Formal Derivation of a Generic Algorithmic Program for Solving a Class of Extremum Problems

In this paper, we derive formally, using PAR method, a generic algorithmic program for solving a class of extremum problems which can be abstract into a algebra structure called semiring. Some typical algorithms, such as minimal sum problem, maximal product problem, longest ascending segment problem, etc, are all instances of the generic algorithmic program. We put emphasis on the algorithmic derivation rather than the algorithmic verification. Not only embody the designer insight but also reveal the main ideas and ingenuity of these algorithms. The example in this paper confirms that PAR method is a simple and practical approach in deriving high-trustworthy generic algorithm programs.