Abstract
We present the iterative solutions of the Towers of Hanoi problems (standard, cyclic, and generalized) using the program transformation methodology of Burstall-Darlington. We derive algorithms with minimal time × space requirements. Their correctness proofs are trivial, as usual when applying the program transformation technique.
Similar content being viewed by others
Change history
09 December 2019
In the originally published version, the author found some subsequent corrections. It should read correct.
28 November 2019
In the originally published version, the author found some subsequent corrections. It should read correct.
References
M. D. Atkinson,The cyclic Towers of Hanoi, Information Processing Letters 13 (1981), 118–119.
P. Buneman and L. Levy,The Towers of Hanoi problem, Information Processing Letters 10 (1980), 243–244.
R. M. Burstall and J. Darlington,A transformation system for developing recursive programs, J.A.C.M., Vol. 24, No. 1 (1977) 44–67.
E. W. Dijkstra,A short introduction to the art of programming, EWD316 (1971).
M. C. Er,The generalized Towers of Hanoi problem, Private Communication.
M. C. Er,An iterative solution to the generalized Towers of Hanoi problem, BIT 23 (1983), 295–302.
P. J. Hayes,A note on the Towers of Hanoi problem, Computer Journal 20 (1977), 282–285.
M. S. Paterson and C. E. Hewitt,Comparative schematology, Conference on Concurrent Systems and Parallel Computation Project MAC, Woods Hole, Mass. June 2–5 (1970), 119–127.
A. Pettorossi,Methodologies for program transformation and memoing. Ph.D. Thesis, Computer Science Department, Edinburgh University (1984).
S. A. Walker and H. R. Strong,Characterization of flowchartable recursions, Journal of Computer and System Sciences 7(4) (1973), 404–447.
T. R. Walsh,Iteration strikes back at the Cyclic Towers of Hanoi. Information Processing Letters, 16 (1983), 91–93.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pettorossi, A. Towers of Hanoi problems: Deriving iterative solutions by program transformations. BIT 25, 327–334 (1985). https://doi.org/10.1007/BF01934378
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01934378