dukeofearl is right that chlorine bleach will kill algae that has discolored the patio concrete, but a dilution of 1 to 10 is adequate and won't kill everything aroung the patio when you rinse.
I recommend you use a powerwasher for this job. you won't need any chemical addition, the water pressure will fully clean and restore the concrete. You could buy an inexpensive electric powerwasher for about $120, or buy a moderate priced gasoline powered one for about $300. If you can't justify the cost, a commercial rental for $65/day will do a lot of work quickly. No scrubbing, just spray away the years of grime.