A Larger disk cannot be placed on a smaller disk. Move the n-1 disk from C to B using A as auxiliary. Tower of Hanoi is the problem of shifting all n disks from source peg to destination peg using auxiliary peg with the following constraints : Only one disk can be moved at a time.Move the remaining nth disk from A to B.Move the top n-1 disks from A to C(auxiliary peg).If n = 1, move the single disk from A to B and stop.This function keeps getting called until the disk you are. Algorithm Of Tower Of Hanoi Puzzle A = source peg, B = destination peg, C = auxiliary peg Our hanoi function is really solving the sub-problem of moving N-1 disks from one location to another. This presentation shows that a puzzle with 3 disks has taken 2 3 – 1 = 7 steps. The objective of the game is to shift the entire stack of disks from one rod to another rod following these three rules : Only one disk can be moved at a time. It is a mathematical game or puzzle that consists of three rods with ’n’ number of disks of different diameters. This function can ignore the third tower for now. In the single disc case, our origin tower contains 1, and the destination tower contains, as its currently empty. Each stack contains the discs currently on that tower. Maybe you noticed our hanoi function did not mutated objects because it calls itself with new arguments rather than using existing objects.Tower of Hanoi puzzle with n disks can be solved in minimum 2 n−1 steps. The Tower of Hanoi is also known as the Tower of Brahma or the Lucas Tower. Our function can take a stack (or list) for each tower. Move the top n-1 disks from A to C(auxiliary. If n 1, move the single disk from A to B and stop. Algorithm Of Tower Of Hanoi Puzzle A source peg, B destination peg, C auxiliary peg. This presentation shows that a puzzle with 3 disks has taken 2 3 1 7 steps. It is important to understand that a recursive function needs a mechanism to stop executing, otherwise it will run forever or in the worst case it will cause errors. Tower of Hanoi puzzle with n disks can be solved in minimum 2 n 1 steps. I do not want you to understand the math behind the Hanoi Tower algorithm, just want you to realize that calling function hanoi in the same function hanoi is recursion. Notice, the arguments are the same but in different order, again allowing us to solve the puzzle. The Tower of Hanoi and Tower of London have become well-established executive function tasks that presumably tap cognitive skills mediated by the frontal cortex. Hanoi(number - 1, auxiliar, origin, destination) Puts "Moved disc from #"įinally, we will call hanoi again because we want to move the disks. Third, we also want to print whenever the disks are moving from one place to another. Hanoi(number - 1, origin, destination, auxiliar)īasically, we are calling the same function ( hanoi) but using new arguments, allowing us to solve the puzzle. Second, we will have to decrement the amount of disks when calling hanoi and pass along the origin, destination and auxiliar. Our next mission is to actually figure out the puzzle (moving all the disks from "A" to "C"). Our program continues executing unless the disks is equal to zero. It must stop when all the disks has been moved to the column C. The idea is to write a function that calls itself until the puzzle is solved.įirst, determine when to stop the function execution. To make this example easier to understand, let's pretend our Hanoi Tower has 4 disks, and columns A, B, C. Enter fullscreen mode Exit fullscreen mode
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