I've been using a home made spray of 1:1 liquid Chloro and water out of a hand held pump sprayer and this does a good job of killing the mold and algae. The green kinds dies and fades away completely in an hour or so. The Black stuff, dies but doesn't fade.*
I did the granular pool chlorine, broom method once and it worked, but it was sort of expensive, was a lot of hard work (i have a large area to do) and the resulting chlorine/water paste the results before sweeping is not good for the dog's paws. You then have to figure out where to put the sweepings. This concoction will kill your grass, burn your skin and is deadly if ingested by kids, pets and other beneficial creatures such as lizards, birds etc. If this gets into your septic system, it'll terminate the microbial action. If you just wash it out onto the street, who knows where it will end up.