An algorithm [48, 63, 77, 97, 115] is a precise description of how to solve a problem. For example algorithms can be used to describe how to add and subtract numbers or to prove theorems. Usually algorithms are constructed with some basic accepted knowledge and inference rules or instructions. Thus programs in programming languages such as C++ and Java are algorithms. Thus an algorithm is a map f: E → A of the input data E to the set of output data A.