六柱Hanoi塔问题研究  

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

作　　者：赵天玉[1] 张卫[1] 

机构地区：[1]长江大学信息与数学学院,湖北荆州434023

出　　处：《长江大学学报（自科版）（上旬）》2008年第1期6-9,共4页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

摘　　要：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.

关 键 词：HANOI塔 算法 时间复杂度 区 剩余盘子数 

分 类 号：O122.4[理学—数学]