#Scheme hanoi towers how to#

Hanoi(disk - 1, aux, dest, source) // Step 3 Hanoi(disk - 1, source, aux, dest) // Step 1 The steps to follow are − Step 1 − Move n-1 disks from source to aux Step 2 − Move n th disk from source to dest Step 3 − Move n-1 disks from aux to destĪ recursive algorithm for Tower of Hanoi can be driven as follows − We can imagine to apply the same in a recursive way for all given set of disks. Our ultimate aim is to move disk n from source to destination and then put all other (n1) disks onto it. The largest disk (n th disk) is in one part and all other (n-1) disks are in the second part. We divide the stack of disks in two parts.

So now, we are in a position to design an algorithm for Tower of Hanoi with more than two disks. And finally, we move the smaller disk from aux to destination peg.Then, we move the larger (bottom) disk to destination peg.First, we move the smaller (top) disk to aux peg.If we have only one disk, then it can easily be moved from source to destination peg. We mark three towers with name, source, destination and aux (only to help moving the disks). Shifting of discs from source tower to target tower. Tower Of Hanoi is a Puzzle involving the usage of Stacks. The Tower of Hanoi puzzle was invented by the French mathematician Edouard Lucas in 1883.

#Scheme hanoi towers how to#

To write an algorithm for Tower of Hanoi, first we need to learn how to solve this problem with lesser amount of disks, say → 1 or 2. Tower of Hanoi (Application Of Stacks) -Vinit Dantkale. This presentation shows that a puzzle with 3 disks has taken 2 3 - 1 = 7 steps. Tower of Hanoi puzzle with n disks can be solved in minimum 2 n−1 steps.

No large disk can sit over a small disk.įollowing is an animated representation of solving a Tower of Hanoi puzzle with three disks.

Only one disk can be moved among the towers at any given time.

A few rules to be followed for Tower of Hanoi are −

The mission is to move all the disks to some another tower without violating the sequence of arrangement. There are other variations of the puzzle where the number of disks increase, but the tower count remains the same. the smaller one sits over the larger one. These rings are of different sizes and stacked upon in an ascending order, i.e. Tower of Hanoi, is a mathematical puzzle which consists of three towers (pegs) and more than one rings is as depicted −