towers of Hanoi

(classic problem)

Definition: Given three posts (towers) and n disks of decreasing sizes, move the disks from one post to another one at a time without putting a larger disk on a smaller one. The minimum is 2ⁿ-1 moves. The "ancient legend" was invented by De Parville in 1884.

Note: A solution using recursion is: to move n disks from post A to post B 1) recursively move the top n-1 disks from post A to C, 2) move the n^th disk from A to B, and 3) recursively move the n-1 disks from C to B. A solution using iteration is: on odd-numbered moves, move the smallest disk clockwise. On even-numbered moves, make the single other move which is possible.

[GCG92] gives generalizations of the puzzle, algorithms, and proofs.

Author: PEB

Implementation

(Python). (JavaScript)

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 21 April 2022.
HTML page formatted Thu Apr 21 14:52:02 2022.

Cite this as:
Paul E. Black, "towers of Hanoi", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 21 April 2022. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/towersOfHanoi.html