Given that sliding window and next greater were new concepts, I guess its better to related this to real world.

Sliding window maximum real world usecases are in gauges, here one would be tracking changes over time, to answer question like:

What is the change in highest usage over a given time-window?

like : cpu or memory usages over time, latencies, temperature changes etc.

In such problems, the data is a stream, and the answer is demanding for an answer within a window.

For example: If the cpu usage metrics looks: [10, 40, 30, 20, 70, 90], measured every ms window. Then to get the max every 3ms window, one would keep a canidate list where:

• 10 can be discarded in the first window
• 30 can be kept in candidate list
• 40 can be discarded in the next window
• 30 then becomes the new max
• 20 can be kept in candidate list, since its after 30
• and, on the next window both 30 and 20 gets discarded b/o 70