Question

What is the output of the following \(\mathrm{C}++\) program segment? Assume all variables are properly declared. for (j = 0; j < 8; j++) { cout << j * 25 << " - "; if (j != 7) cout << (j + 1) * 25 - 1 << endl; else cout << (j + 1) * 25 << endl; }

Short answer

The program outputs eight lines: "0 - 24", "25 - 49", "50 - 74", "75 - 99", "100 - 124", "125 - 149", "150 - 174", "175 - 200".

Step-by-step solution

Understanding the Loop Structure

The given code uses a `for` loop that initializes the loop variable `j` to 0 and continues to iterate until `j` is less than 8, increasing `j` by 1 during each iteration. This means the loop will execute a total of 8 times, with `j` taking values from 0 to 7.

Analyzing the Output for Each Iteration

During each iteration, the program prints `j * 25`. Then it checks if `j` is not equal to 7. If this condition is true, it prints `(j + 1) * 25 - 1`, followed by a newline. If `j` is equal to 7, meaning it's the last iteration, it prints `(j + 1) * 25`, followed by a newline.

Calculating Output for Each Iteration

We'll calculate and list the output for each iteration: - When `j = 0`: Outputs `0 * 25 = 0`, then checks `j != 7` and it outputs `(1 * 25) - 1 = 24`. - When `j = 1`: Outputs `1 * 25 = 25`, then outputs `(2 * 25) - 1 = 49`. - When `j = 2`: Outputs `2 * 25 = 50`, then outputs `(3 * 25) - 1 = 74`. - When `j = 3`: Outputs `3 * 25 = 75`, then outputs `(4 * 25) - 1 = 99`. - When `j = 4`: Outputs `4 * 25 = 100`, then outputs `(5 * 25) - 1 = 124`. - When `j = 5`: Outputs `5 * 25 = 125`, then outputs `(6 * 25) - 1 = 149`. - When `j = 6`: Outputs `6 * 25 = 150`, then outputs `(7 * 25) - 1 = 174`. - When `j = 7`: Outputs `7 * 25 = 175`, then outputs `(8 * 25) = 200`.

Compile Full Output

Arranging the individual outputs: - `0 - 24` - `25 - 49` - `50 - 74` - `75 - 99` - `100 - 124` - `125 - 149` - `150 - 174` - `175 - 200` Each pair of numbers in this sequence represents one line of output.

Key concepts

For Loop

In C++, a **for loop** allows you to repeatedly execute a block of code a certain number of times. The general structure of a for loop is `for (initialization; condition; increment)`. Here, **initialization** sets the starting point, **condition** determines when the loop should stop, and **increment** changes the loop variable each time the loop runs.
In our example:

• Initialization: `j = 0` starts the loop with `j` set to 0.
• Condition: `j < 8` allows the loop to run while `j` is less than 8.
• Increment: `j++` increases the loop variable `j` by 1 in each iteration.

This setup loops exactly 8 times, executing the code block with values of `j` ranging from 0 to 7. It's effective for tasks where precise repetition and control of the iteration variable are needed. The simple structure helps simplify the code when you know how many times you need to iterate.

Iteration Analysis

**Iteration analysis** involves studying each pass through the loop to understand what happens at each step. This analysis is crucial for predicting the loop's output and behavior. Within each iteration of this loop, two main actions occur:

• First, the program calculates and prints `j * 25`.
• Next, it decides which additional value to print based on whether `j` is equal to 7.

For `j` values from 0 to 6, an additional calculation and comparison take place: `(j + 1) * 25 - 1`. This logic ensures a specific pattern in the output, where each line lists two calculated numbers. Analyzing each step helps identify the logical flow and predict behavior, which enlarges understanding of loop functionality.

Output Calculation

**Output calculation** involves determining the exact results produced by the loop during execution. The `cout` statements within the loop dictate what appears on each line, based on calculations involving the current value of `j`. For each value of `j`:

• Calculate `j * 25`, print it, and follow with `" - "`.
• If `j` is not 7, compute `(j + 1) * 25 - 1` and print it.
• If `j` is 7 (the last iteration), simply calculate and print `(j + 1) * 25`.

This methodology produces pairs of numbers. For instance, when `j` equals 0, the first run outputs `0` and `24`, giving `"0 - 24"`. Each subsequent line follows a similar pattern, creating a predictable, patterned output. By mapping out these calculations step-by-step, you can visualize and verify how each piece of output arises from specific code logic.