基于0-1规划的五连珠问题求解

0-1 Planning Solution to Five-Sub-Alignment Question

五连珠问题是五子棋中抽象出来的问题,通过建立0-1规划模型,求解得出一维、二维以及三维情况下五子连珠问题的可行解。类比晶体学中晶体的成核与生长过程,建立了晶胞构成模型。相比单纯的0-1规划模型,晶胞构成模型有运算规模小、运行速度快等优点。拓展至高维度情况下的连珠问题,讨论不同维数规划模型的约束类型的个数。该模型对于N子连珠问题以及八皇后的求解有一定的借鉴意义。

By establishing a 0-1 planning model,a feasible solution to the five-sub-alignment question can be obtained in one-dimensional,two-dimensional and three-dimensional situations.The nucleation and growth process of crystals in crystallography has also been introduced to establish an unit cell-composed model.Compared with a simple 0-1 planning model,the latter has the advantages of not only small scale of but also high speed of operation.Further extend the problem to high dimensions,and discuss the number of constraint types of the planning model under different dimensions.The model has certain reference significance for the relevant question such as the N-sub-alignment question and solution of the eight queens.