Task Scheduler - Why This Works

Why does scheduling the most frequent task first minimize idle time? Think of it this way: the most frequent task determines the structure.

If task A appears $f$ times with cooldown $n$, you need at least $(f-1) \times (n+1) + 1$ slots for A alone. Other tasks fill the gaps. By handling the most constrained task first, you create a framework and fill in the rest.

If you start with less frequent tasks, you might create unnecessary idle slots.