The weighted Tower of Hanoi
El-Mehdi Mehiri, Hacène Belbachir · Discrete Mathematics Algorithms and Applications · 2023
The weighted Tower of Hanoi problem is a new generalization of the classical Tower of Hanoi problem, where a move of a disc between two pegs [Formula: see text] and [Formula: see text] is weighted by a positive real [Formula: see text]. This new problem generalizes the concept of finding the minimum number of moves to solve the Tower of Hanoi, to find a sequence of moves with the minimum total weight. We present an optimal dynamic algorithm to solve the weighted Tower of Hanoi problem, as well as some of its properties. We also show the link of this generalization to the Tower of Hanoi variants with restricted disc moves, and how this new problem can generalize the concept of restricting a disc move.