Tower Of Hanoi Program In C Using Graphics To Show

This C Program uses recursive function & solves the tower of hanoi. The tower of hanoi is a mathematical puzzle. It consists of threerods, and a number of disks of different sizes which can slideonto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top. We have to obtain the same stack on the third rod.

Here is the source code of the C program for solving towers of hanoi. The C Program is successfully compiled and run on a Linux system. The program output is also shown below.

Code for Program that displays graphical representation of tower of hanoi in. Transfer(n,'L','R','C'); coutView The Solution Graphically. Transfer(int n,char from,char to,char temp) if(n0) transfer(n-1,from,temp,to). As a Linear Queue ( in graphics ) Library Management System Program to.

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• Algorithm

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Tower of Hanoi, is a mathematical puzzle which consists of three towers (pegs) and more than one rings is as depicted −

These rings are of different sizes and stacked upon in an ascending order, i.e. the smaller one sits over the larger one. There are other variations of the puzzle where the number of disks increase, but the tower count remains the same.

Rules

The mission is to move all the disks to some another tower without violating the sequence of arrangement. A few rules to be followed for Tower of Hanoi are −

• Only one disk can be moved among the towers at any given time.
• Only the 'top' disk can be removed.
• No large disk can sit over a small disk.

Following is an animated representation of solving a Tower of Hanoi puzzle with three disks.

Tower of Hanoi puzzle with n disks can be solved in minimum 2ⁿ−1 steps. This presentation shows that a puzzle with 3 disks has taken 2³ - 1 = 7 steps.

Algorithm

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. We mark three towers with name, source, destination and aux (only to help moving the disks). If we have only one disk, then it can easily be moved from source to destination peg.

If we have 2 disks −

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• First, we move the smaller (top) disk to aux peg.
• Then, we move the larger (bottom) disk to destination peg.
• And finally, we move the smaller disk from aux to destination peg.

So now, we are in a position to design an algorithm for Tower of Hanoi with more than two disks. We divide the stack of disks in two parts. The largest disk (n^th disk) is in one part and all other (n-1) disks are in the second part.

Our ultimate aim is to move disk n from source to destination and then put all other (n1) disks onto it. We can imagine to apply the same in a recursive way for all given set of disks.

The steps to follow are −

A recursive algorithm for Tower of Hanoi can be driven as follows −

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To check the implementation in C programming, click here.