The Strategy Research Of The Formal Derivation Of Algorithms For Three Kinds Of Combinatorial Mathematical Problems

Combinatorial mathematics is the science which researches discrete objects,while computer processing objects are mainly discrete data.Therefore,the research on algorithms for combinatorial mathematical problems has always been one of the important research fields of computer science.However,in many related literatures,most of the related algorithms for the solution of combinatorial mathematics are obtained by simple analysis using traditional algorithm design methods.The detailed design process of the algorithm program is not given,which makes the reader be unable to understand the essence of the algorithms.The correctness of the program of algorithm cannot be guaranteed.In this paper,through the analysis and comparison of several algorithm design methods,the formal method of algorithm based on recursive technique is used to carry out in-depth research and formal development of algorithms for several problems in combinatorial mathematics.The formal method of algorithm based on recursive technique first requires formal description of the functional specification of the problem solved,and then uses a strict program specification transformation technique to perform a series of equivalent transformations on the protocol to obtain the recursive relation of the problem,and then the loop algorithm is used to give the final algorithm program based on the obtained recursive relationship.In this paper,several problems in combinatorial mathematical problems are researched in depth.By analyzing and comparing the characteristics and commonalities of these problems,these combinatorial mathematical problems are divided into three types of problems: Continuous subsequence solving problem,the division problem of "same element" and the classification problem of "different elements".Then,for these three categories of combinatorial mathematical problems,this paper selects several examples respectively using the formal method of algorithm based on recursive technique to show formal derivation process of the algorithm program in detail.Finally,according to the common characteristics of each of the three kinds of problems,the definition of the lexical vector of different meanings expresses the program specification of each type of problem,and at the same time extracts the unified solution strategy of the formal derivation of the three kinds of combined mathematical problem algorithms,and These unified solution strategies are further applied to algorithm development for specific combinatorial mathematical problems.The significance of the research work in this paper is as follows: 1)Using the formal method of algorithm based on recursive technique to develop the algorithm program of combinatorial mathematical problem,starting from the formal program specification of the problem,using the protocol transformation rule to carry out a series of equivalent transformations on the program specification,Obtaining the recursive formula of the problem solving sequence,based on this,the algorithm program for solving the problem clearly shows the detailed derivation process from the problem requirement to the algorithm program,and effectively solves the algorithm of these combinatorial mathematical problems.The process is helpful to help the reader understand the nature of these algorithms;2)In the process of derivation,the final algorithm of the problem is based on the recursive relationship.Since the recursive relation of the problem is obtained through strict mathematical transformation,we guarantee the correctness of the final algorithm program by guaranteeing the correctness of the problem recursive relation.3)The algorithm program for solving the problem by using the recursive relation Firstly,obtaining the solution of the sub-problem,and then further obtaining the solution of the larger problem through the sub-problem solution,and finally obtaining the solution of the original problem.This way can avoid many repetitive calculations and effectively improve the execution efficiency of the algorithm program;4)The program specification expression method and algorithm derivation unified strategy for three kinds of combinatorial mathematical problems are proposed,which provides an effective reference way for developing reliable algorithm programs for combinatorial mathematical problems.