![]() ![]() To check the implementation in C programming, click here. 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 − This video is about an in depth look at one of the most challenging recursive problems for computer science students: Towers of Hanoi. 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). 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. 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. The Tower of Hanoi problem is generalized in such a way that the pegs are located at the vertices of a directed graph GG, and moves of disks may be made only along edges of G. 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. PJFBTSEAQS Childrens 10-Layer Hanoi Tower Wooden Tower Ring Puzzle, Develop Logical Thinking Clearance Toy Hanoi Tower Educational Toy Wooden Puzzle.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. 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, is a mathematical puzzle which consists of three towers (pegs) and more than one rings is as depicted − 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. 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. 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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