Assume the maximum number of disks to be 6. We have to obtain the same stack on the third rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top. It consists of three rods and a number of disks of different sizes which can slide onto any rod. Thus, we come to the conclusion that for n disks we need to make (2^n)-1 moves.Īnd so on. The tower of Hanoi is a mathematical puzzle. Moving disk 1From rod:B To Rod:C Conclusion for Tower Of Hanoi The minimal number of moves required to solve a Tower of Hanoi puzzle is 2 n 1, where n is the number of disks. The objective of the puzzle is to move the entire. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. Void hanoi(int n,char from,char mid,char to)Ĭout<<"Moving disk "<< n <<"From rod:"<< from <<" To Rod:"<< to <<endl The Tower of Hanoi is a mathematical game or puzzle. ![]() } C++ Program for Tower Of Hanoi #include Moving the disks on top of already moved first disk ("Moving disk "+n+"From rod:"+from+"To Rod"+to) Move N-1 disks form auxiliary peg to the destination peg. Move Nth disk from source peg to destination peg. ![]() Steps to solve N number of disks via recursion: First, move top N-1 disks to auxiliary peg. Public static void hanoi(int n,char from,char mid,char to) The formula for calculating moves for solving N disks of Hanoi tower is: Total moves 2N - 1. JAVA Program for Tower Of Hanoi public class hanoi Let us now look at a recursive implementation of the same. We are thus moving n-1 disks on to the second tower, the last disk to the third tower and n-1 disks onto the first disk thus completing the shift. We would need 7 steps to shift all of them to the third ring. (3 moves)Īssumption: The disks are initially sorted We move the top(small) disk onto the next tower after which we move the second disk to the third tower and then eventually shift the first disk as well on to the third tower. The Tower of Hanoi is a mathematical puzzle containing 3. This simple recursive solution works for any number of disks.Let us look at how this problem can be handled when we have two disks In this post, you will learn the Tower of Hanoi program using the Java programming language. Try giving a different number of dicks as user input and check the output. Hanoi(disks - 1, auxiliary, source, target)ĭisks = int(input('Enter number of disks: '))Ĭase 1: when number of disk is 4 Enter number of disks: 4Ĭase 2: when number of disk is 2 Enter number of disks: 2Ĭase 3: when number of disk is 1 Enter number of disks: 1 The Wikipedia page on Tower of Hanoi has a section on a binary solution where the steps for an N-disk Tower of Hanoi are encoded in the binary representation of the numbers 0 to 2 N. Move (N-1) disks from peg B to peg C using the intermediate peg A.ĭef hanoi(disks, source, auxiliary, target): It can be programmed without recursion and without stacks (or simulated stacks).Move disk N (largest) from peg A to peg C using intermediate peg B.Move the first(N-1) disks from peg A to peg B using intermediate peg C.When N>1, then you can divide the original problem into three subproblems and solve them sequentially as follows. ![]() The problem has a recursive nature which leads to a straight forward recursive solution.Īssume there are N disks, if N=1, then you simply shift the disk from peg A to peg C. In case of three disks you can find the solution manually but for a larger number of disks like four or more than four then the situation becomes quite complex. Here is how you can solve the Tower of Hanoi problem for three disk.
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