The Tower of Hanoi Problem and its Variants
نویسندگان
چکیده
منابع مشابه
Exponential vs. Subexponential Tower of Hanoi Variants
We deal here with Tower of Hanoi variants played on digraphs. A major source for such variants is achieved by adding pegs and/or restricting direct moves between certain pairs of pegs. It is natural to represent a variant of this kind by a directed graph whose vertices are the pegs, and an arc from one vertex to another indicates that it is allowed to move a disk from the former peg to the latt...
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The generalized Tower of Hanoi problem with h ≥ 4 pegs is known to require a sub-exponentially fast growing number of moves in order to transfer a pile of n disks from one peg to another. In this paper we study the Pathh variant, where the pegs are placed along a line, and disks can be moved from a peg to its nearest neighbor(s) only. Whereas in the simple variant there are h(h−1)/2 possible bi...
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We study two aspects of a generalization of the Tower of Hanoi puzzle. In 1981, D. Wood suggested its variant, where a bigger disk may be placed higher than a smaller one if their size difference is less than k. In 1992, D. Poole suggested a natural disk-moving strategy for this problem, but only in 2005, the authors proved it be optimal in the general case. We describe the family of all optima...
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By making the moving direction of each disc explicit in the representation, a bit-string so constructed can be used to drive the Tower of Hanoi algorithm. The behaviour of disc moves is further analyzed based on the bit-string representation. It has been shown that the bit-string for moving n discs can be used to generate successively the Gray codes of n bits.
متن کاملOn a question of Leiss regarding the Hanoi Tower problem
The Tower of Hanoi problem is generalized in such a way that the pegs are located at the vertices of a directed graph G, and moves of disks may be made only along edges of G. Leiss obtained a complete characterization of graphs in which arbitrarily many disks can be moved from the source vertex S to the destination vertex D. Here we consider graphs which do not satisfy this characterization; he...
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ژورنال
عنوان ژورنال: GANIT: Journal of Bangladesh Mathematical Society
سال: 2016
ISSN: 2224-5111,1606-3694
DOI: 10.3329/ganit.v35i0.28578