Well, let's go back to the examples.
How would you estimate the amount of traffic lights in Manhattan?
There are 4 phases I'd take in answering this.
The first phase is the simple answer, which is to look it up. There's gotta be a recent statistic somewhere.
The second phase, if the first one fails, is to use good ol' sampling. Map out a sector of the city (3%, maybe) and count the traffic lights by hand. Then multiply that number by the total number of sectors in the city.
The third phase is needed if you need something a little more accurate. I'd look to see if there are any rules or standards in place for traffic light placement, then apply an algorithm to those rules and the mappings of the streets (which can be found easily).
The fourth phase, to be applied when all else fails... hire a team of interns to count them all.
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