Welcome back! As we move forward with our JavaScript algorithmic journey, today will keep working with stacks. During your coding interviews, it’s common to encounter puzzles that these structures can solve gracefully and efficiently. By diving into two stack-centric problems today, you'll see firsthand just how invaluable a well-implemented stack can be for writing clean and efficient code.

Consider a sequence of integers like the peaks and valleys of a mountain range. Each peak has a height represented by an integer, and you're hiking from left to right, recording peaks shorter than the one you're currently on. For each peak, we want to find out the height of the nearest preceding peak that's lower than it — a classic problem where stacks excel.

Envision analyzing daily temperatures over several months. You're interested in knowing the last cooler day for each day you examine. This mirrors our array problem, where we're seeking the previous smaller number before each entry in the array. It’s these kinds of time-sensitive queries that stack operations handle without breaking a sweat.

You might be tempted to approach this problem with the vigor of a brute force assault — looking behind each element to find a smaller one. However, this could mean reviewing multiple times and spending unforgiving time as you consider each element repeatedly. In a vast data set, this would be akin to retracing your steps on each day's hike to find a shorter peak, an exhausting proposition!

With stacks, we take on the role of a librarian who cleverly keeps track of how the heights of books change as she adds new ones to the shelf. Thus, the librarian can instantly recall the last book, shorter than the current one, by looking at the top of the stack.