I think that it's perfectly fine to give a random hot woman a compliment but here's how to follow it up: Follow the divestment procedure and by that I mean to do these things: 1) Watch her reaction; 2) Leave if she looks at you like you are trying to rape her (it's a sure fire sign that she either takes herself way too seriously or she's otherwise not reasonable); 3) Smile back if she smiles at you! And if it's 3) and not 2) then do 4-6: 4) Introduce yourself and ask her name; 5) Let her know what brought you out to where you guys met, and 6) If she seems interested, ask her for her phone number and if she doesn't want to give it to you, 7) Tell her "It's nice to meet you!" and try not to laugh here, "Do a #2!"

I try to apply the same logic to other people as I do with myself so I’m operating under the assumption that people are just trying to survive the day and get home as soon as possible with as few interactions with other people as they can get away with. So in this day age and with my own philosophy on life, I’m guessing you can’t and shouldn’t compliment a random woman on her looks. The chances of making the recipient of the compliment uncomfortable is extremely high and most people aren’t going to want to deal with some stranger’s bullshit anyways. Just don’t do it.