Algorithm design by successive transformation

Algorithms courses are typically organized either by application area or by design technique. Each of these organizations has its strength, but neither effectively reflects the fact that sophisticated algorithms are not designed in a single pass. This paper describes and gives an example of the strategy of successive transformation, in which a sequence of algorithms is generated to solve a single problem. Design of algorithms by successive transformation requires more time per problem, since each problem requires multiple phases of analysis. To the extent that this method is used, the breadth of the course in terms of areas and algorithms is reduced. However, we assert that at least a few such experiences are indispensable, because such painstaking analysis is representative of algorithm design as it really is, and because successive transformation is an excellent way to show students the power of theory to improve applications.