Question

Suppose list is an array of five components of type int. What is stored in list after the following $\mathrm{C}++$ code executes? for (int i = 0; i < 5; i++) { list[i] = 2 * i + 5; if (i % 2 == 0) list[i] = list[i] - 3; }

Short answer

The list becomes [2, 7, 6, 11, 10].

Step-by-step solution

Initialization

First, understand that we have a list named `list` with 5 integer components. We will iterate over this list using a `for` loop with an index `i` that will range from 0 to 4.

Loop Through the List

The loop structure is `for (int i = 0; i < 5; i++)`. This means we will perform operations on each element `list[i]` from `i=0` to `i=4`.

First Operation in Loop

For each iteration, compute `list[i]` using the expression `list[i] = 2 * i + 5`. This operation initializes `list[i]` to `2 * i + 5`.

Conditional Check

Next, check if `i` is even using `if (i % 2 == 0)`. If true, perform the operation `list[i] = list[i] - 3`.

Iterating and Modifying Elements

Iterate over each index and modify `list[i]` based on the above conditions: - For `i=0`: `list[0] = 2*0 + 5 = 5`; since 0 % 2 == 0, update `list[0]` to `5 - 3 = 2`. - For `i=1`: `list[1] = 2*1 + 5 = 7`; do not subtract 3, as 1 % 2 != 0, so it remains 7. - For `i=2`: `list[2] = 2*2 + 5 = 9`; since 2 % 2 == 0, update `list[2]` to `9 - 3 = 6`. - For `i=3`: `list[3] = 2*3 + 5 = 11`; do not subtract 3, as 3 % 2 != 0, so it remains 11. - For `i=4`: `list[4] = 2*4 + 5 = 13`; since 4 % 2 == 0, update `list[4]` to `13 - 3 = 10`.

Key concepts

Iterative Loops

In C++, an iterative loop is a powerful construct that enables you to repeat a block of code a specified number of times or until a certain condition is met. The "for loop" is a common type of iterative loop used to iterate over arrays or lists. Let's break down the essential parts of a 'for loop' to better understand its mechanics:

• Initialization: This step involves setting a starting point for the loop, usually where a variable (commonly referred to as an iterator) is initiated. For example, `int i = 0` initializes the iterator `i` to 0.
• Condition: The loop continues to execute as long as this condition remains true. For instance, `i < 5` means the loop will keep executing until `i` is less than 5.
• Increment/Decrement: After executing the loop's body, this step adjusts the iterator's value, generally by increasing it with each iteration, e.g., `i++` which increases `i` by one.

These parts work together to ensure that the loop executes the required number of times. In the given exercise, the loop allows each element in the array `list` to be accessed and modified one at a time, specifically from index 0 through 4.

Conditional Statements

Conditional statements in C++ are used to perform different actions based on different conditions. The fundamental type of conditional statement is the `if` statement, which allows your program to make decisions based on the truthfulness of a condition you specify.

In the exercise provided, the condition `if (i % 2 == 0)` checks whether the index `i` is even. The modulus operator `%` is particularly useful here because it finds the remainder of division between two numbers; if `i` divided by 2 leaves a remainder of 0, then `i` is even.

• If the condition `i % 2 == 0` evaluates to true, the statement inside the if block will execute. In this case, the code subtracts 3 from the current value at `list[i]`.
• If the condition is false, and no additional else clause is provided, the program skips the statement inside the if block and continues with the rest of the code in the loop.

This mechanism allows for adding logic to your loops, enabling dynamic behavior based on whether certain conditions in data are met.

Array Indexing

Arrays in C++ serve as a way to store multiple items of the same data type together, with each item accessed via an index. Indexing is a crucial concept when dealing with arrays because it allows direct access to any element within the array.

In C++, array indices start at 0, which means that for an array of size 5, the index range is from 0 to 4. Each element within the array can be modified or accessed using these indices. In the provided exercise, the loop iterates over each index from 0 through 4. Here's how it works in detail:

• `list[0]` refers to the first element of the array.
• `list[1]` refers to the second element, and so on up to `list[4]` for the fifth element.

Array indexing is particularly powerful because it allows the assignment of values to elements in an array inside loops and conditional statements, which are essential for programming tasks where arrays are involved. This facilitates iteration over data sets and modification of their elements based on certain criteria, as demonstrated in the exercise example.