六柱Hanoi塔问题研究

Algorithm and Time Complexity Analysis of Six - pole Hanoi Tower Problem

运用分治与递归方法,得到一个求解六柱Hanoi塔问题的算法,用这种算法对问题进行求解,得出了n≤15时移动盘子的最少步数,采用分割自然数集的思想,给出了用该算法求解n个盘子的六柱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,并用数学归纳法进行了证明。

By using dividing,combining and recursive method in this paper,it gives algorithm for solving 6-pole Hanoi tower problem,lists the step numbers of movements necessary for the 6-pole Hanoi tower problem by applying this algorithm.Based on the idea of cutting natural number set,it puts forward a time complexity formula and the number of remaining disks to calculate step numbers of movements necessary for the 6-pole Hanoi tower problem,and proves time complexity formula by using mathematical induction.