In pseudo-code (i.e. To solve a 1-disk Tower of Hanoi, simply move the disk from post A to post C. Szegedy, M.: In how many steps the k peg version of the towers of hanoi game can be solved? In: Meinel, C., Tison, S. The simplest form of the Tower of Hanoi puzzle has only 1 disk. Poole, D.: The Bottleneck Towers of Hanoi Problem. Manuscript (2005)ĭinitz, Y., Solomon, S.: Optimal algorithms for tower of hanoi problems with relaxed placement rules. of Mathematics and Computer Science, Ben-Gurion University (1998)Ĭhen, X., Tian, B., Wang, L.: Santa Claus’ Towers of Hanoi. Final Project Report, supervised by Berend, D., Dept. This process is experimental and the keywords may be updated as the learning algorithm improves.īeneditkis, S., Safro, I.: Generalizations of the Tower of Hanoi Problem. These keywords were added by machine and not by the authors. In this approach we recursively call a function twice to place the disk in desired places or.
Finally, we prove that the average length of shortest sequence of moves, over all pairs of initial and final configurations, is the same as the above diameter, up to a constant factor. Following is the approach for solving the tower of hanoi problem. Besides, we prove a tight bound for the diameter of the configuration graph of the problem suggested by Wood. We describe the family of all optimal solutions to this problem and present a closed formula for their number, as a function of the number of disks and 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. But you cannot place a larger disk onto a smaller disk. 2) Each move consists of taking the upper disk from one of the stacks and placing it on. Object of the game is to move all the disks over to Tower 3 (with your mouse).
The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: 1) Only one disk can be moved at a time. 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. Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. We study two aspects of a generalization of the Tower of Hanoi puzzle.