What kind of algae? Green or purple/calcerious? If it's the former, bleach is fine, IMO, as long as you rinse the whole thing thoroughly afterwards (preferably in warm water with a chlorine neutralizer like Prime). If the latter, vinegar will remove it quite nicely with no elbow grease.
If you do bleach, don't use it full strength, but rather fill up the tank and add bleach giving it time to work. Same thing for the vinegar. I usually put a power head in to keep things circulating and maximize your chemical reaction.