There are three phylums of algae:
An example of Chlorophyta found in coral reefs is known as Ulva lactuca, (sea lettuce)
A second example of Chlorophyta found in coral reefs is known as Halimeda (macroalgae)
Alevizon, Dr. William. "Coral Reef Plants." Coral Reef Plants | Common Plant Life of Coral Reef Ecosystems. 2010-2013, http://www.coral-reef-info.com/coral-reef-plants.html.
Themes, Elegant. "Halimeda." Freakin Fucus. 2015. http://freakinfucus.co.uk/halimeda/.
Ulva lactuca:
Halimeda:
An example of Rhodophyta found in coral reefs is known as Crustose Coralline Algae.
Johnson, Maggie D. "Coralline Algae: The Unsung Architects of Coral Reefs." Ocean Portal | Smithsonian. August 23, 2016. Accessed March 06, 2017. https://ocean.si.edu/blog/coralline-algae-unsung-architects-coral-reefs.
Another example of Rhodophyta found in coral reefs is known as Gelidium Amansii.
Rasser, Michael. "Introduction to the Rhodophyta." Introduction to the Rhodophyta. http://www.ucmp.berkeley.edu/protista/rhodophyta.html.
Gelidium Amansii:
An example of Phaeophyta found in coral reefs is Sargassum
US Department of Commerce, National Oceanic and Atmospheric Administration. "What is Sargassum?" NOAA Ocean Explorer Podcast RSS. July 16, 2014. http://oceanexplorer.noaa.gov/facts/sargassum.html.
Another example of Phaeophyta found in coral reefs is Fucus Serratus
Harris, Ben. "Fucus vesiculosus." The Brown Alga Fucus vesiculosus (Bladderwrack) - Reproduction and Life Cycle. 2007. http://bioweb.uwlax.edu/bio203/2011/harris_benj/reproductionlifecycle.htm.
Sargassum:
Fucus Serratus: