean condition. It is a versatile tool for automating repetitive tasks, such as iterating over arrays.
In the given code, the for loop is structured as follows:

• **Initialization**: `int i = 0;` sets the starting point.
• **Condition**: `i < 5;` checks if the loop should continue running.
• **Iteration**: `i++` increases the counter by 1 after each loop cycle.

This loop performs its block of operations a set number of times (in this case, 5), affecting the first five elements of the array `list`. It begins with `i = 0` and continues until `i` is less than 5, making sure that each step within the loop is executed in order.

Using the Modulus Operator

The modulus operator, represented by `%`, is a mathematical operation that returns the remainder of a division between two numbers. In programming, it is often used for determining odd and even numbers, repeating cycles, or conditions that rely on periodic behavior.
In the context of the provided code, `i % 3 == 0` checks whether the value of `i` is evenly divisible by 3. If it is, the condition evaluates to true. For array indices that equate to multiples of 3, a specific operation is performed (i.e., `list[i] = list[i] + i;`). This introduces a conditional branching within the loop to manipulate the data differently based on `i`'s divisibility.

Array Initialization in C++

Before you can use an array in C++, it must be initialized, meaning you set up the array structure in which the data will be held.
The code `int list[10];` initializes an integer array of size 10, creating a continuous block of memory capable of storing up to ten integer values. Initially, these values are undefined until explicitly assigned.
In our particular example, only the indices 0 through 4 are actively used and assigned new values through the loop's iterations. The rest of the array (elements 5 to 9) remains uninitialized by the loop, maintaining whatever random or garbage values existed in memory prior, unless explicitly handled elsewhere in the code.

Working with Conditional Statements

Conditional statements are a fundamental part of programming, allowing code to make decisions based on particular conditions.
In the given C++ exercise, the `if` statement introduces a decision-making structure within the loop. The condition `if (i % 3 == 0)` checks if the current loop index is a multiple of 3. Depending on the outcome, it modifies the array differently.
If the condition is true for an index, `list[i] = list[i] + i;` will execute, adding the index to its current value. Otherwise, the `else` block `list[i] = list[i] - i;` subtracts the index from its corresponding array element. This results in different transformations applied to the array elements, influencing the final stored values based on these conditions.