When it comes to Longest Increasing Subsequence (LIS) in carpet cleaning, think of it as uncovering the "hidden order" in deep-cleaning strategies for consistently impressive results. Just as the LIS algorithm identifies the longest subsequence of numbers in ascending order, effective carpet cleaning requires a sequence of steps, each building on the last to enhance cleanliness without redundancy. Starting with dry vacuuming, we lay a clean foundation, removing loose debris to avoid clogging the cleaning solutions. Next, pre-treating tough stains before the main wash ensures that we address the most embedded dirt, making it easier for deep-clean extraction to follow. Finally, each rinse and drying step solidifies this sequence, leaving a fresher, thoroughly cleaned carpet. By following a structured approach, we achieve not just clean but sustained cleanliness—much like finding that perfect sequence to optimize the outcome!