Generalized multi-peg tower of hanoi problem
نویسندگان
چکیده
منابع مشابه
Complexity of the Path Multi-Peg Tower of Hanoi
The Tower of Hanoi problem with h ≥ 4 pegs is long known to require a sub-exponential number of moves in order to transfer a pile of n disks from one peg to another. In this paper we discuss 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 bi-directional interconnectio...
متن کاملExplorations in 4-peg Tower of Hanoi
Finding an optimal solution to the 4-peg version of the classic Tower of Hanoi problem has been an open problem since the 19th century, despite the existence of a presumed-optimal solution. We verify that the presumed-optimal Frame-Stewart algorithm for 4-peg Tower of Hanoi is indeed optimal, for up to 20 discs. We also develop a distributed Tower of Hanoi algorithm, and present 2D and 3D repre...
متن کاملCombinatorics of topmost discs of multi-peg Tower of Hanoi problem
Combinatorial properties of the multi-peg Tower of Hanoi problem on n discs and p pegs are studied. Top-maps are introduced as maps which reflect topmost discs of regular states. We study these maps from several points of view. We also count the number of edges in graphs of the multi-peg Tower of Hanoi problem and in this way obtain some combinatorial identities.
متن کاملOn the Frame-Stewart algorithm for the multi-peg Tower of Hanoi problem
It is proved that seven different approaches to the multi-peg Tower of Hanoi problem are all equivalent. Among them the classical approaches of Stewart and Frame from 1941 can be found.
متن کاملToward a Dynamic Programming Solution for the 4-peg Tower of Hanoi Problem with Configurations
The Frame-Stewart algorithm for the 4-peg variant of the Tower of Hanoi, introduced in 1941, partitions disks into intermediate towers before moving the remaining disks to their destination. Algorithms that partition the disks have not been proven to be optimal, although they have been verified for up to 30 disks. This paper presents a dynamic programming approach to this algorithm, using tabli...
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ژورنال
عنوان ژورنال: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
سال: 1996
ISSN: 0334-2700,1839-4078
DOI: 10.1017/s033427000000059x