#MOVE METHOD HANOI TOWERS CODE#
#MOVE METHOD HANOI TOWERS SERIES#

#MOVE METHOD HANOI TOWERS SERIES#

+ 2 n-1 which is a GP series having common ratio r=2 and sum = 2 n - 1. Minimum steps required to move n disks from source to destįrom the above table, it is clear that for n disks, the minimum number of steps required are 1 + 2 1 + 2 2 + 2 3 +. The minimum number of steps required to move n disks from source to dest is quite intuitive from the time complexity analysis and also from the raw examples as shown in the table, Hence, the time complexity of the recursive solution of Tower of Hanoi is O(2n) which is exponential. $$TowerofHanoi(n, source, dest, aux) = ext-1$ Hence, the recursive solution for Tower of Hanoi having n disks can be written as follows, (again move all (n-1) disks from aux to dest. And finally, move disk 1 and disk 2 from aux to dest tower i.e.Then, move the 3 rd disk from source to dest tower i.e.First, move disk 1 and disk 2 from source to aux tower i.e.We can break down the above steps for n=3 into three major steps as follows, And at last, move disk 1 to dest tower on top of 2.Then move disk 2 to dest tower on top of disk 3.Again Move disk 1 from aux to source tower.Then, move disk 3 from source to dest tower.Now move disk 1 from dest to aux tower on top of disk 2.First, move disk 1 from source to dest tower. There are three poles in a row, the one on the left containing a series of discs of decreasing size, with the other two, empty.To solve this problem, we need to just move that disk to dest tower in one step. Let’s start the problem with n=1 disk at source tower. if disk 1 is on a tower, then all the disks below it should be less than 3. No large disk should be placed over a small disk.You can move only one disk at a time from the top of any tower.The task is to move all the disks from one tower, say source tower, to another tower, say dest tower, while following the below rules, Here’s what the tower of Hanoi looks for n=3, nth disk at the bottom and 1st disk at the top. These disks are stacked over one other on one of the towers in descending order of their size from bottom i.e. This is how you solve the Tower of Hanoi using recursion.Tower of Hanoi is a mathematical puzzle which consists of three towers(or pegs) and n disks of different sizes, numbered from 1, the smallest disk, to n, the largest disk. The formula to calculate the number of steps for n disks is : (2^n)-1 The output for n=5 is : Take disk 1 from rod A to rod C

#MOVE METHOD HANOI TOWERS CODE#

You can run the code for any number of disks. We can understand the process using the following illustration. The output for the code is: Take disk 1 from rod A to rod C The base case in our code is when we only have one disk. Let’s begin with understanding the two main parts of the code to solve the Tower of Hanoi problem. Implementing the Solution to Tower of Hanoi in Java In the function we write, we will print the movement of the disks. However, we can use this to create a function that does it recursively. Of course, you can’t do it like this because of the constraints. Take the disk number 1 and 2 to tower B.To get the three disks over to the final tower you need to : We solve this question using simple recursion. Let’s name the towers as A,B,C and the disks as 1,2,3. Theoretical Solution to the Tower of Hanoi Problem Since you can only move one disk at a time, the disk you move will have to be at the top of its tower. To do this you have an extra tower, it is known as helper/auxiliary tower. You can only move one disk at a time and never place a smaller disk over a larger disk. So you need to move all the disks from the first tower over to the last. A larger disk can not be placed on a smaller disk. While moving the disks, certain rules must be followed. Problem Statement Move all the disks stacked on the first tower over to the last tower using a helper tower in the middle. The problem is to move the discs, one at a time from peg to peg in such a way that this is always true and to. It is associated with a legend of a Hindu temple where the puzzle was supposedly used to increase the mental discipline of young priests. A disc is never stacked on top of a smaller disc. Tower of Hanoi Default Setupįun fact : This game was invented by a French mathematician Édouard Lucas in the 19th century. The disks are stacked in such a way that a disk is always over a disk bigger than itself. Initially all the disks are stacked on the first tower. The disks can be moved from one peg to another. The problem setup consists of three rods/pegs and n disks. The Tower of Hanoi is a classic problem in the world of programming.

Move method hanoi towers