晶胞构造求解五子连珠问题  

Crystal Cell Structure for Solving the Pentagram Problem

作　　者：吴晶晶 毛自森 许玲玲 

机构地区：[1]陆军工程大学,指挥控制工程学院学,江苏 南京 [2]陆军工程大学,基础部,江苏 南京 [3]萍乡学院,工程与管理学院,江西 萍乡

出　　处：《应用数学进展》2022年第10期7430-7439,共10页Advances in Applied Mathematics

摘　　要：五子连珠问题由五子棋抽象而来,类比晶体学中晶体的成核与生长过程,运用回溯法求出所有最佳晶胞,基于棋盘空间分解与不同维度晶胞的生长,得出最少放置数的求解公式,给出数学证明,同时快速给出所有最优放置,具有运算速度快、结果全面的优点。The five-sub-alignment problem comes from the abstraction of gobang. Analogize the nucleation and growth process of crystals in crystallography. The backtracking method is used to find all the best cells. Based on the spatial decomposition of the chessboard and the growth of cells in different dimensions, the formula for solving the minimum number of placements is obtained. At the same time, give all the optimal places quickly, which has the advantages of fast calculation speed and comprehensive results.

关 键 词：五子连珠 晶胞生长 模N皇后问题 分割法 分治算法 回溯算法 0-1规划 组合优化 

分 类 号：O29[理学—应用数学]