Programming hanoi towers code#

No disk may be placed on top of a smaller disk. Towers of Hanoi 8.6 Towers of Hanoi: In the classic problem of the Towers of Hanoi, you have 3 towers and N disks of different sizes which can slide onto any tower.

a disk can only be moved if it is the uppermost disk on a stack.

Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e.

The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: 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. Tower of Hanoi (also called the Tower of Brahma or Lucas’ Tower, and sometimes pluralized) is a mathematical game or puzzle. Scanner scanner = new Scanner(System.in) Public static final String SPARE_PEG = 'Spare' Public static final String TARGET_PEG = 'Target' Public static final String SOURCE_PEG = 'Source'

Programming hanoi towers code#

Towers of Hanoi solution source code in Java The program will print the moves of the towers of Hanoi solution in the console. The following Java program uses the above recursive strategy to solve Towers of Hanoi puzzle. The termination condition for recursion will be n=1. The first step of moving n-1 discs from source to spare peg is identical to our original problem, only difference being that the roles of the pegs change (spare peg becomes target and target peg becomes the spare peg)! This shows that we can recursively solve Towers of Hanoi.

Move n-1 discs from spare peg to target peg.

Move last disc from source peg to target peg.

Move n-1 discs from source peg to spare peg.

Move disc 1 from spare peg to target pegįor n number of discs we can generalize the above strategy as follows,.

Move disc 2 from source peg to target peg.Move disc 1 from source peg to spare peg.The iterative method in C is designed for do.

Let us look at the strategy of solving towers of Hanoi with just 2 discs. This method is used to repeat a specific group of statements until the program meets the termination condition. This puzzle can be concisely solved using recursion. For example, it would take 7(2 raised to 3 - 1) steps to move 3 discs from source peg to target peg.

The number of steps required to move n discs from source page to target peg is (2 raised to n - 1). Interestingly if the moves are made at the rate of one move per second, it will take more than 500 billion years to solve the puzzle! Solving Towers of Hanoi Using Recursion Priests believed that when the last move of the puzzle is completed, world will end. One popular myth about towers of Hanoi suggests that there was a temple in India where priests worked on solving a 64 disc towers of Hanoi puzzle (known as tower of Brahma). A disc cannot be placed over a smaller discįrench mathematician Edouard Lucas invented towers of Hanoi in 1883.Each move consists of taking one disc from a peg and putting on top of another peg.The aim of the game is to move all the discs to a target peg with the same order using just a spare peg. The size of the discs are different and they are kept on the source peg with the smallest on the top and the biggest one on the bottom. Towers of Hanoi is a well known mathematical game/puzzle involving three pegs and a number of discs.