A unified approach called partition-and-recur for developing efficient and correct algorithmic programs is presented. An algorithm (represented by recurrence and initiation) is separated from program, and special attention is paid to algorithm manipulation rather than program calculus. An algorithm is exactly a set of mathematical formulae. It is easier for formal derivation and proof. After getting efficient and correct algorithm, a trivial transformation is used to get a final program. The approach covers several known algorithm design techniques, e.g. dynamic programming, greedy, divide-and-conquer and enumeration, etc. The techniques of partition and recurrence are not new. Partition is a general approach for dealing with complicated objects and is typically used in divide-and-conquer approach. Recurrence is used in algorithm analysis, in developing loop invariants and dynamic programming approach. The main contribution is combining two techniques used in typical algorithm development into a unified and systematic approach to develop general efficient algorithmic programs and presenting a new representation of algorithm that is easier for understanding and demonstrating the correctness and ingenuity of algorithmic programs.
展开▼
