Question

Consider the following for loop: int j, s; s = 0; for (j = 1; j <= 10; j++) s = s + j * (j - 1); In this for loop, identify the loop control variable, the initialization statement, the loop condition, the update statement, and the statement that updates the value of \(\mathbf{s}\)

Short answer

Loop control variable: \( j \); Initialization: \( j = 1 \); Condition: \( j \leq 10 \); Update: \( j++ \); \( s \) update: \( s = s + j \times (j - 1) \).

Step-by-step solution

Identify the Loop Control Variable

The loop control variable is the variable that controls the execution of the loop. In the given for loop, the loop control variable is \( j \).

Determine the Initialization Statement

The initialization statement is the part of the loop where the control variable is initialized. In this case, the statement is \( j = 1 \), setting the starting value of the loop control variable.

Identify the Loop Condition

The loop condition determines how long the loop will execute. Here, the loop will continue as long as \( j \leq 10 \). This ensures the loop executes while \( j \) is less than or equal to 10.

Specify the Update Statement

The update statement modifies the loop control variable after each iteration. In this loop, the update statement is \( j++ \), which increments \( j \) by 1 after each pass through the loop.

Examine the Statement that Updates the Value of \( s \)

Inside the loop, the value of \( s \) is updated with the statement \( s = s + j \times (j - 1) \). This computes \( j \times (j - 1) \) at each step, adding it to \( s \).

Key concepts

Loop Control Variable

In the context of a C++ for loop, the loop control variable is critical for guiding the loop's execution. In the provided example, the variable 'j' is the loop control variable. This variable acts as a counter, keeping track of the number of times the loop block executes. It starts with an initial value defined by the initialization statement, progresses through each iteration, and is modified by the update statement. The role of the loop control variable is crucial because it dictates the loop's progression and termination, ensuring the sequential execution of loop tasks.

Monitoring the loop control variable helps in understanding the loop flow and is essential for debugging loops to ensure they run correctly. Remember that altering this variable within the loop's body can lead to unintended behaviors, such as infinite loops or incorrect execution counts.

Initialization Statement

The initialization statement in a C++ for loop assigns an initial value to the loop control variable. This step guarantees that the loop variable starts at a known state before entering the loop's body. In the given for loop, the initialization statement is `j = 1`. This statement sets `j` to 1, establishing the starting point from which the loop will begin its execution.

The initialization statement is only executed once, at the very start of the loop. It sets up the loop control variable, preparing it to check against the loop condition. Without a proper initialization, the loop might not perform as expected, as the loop control variable might not have a defined value to work with from the onset.

• Executed only once.
  
• Sets starting condition.
  
• Prepares for loop execution.
  

Loop Condition

The loop condition plays a pivotal role in determining how many times the loop will execute. It is a logical statement evaluated before every loop iteration, checking whether the loop should continue or not. In the example given, the loop condition is `j <= 10`. This means the loop will keep executing as long as `j` is less than or equal to 10.

The loop condition is essential for preventing infinite loops, which occur when the condition never becomes false.
It's also useful for defining the loop's range and duration.

• Assessed before each iteration.
  
• Prevents infinite loops.
  
• Controls loop range.
  

Understanding and setting a correct loop condition helps in designing robust and efficient loops that perform their intended tasks within specified bounds.

Update Statement

The update statement is the component of a C++ for loop that alters the loop control variable after every iteration. It ensures that the loop progresses and eventually terminates by modifying the variable that the loop condition evaluates. In this scenario, the update statement is `j++`. This notation is shorthand for incrementing `j` by 1, moving the loop control variable closer towards fulfilling the loop termination condition.

It's critical to place the update statement accurately, as improper updates can lead to situations where the loop condition is never met (resulting in infinite loops), or met too soon (causing premature loop termination).

• Executed after each iteration.
  
• Moves loop towards termination.
  
• Influences loop's duration.
  

By correctly implementing the update statement, you ensure that the loop achieves its iterative goals efficiently and finishes as intended.