Algae and protozoa are in the same kingdom, Protista, because the initial creation of this kingdom was done on the basis of superficial resemblance, and these eukaryotic and largely single-celled organisms seemed to resemble one another more than any other group. The three major groups of protists -- protozoa, algae and slime molds -- are not particularly closely related. Yeasts, despite being single-celled eukaryotes, are classified as fungi, not protists.
Protista is really a kingdom of organisms that does not fit within any of the other established kingdoms. While its overall character is of single-celled organisms with a nucleus, many multicellular species, particularly algae, are included in it. Slime molds, another unrelated group, sometimes grow as giant, macroscopic single cells with millions of nuclei, according to the Intermountain Herbarium at Utah State Univerisity. Protists are defined more by what they are not than by what they are, and this definition is controversial.
The classification of algae is particularly disputed. Algae include most photosynthetic protists, but some groups, such as dinoflagellates, are actually more closely related to protozoa than algae, such as kelp. Further, the distinction between many types of algae, particularly multicellular algae, and plants isn't very well-defined, and some scientists propose they should be grouped together apart from the protozoa.