Question

include using namespace std; int main() { int beta[7] = {3, 5}; for (int i = 2; i < 7; i++) { beta[i] = 3 * i +… # What is the output of the following C++ code? #include using namespace std; int main() { int beta[7] = {3, 5}; for (int i = 2; i < 7; i++) { beta[i] = 3 * i + 2; beta[i - 1] = beta[i - 1] + beta[i]; beta[i - 2] = beta[i - 2] + beta [i - 1]; } for (int i = 0; i < 7; i++) cout << beta[i] << " "; cout << endl; return 0; }

Short answer

The output of the program is: 322 344 163 61 20 17 17

Step-by-step solution

Initialize Array and For Loop

The array `beta` is declared with 7 elements and initialized with the first two elements as 3 and 5 respectively. The rest are initially set to zero. The code then enters a `for` loop starting with `i = 2`.

Compute and Update beta[i]

Within the loop, `beta[i]` is calculated using the formula \( \beta[i] = 3 \times i + 2 \). For example, when \( i = 2 \), \( \beta[2] = 3 \times 2 + 2 = 8 \). This calculation updates the current `beta[i]` position.

Update beta[i-1]

The value at `beta[i-1]` is then updated by adding the newly computed `beta[i]`: \( \beta[1] = \beta[1] + \beta[2] = 5 + 8 = 13 \) when \( i = 2 \).

Update beta[i-2]

Next, `beta[i-2]` is updated by adding the new `beta[i-1]`: \( \beta[0] = \beta[0] + \beta[1] = 3 + 13 = 16 \) when \( i = 2 \).

Iterate Through Loop

The loop continues with these operations for `i = 3` to `i = 6`, updating each element based on the formulas. For `i = 3`, \( \beta[3] = 3 \times 3 + 2 = 11 \), then \( \beta[2] = \beta[2] + \beta[3] = 8 + 11 = 19 \), and \( \beta[1] = \beta[1] + \beta[2] = 13 + 19 = 32 \). This logic continues until \( i = 6 \).

Calculate Start-To-Finish Array State

Each loop iteration modifies several past elements, leading to a cumulative update sequence. By the time the loop is finished, the array `beta` has endured a series of chaotic transformations, leaning largely on each computed `beta[i]` element added linearly in sequence.

Output the Final State of Array

Finally, the second `for` loop iterates over each element of `beta` and outputs them, separated by spaces, showing the final computed state of the array.

Key concepts

Array Initialization

In C++, an array is a collection of elements, all of which are of the same type, that are stored in contiguous memory locations. Initializing an array in C++ involves defining its size and, optionally, providing initial values for its elements. In our given C++ code, the array `beta` is declared to hold 7 integer elements.

The initialization part of the array is crucial. Here, `beta` is initialized with the values `{3, 5}` for the first two elements, while the rest of the elements default to zero. It is important to note that if an array is not fully initialized, C++ fills the remaining entries with zero values. This initialization ensures that we have a starting point for array manipulation later in the code.

For Loop

A `for` loop in C++ is a control flow statement that allows code to be executed repeatedly based on a given condition. The loop runs as long as the specified condition is `true`. In our exercise, the `for` loop is used to iterate over the array `beta`, starting from index 2.

The loop structure looks like this: `for (int i = 2; i < 7; i++)`. This means the loop starts with `i` set to 2 and continues as long as `i` is less than 7, incrementing `i` at the end of each iteration. The purpose of this loop is to perform a series of calculations and updates on the array's elements. This systematic pattern helps efficiently manipulate and compute array values without the risk of hardcoding each step.

Array Manipulation

Array manipulation refers to the processes involved in accessing and modifying the data stored in an array. In the exercise, the array `beta` undergoes several changes within the `for` loop.

During each iteration, different elements of `beta` are computed and updated based on specific formulas:

• `beta[i]` is calculated using the formula `3 * i + 2`.
• `beta[i - 1]` is then updated by adding the newly calculated `beta[i]` to it.
• `beta[i - 2]` is further altered by adding the updated `beta[i - 1]`.

These operations are designed to involve not just the current index but also affect preceding elements, leading to a mix of direct and cascading changes throughout the array.

Iterative Computation

Iterative computation is the process of repeatedly performing a set of operations, typically using loops, to gradually build up results. In our given C++ program, this occurs as the `for` loop iterates through the array `beta`.

At each step, calculations are performed based on the index `i`, which in turn update not just the current element but also the two preceding elements. This leads to complex interactions between the elements as each update ripples backward slightly through the array.

The computation can be observed as a sequence of cumulative modifications. Initially simple values are transformed into complex outputs through iterative recalculations, illustrating the power of loops to manage complex data flows efficiently. By conclusion of the loop, each element in the array comes to embody both direct computations and a compounded history of prior changes.