#Hanoi towers problem how to

In this article, we’ll study algorithms and the complexity of the Towers of Hanoi problem. Originally invented by a French mathematician named Édouard Lucas, this puzzle illustrates the power and elegance of recursion. Here the number of disks are 2, so this algorithm took (2 pow 3) – 1 = 8 – 1 = 7 steps. The Towers of Hanoi is a classic mathematical puzzle that has applications in both computer science and mathematics.

Here the number of disks are 2, so this algorithm took (2 pow 2) – 1 = 4 – 1 = 3 steps. '.format(disks, source, target))ĭisks = int(input('Enter number of disks: ')) Python Code: def tof(disks, source, middle, target):

Finally, move n-1 disks from the middle tower to the destination tower.

Then, move the nth disk from source tower to destination tower.

Move n-1 disks from source tower to middle tower.

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. The problem is based on 3 pegs (source, auxiliary and destination) and n disks. The algorithm for this problem as follows:- The tower of Hanoi is very well known recursive problem, also known as Tower of Lucas.

#Hanoi towers problem how to

How to solve the Tower of Hanoi Problem Algorithm for Tower of HanoiĬonsider the three towers as the source, middle, destination. See this animation below to understand more clearly: For example, if there are 3 disks, then the time to complete this algorithm takes (2 pow 3) -1 = 8 – 1 = 7 steps. Tower of Hanoi algorithm can be solved in (2 pow n) – 1 steps. A disk can be moved from one tower to another tower only if there is no disk on the top of the disk to be moved.That means no disk should be placed on top of a disk. The only small disk should have stayed at the top.In order to move the disks, some rules need to be followed. The main aim of this puzzle is to move all the disks from one tower to another tower. Tower of Hanoi is a mathematical puzzle which consists of three towers or rods and also consists of n disks. Thus, we have put an animation (collected from Wikimedia Commons) to make it more clear to the learners. With words it not easy to understand the problem of Tower of Hanoi. Self.In this Python tutorial, we will learn what is Tower of Hanoi algorithm and how to solve Tower of Hanoi problem in Python. Self.move(1, source, destination, auxiliary) Self.move(disc - 1, source, auxiliary, destination) Print(''.format(source, destination))ĭef move(self, disc, source, destination, auxiliary): Note: There must be a termination condition in the recursion problems.ĭef printMove(self, source, destination): In Backtracking we attempt solving a sub-problem, and if we don't reach the desired solution, then undo whatever we did for solving that sub-problem, and try solving another sub-problem ( Until we get to the goal). Let's suppose we have a problem A we subdivided it into B, C, and D. Recursion and backtracking: When a function calls itself, its called Recursion. (Breaking problem into smaller problems). Note: Tower of hanoi problem is an example of recursion and backtracking. Total move required to reach destination pillar is means if we have 3 disks we required (4 moves to reach destination pillar), if 4 disks 8 moves required and so on.

Įventually, you figure out that there is some pattern to the puzzle and with each increment in disks, the pattern could be followed recursively. So, basically when we have 2 disks we required 3 move to reach the destination. Step3: Move small disk to the Destination pillar(B).4 Step2: Move large disk to the Destination pillar (B). Step1: Move small disk to the auxiliary pillar (A). (let's take a look how many steps/ moves are required to make this happen). In the above diagram, following the rule of the game our target is move the disks from source pile (pillar) to the destination pillar. When we have two disk and 3 pillars (pile, A, B, C) So, here we are trying to solve that how many moves are required to solve a problem (It depends on number of disk). Īll disk move to destination pile from source pile.The larger disk should always be on the bottom and the smaller disk on top of it.(Even during intermediate move) Tower of hanoi is mathematical game puzzle where we have three pile (pillars) and n numbers of disk.