Hydrogen peroxide (H2O2) is great for cleaning (especially outdoors) because its fairly caustic at first, but changes into regular water after exposure to sunlight. It readily kills single celled organisms such as bacteria (or in this case algae) growing on almost any surface without damaging (for the most part) what's below it.
I used it to clean off the slippery when wet steps of a wooden deck.
This is going to be a short instructable.
Buy consumer grade H2O2 from the drugstore, get a good scrub brush, pour on, then scrub. I used 2 x 32oz bottles for this much. I could've made it go further if i had just scrubbed more however.
You want to let scrub it in for 30 seconds or so, and let it sit for a minute or 2. But then remove the foam (i just scraped it off with the brush) that will appear. That foam is mostly the dead bodies of whatever was growing there. Repeat a few times, then rinse off with a hose.
It will "smoke" and foam up a bit, this is normal. Don't worry about getting some on your skin, just rinse it off with water. You might want to keep a cup of it out there just in case. Take care not to get the H202 or the foam on the lawn, it will damage the grass.
I didn't really do a great job with "before" pictures, so the last few are a non-steps section of the deck that I wanted to show the difference. The last pic is the steps almost dry.