Question

What is the output of the following \(\mathrm{C}++\) code? int count \(=10\); double sum \(=0\); while (count > 8) $$\begin{array}{l}\text { Sum = sum + pow (count, 2.0) } \\ \text { count- - ; }\end{array}$$\\} cout \(<<\) sum \(<<\) endl:

Short answer

The output of the code is 181.

Step-by-step solution

Initialize Variables

The code starts by initializing two variables: an integer \( ext{count} \) with a value of 10 and a double \( ext{sum} \) with a value of 0. These variables will be used to control the loop and accumulate a total sum.

Evaluate Loop Condition

The while loop condition \( ext{count} > 8 \) is checked. Since \( ext{count} \) is initially 10, the condition is true, and the loop will execute.

First Iteration of the Loop

Inside the loop, the statement \( ext{sum} = ext{sum} + ext{pow(count, 2.0)} \) calculates the square of \( ext{count} \), which is \( 10^2 = 100 \), and adds it to \( ext{sum} \). So, \( ext{sum} \) becomes 100. Then, \( ext{count} \) is decremented by 1, becoming 9.

Second Iteration of the Loop

The loop condition \( ext{count} > 8 \) is checked again. With \( ext{count} = 9 \), the condition is true. The square of \( ext{count} \) is calculated as \( 9^2 = 81 \), and added to \( ext{sum} \), making \( ext{sum} = 100 + 81 = 181 \). \( ext{count} \) is decremented again to 8.

Exit the Loop

Now \( ext{count} \) is 8, so the while condition \( ext{count} > 8 \) is false, causing the loop to terminate. No further additions to \( ext{sum} \) occur.

Output the Result

The final value of \( ext{sum} \) is printed using the statement \( ext{cout} << ext{sum} << ext{endl} \). The result is 181.

Key concepts

Understanding the while Loop

A "while loop" in C++ is a control flow statement, used to repeatedly execute a block of code as long as a specified condition remains true. The "while loop" checks the condition before executing the block of code. In the given exercise, the condition is \( \text{count} > 8 \), which means the loop will continue as long as the value of "count" is greater than 8.

• If the condition is true, the statements inside the loop are executed.
• If the condition is false, the loop terminates, and the program resumes with the next statement outside the loop.

This type of loop is useful when you don't know beforehand how many times you need to loop through the code.

The Power of the pow Function

The "pow function" in C++ is a part of the "cmath" library, used to calculate power/exponentiation, i.e., it raises one number (the base) to the power of another number (the exponent). The syntax is \( \text{pow(base, exponent)} \). In the exercise, "pow" is used to find \( \text{count}^2 \) during each iteration of the loop.

• The first parameter is the number to be raised to a power.
• The second parameter is the exponent to which the base number is raised.

The pow function makes it easy to perform exponentiation with just a simple function call.

The Importance of Variable Initialization

"Variable initialization" in C++ means assigning an initial value to a variable at the time of its declaration. It is crucial because it sets up variables with known values, which can be important when using them in expressions or loops. In the given task, two variables are initialized:

• An integer variable "count" starts at 10.
• A double variable "sum" starts at 0.

Initializing "sum" to 0 is important as it serves as the starting point for accumulating values within the loop, whereas "count" determines how long the loop continues to run.

How Loop Iteration Works

"Loop iteration" refers to the process of repeatedly executing a set of instructions within a loop. Each pass through the loop is considered one iteration. Every iteration of the loop in the exercise performs the following steps:1. Compute the square of the "count" value using the pow function.2. Add this squared value to the "sum".3. Reduce the "count" by 1 using a decrement operation.Each iteration moves the program closer to meeting the loop's termination condition. The loop will continue while the condition \( \text{count} > 8 \) holds true. Only then does it break out of the loop, at which point the accumulated "sum" can be outputted, showcasing the final result of all iterations combined.