五柱Hanoi塔问题研究

Research on Five-pole Hanoi Tower Problem

运用分治与递归方法,得到一个求解五柱Hanoi塔问题的算法。并用这种算法对问题进行求解,得出了n≤29时移动盘子的最少步数。采用分割自然数集的思想,给出了用此算法求解n个盘子的五柱Hanoi塔问题的时间复杂度(最少步数)公式及分次移动的剩余盘子数公式。

Dividing,combining and recursive method is used in this paper,solving algorithm of five-pole Hanoi tower problem is obtained.The step numbers of movements necessary for the 5-pole Hanoi tower problem are listed by applying this algorithm while.Based on the idea of cutting natural number set,a time complexity formula and the number of remaining disks are put forward to calculate step numbers of movements necessary for the 5-pole Hanoi tower problem,and the time complexity formula using mathematical induction are proved.