I kind of have to disagree with a few things on this thread. Not that these things are totally wrong but I have a few small problems with some of it.
I have been getting cycles of algae on and off for about 25 years, (the first ten years there was very little algae the tank is now 35) I have all the snails, crabs, rabbitfish, sea hares, skimmers, etc. and my nitrates are always zero. It's not likely that there is still anything leaching out of my rock at this point. I collected the rock my self in the Caribbean and Hawaii so I know it was clean (but that was long ago) You can not "cure" algae because it is not a disease, of course, we don't want to see it on our corals but if there is algae growing, your tank may be healthier. (thats for another thread)
You also can't and should not strive to eliminate all nutrients as your corals need some of these to support the symbiotic algae in their tissues.
Snails etc. will no doubt eat algae but unless we can teach them to poop outside the tank you will not accomplish much. Algae in the sea will grow almost as fast as it does in a tank but the hoardes of tangs and urchins eliminate it as soon as it starts to grow. There is enough water in the sea to dilute these nutrients and most of that water is too deep for algae.
I have hair algae in my tank but I found a way that me and the algae can be happy. I built a shallow trough 5' long which sits above the water, to the rear and just under the lights. It is free to operate. There is a plastic screen infused with cement in the trough (hair algae loves cement)
The trough is tilted so the water moves fast. The conditions in the trough are much better for growing algae than in the reef. Algae is forced to grow there and since a tank can only support so much algae, it works. After 35 years I finally figured out that since I can'r beat it, I joined it.
Have a great day.
Paul