Count peak power minutes
A plant pays a surcharge for every minute of the day when too many machines drew power at once, so the energy team needs that figure from the run log. runs holds one entry per machine run, written as [start, end] in minutes since midnight, and the run occupies the minutes start through end minus 1, so a run that ends exactly as another begins never shares a minute with it. The log is in no particular order, runs may overlap or repeat, and a cancelled run carries end equal to start. No end is earlier than its start. Return how many minutes had at least threshold runs going at the same time. Count each such minute once, however many runs cover it. When threshold is 0 or negative every minute would qualify, which bills nothing useful, so return 0.
high_demand_minutes(runs: list[list[int]], threshold: int) → int[[[540,600],[560,620],[610,660]],2]out50[[[0,30],[30,60],[10,20]],2]out10State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
[[[540,600],[560,620],[610,660]],2]50not run yetsample[[[0,30],[30,60],[10,20]],2]10not run yetsample