I used bleach to kill algae in our new hot tub in which we use bromine instead of chlorine. Bromine doesn't kill algae.
The water was green and a half cup of bleach turned the water clear in a split second!
Instead of paying too much money for 'alkaline up' (which you definitely need when using chlorine as your sanitizer, get to the store and buy cheap baking soda - I need to check Sam's Club and see if they have a huge box there.
When we lived in MI, Meijer had the bigger and cheaper boxes.