利用位序法求标准拉丁方算法

Searching Standard Latin Square Algorithm with Order

文章根据排列与组合可计数的特点,给出了利用位序法求标准拉丁方的算法。在实现此算法时,构造了一套字符化的大整数运算系统,解决了随拉丁方阶数增大位序值剧增在计算机上无法表示或处理的问题。通过在分布式并行计算环境MPIBD中的实验,给出了所有4阶与5阶标准拉丁方。

Noticing that the Latin square has order like permutation and combination,this paper gives algorithm of searching standard Latin square fellowing this order.Since arithmetic operations of large magnitude integers can not be carried out directly,a set of sburoutines for large magnitude integer arithmetic operations are developed by characteriz-ing the large integers.By experiment at Distributed Parallel Computing Environment MPIBD,the paper lists all standard4-latin squares and5-latin squares.