多柱汉诺塔问题研究

Study of Hanoi Tower Problem with Multi-Pegs

对多柱汉诺塔问题进行了研究。采用动态规划的想法,给出了多柱汉诺塔问题最少移动步数的递推公式和具体表达式,并使用3层数学归纳和纯组合的方法对其进行了证明。

The authors investigate the Hanoi Tower problem with multi-pegs more than three. Based on the idea of dynamic programming, the reeursion formula of the least number of movements necessary for this problem is presented. The direct formula of the least number of movements necessary for this problem is given and proved by triple mathematical induction and pure eombinatorics.