Algae is found in all three kingdoms. Its classification depends on what kind of algae it is. One kind of algae called the blue green algae also called cyanobacteria that falls under monera (as archae bacteria) . All eukaryotic unicellular algae despite being photosynthetic is placed under protista. eg: Euglena, Diatoms etc
All multicellular eukaryotic algae is placed under the kingdom plantae. Eg; Chorophycae (green algae) , Rhodophycae (Red algae) etc. BUT IN GENERAL MOST OF THE ALGAE IS FOUND UNDER THE KINGDOM PROTISTA. So if for exams its an mcq question , u can choose protista