Question

include #include using namespace std; int main() { int temp = 0; for (int counter = 1; counter <= 100; counter++)… # Consider the following C++ program: #include #include using namespace std; int main() { int temp = 0; for (int counter = 1; counter <= 100; counter++) if (pow(floor(sqrt(counter / 1.0)), 2.0) == counter) temp = temp + counter; cout << temp << endl; return 0; } a. What is the output of this program? b. What does this program do?

Short answer

The output is 385. The program sums all perfect squares from 1 to 100.

Step-by-step solution

Understand the Program Structure

The program begins by including the necessary libraries for input/output and mathematical computations. The `main` function initializes an integer variable `temp` to zero and starts a `for` loop running from 1 to 100.

Analyze the Loop

Within the loop, for each `counter`, the program calculates `sqrt(counter)`, floors the result, then squares it again. This checks if the number is a perfect square (since squaring the floored square root should return the original number for perfect squares). If it is, `counter` is added to `temp`.

Check the Condition

The key logic is the condition `pow(floor(sqrt(counter / 1.0)), 2.0) == counter`. This verifies if `counter` is a perfect square by comparing it to the squared value of its floored square root. If true, `counter` is a perfect square and it's added to `temp`.

Implement the Calculation

Only numbers like 1, 4, 9, ..., 100 will satisfy this condition, as they are perfect squares up to 100. The program sums these perfect squares: 1 + 4 + 9 + 16 + ... + 100.

Output the Result

After the loop, the final value in `temp`, which is the sum of all perfect squares from 1 to 100, is printed using `cout`.

Determine Program Output

The perfect squares between 1 and 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Their sum is calculated to be 385. Thus, the program outputs `385`.

Summarize Program Function

The program calculates the sum of all perfect squares from numbers 1 to 100 and outputs the result.

Key concepts

Perfect Squares

Perfect squares are numbers that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares of 1, 2, 3, 4, and 5, respectively. Perfect squares have whole numbers as their square roots.

In C++ programming, identifying if a number is a perfect square can be done through mathematical operations. In the given exercise, the program uses

• the square root function `sqrt` to find the square root,
• `floor` to drop any decimal parts, ensuring the root is an integer,
• and then squares the floored result to check if it gives back the original number.

This method effectively checks if the initial number is a perfect square, without requiring any lists or data structures.

For Loop

In the context of the given C++ program, the `for loop` plays a vital role. A `for loop` is used to repeat a section of code multiple times until a specified condition is no longer true.

The structure of a `for loop` in C++ is:

• Initialization: where you define a counter, such as `int counter = 1`.
• Condition: determines how long the loop will run, in this case, `counter <= 100`.
• Iteration: updates the counter, written as `counter++`, which increments the counter by 1 each loop.

In the provided program, the loop runs from 1 to 100. It checks each number to see whether it is a perfect square and adds it to `temp`, accumulating the sum of all perfect squares within this range.

Program Output

Program output is the result displayed after executing a program's logic. In C++, this is commonly handled with `cout` from the iostream library, which allows you to send output to the console.

In the exercise, once all numbers from 1 to 100 have been checked for being perfect squares and added to the variable `temp`, this final sum is output using: `cout << temp << endl;`.
After executing the loop, the program outputs `385`, which is the total sum of perfect squares between 1 and 100. Understanding the output requires knowledge of what calculation the program is designed to perform and analyze how it processes data, particularly with mathematical operations.

Mathematical Operations

Mathematical operations are the backbone of many programming exercises, including this one. In C++, standard arithmetic and mathematical functions are available, often included via the `` library.

The most significant mathematical operations in this exercise are:

• `sqrt`: computes the square root of a number.
• `floor`: rounds down to the nearest whole number, removing decimals.
• `pow`: raises a number to a specified power, in this case, squaring a number.

These operations work together to determine if a number is a perfect square: calculating the square root, flooring it, and then squaring it again. This chain of operations must return the original number for it to be a confirmed perfect square.

Properly utilizing these operations allows the program to effectively identify and sum perfect squares from 1 to 100.