Welcome back! As we continue to master the art of interview-oriented problems using linked lists in PHP, we're setting our sights on practical, algorithmic challenges you will likely face.

Consider the following real-life problem: You’re tasked with organizing a digital library where some books have been accidentally duplicated. You aim to identify and remove these redundant entries to ensure each title is unique in your catalog.

A naive approach would be to browse each book and compare it with every other title in a nested loop fashion. As with any large library, this approach would be cumbersome, with a time complexity of $O(n^2)$. It also scales poorly with larger datasets because the time taken to process increases exponentially with each additional book — much like searching an entire library to check for duplicates each time a new book is added.

To address the issues of the naive approach, we use a more strategic method akin to maintaining a checklist: marking off each book we come across. This method, replicated in our algorithm, employs an associative array to record unique titles. Consequently, we reduce our time complexity to $O(n)$.

Let's delve into the step-by-step code:

With this explanation, we've clarified the importance of each line of code in the context of the overall strategy for duplicate elimination. We implemented a systematic approach to traverse the list and used an associative array to avoid repetitively processing the same value while maintaining efficient traversal.

Now, think of a long-distance race where you must analyze the runners' performance at every third checkpoint to gauge the race's progress.

The task requires calculating the average time at regular intervals throughout the racecourse. This problem aligns with our linked list scenario, wherein the list represents checkpoint timings, and the objective is to find the average time at every third checkpoint.

We will simply traverse the given linked list and track the sum and amount of every third element. It sounds easy, but let's examine the solution to see if everything is clear!

Here is our strategy translated into code, explained in detail:

The detailed commentary for each code block elucidates the purpose behind the lines of code, aligning them with our race-timing analogy. This enhances understanding by connecting the implementation directly to the problem-solving strategy.

Through this lesson, we've explored optimization strategies for common linked list challenges, addressing the reasoning behind efficient algorithms and their practical coding implementation. We've moved from understanding the 'how' to grasping the 'why,' deploying tailored, scalable solutions that will serve you well in technical interviews. Having navigated through the theory and dissected the code, it's your turn to practice and embed these concepts!