The document describes the Tower of Hanoi puzzle and its solution. The puzzle consists of three rods and disks of different sizes that can slide onto any rod. The goal is to move all disks from one rod to another, following three rules: only one disk can be moved at a time, only the top disk can be removed, and no disk can be placed on top of a smaller disk. The document provides an algorithm and recursive function to solve the puzzle by moving disks one by one from the source rod to the auxiliary rod and then to the destination rod. It also includes a C++ program that implements the Tower of Hanoi puzzle and solution.

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Tower of Hanoi

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  • It consistsof three rods, and a number of disks ofdifferent sizes which can slide onto any rod.• The puzzle starts with the disks in a neat stack inascending order of size on one rod, the smallest atthe top, thus making a conical shape.
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  RULES• The missionis to move all the disks to some anothertower without violating the sequence of arrangement.A few rules to be followed for Tower of Hanoi are −1. Only one disk can be moved among the towers at anygiven time.2. Only the "top" disk can be removed.3. No large disk can sit over a small disk.• Following is an animated representation of solving aTower of Hanoi puzzle with three disks.• Tower of Hanoi puzzle with n disks can be solved inminimum 2n−1 steps. It is shows that a puzzle with 3disks has taken 23 - 1 = 7 steps.
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  ALGORITHM• If wehave only one disk ,then it can easily be moved fromsource to destination peg.• If we have 2 disks −• First, we move the smaller (top) disk to aux peg.• Then, we move the larger (bottom) disk to destinationpeg.• And finally, we move the smaller disk from aux todestination peg.• To move n disks from source to destination, The steps tofollow are -• Step 1 − Move n-1 disks from source to aux• Step 2 − Move nth disk from source to dest• Step 3 − Move n-1 disks from aux to dest
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  A recursive algorithmfor Tower of Hanoi can bedriven as follows −• START• ProcedureHanoi(disk, source,dest, aux)• IF disk ==1, THEN– move disk from source to dest• ELSE• Move(disk -1, source, dest, aux)// Step 1• Move(1, source, aux,dest)// Step 2– move disk from source to dest• Move(disk -1, aux, source, dest)// Step 3• END IF• ENDProcedure• STOP
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  PROGRAM TO IMPLEMENTTOWEROF HANOI:• #include <iostream.h>• #include <conio.h>• void tower(int a, char source, char aux, char dest)• {• if(a==1)• {• cout<<"ttMove disc 1 from "<<source<<" to "<<dest<<"n";• return;• }• else{• tower(a-1,source,dest,aux);• cout<<"ttMove disc "<<a<<" from "<<souce<<" to "<<dest<<"n";• tower(a-1,aux,source,dest);• }• }
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  • void main()•{• clrscr();• int n;• cout<<"ntt*****Tower of Hanoi*****n";• cout<<"ttEnter number of discs : ";• cin>>n;• cout<<"nn";• tower(n,'A','B','C');• getch();• }
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  OUTPUT
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  Thank You