The towers of hanoi: generalizations, specializations and algorithms

Abstract

Some variants of the classical problem of Towers of Hanoi incorporating new pragmatic constraints are considered. The classical problem is extended to the multi-peg case. A batched online variant is also proposed. The case wherein not all disks are distinct is also considered. Recursive algorithms for solving variants of the Towers of Hanoi problem incorporating one or more of the above constraints are proposed and their optimality properties are discussed.

Keywords:

• Algorithm design and analysis
• combinatorial algorithms
• Towers of Hanoi
• recursive definition
• dynamic programming