By the extension and the modification of the efficient aigorithms for the DCT-III, the fast algorithms to compute three versions for DCT, four versions of DST, and a DHT are developed. It is shown that the algorithms developed in this paper have simple structures and the numbers of multipication and addition are reduced as comparies with the existing efficient algorithms. The algorithms presentes in this paper indicate the close relationship amng different versions of the DCT and DST as well as a DHT. The formulas to compute the numbers of multiplication and addition of them are derived.