A loopless approach to the multipeg towers of hanoi

Abstract

In [10] a recursive algorithm was proposed for the multipeg Towers of Hanoi problem, a generalization of the standard problem. Based on the observation of the recursive algorithm, a nonrecursive approach is obtained in this paper and many characteristics disclosed to remove the recursion. Among those is the interesting relation between the Towers and the binary representation of nonnegative integers, which greatly helps the establishment of the new approach. In addition, several classes of nonnegative integers with elegant combinatorial properties will be involved in establishing and analysing the new algorithm.

Keywords:

• Multipeg Towers of Hanoi
• standard Tower
• (w h)-Tower
• full Tower
• Tower level
• Tower depth
• moving route
• moving way
• binary controlling string
• f-number