Question

use c++

Every programmer must grapple with certain classic problems,
and the Towers problem is one of the most famous of these. Legend has it that
in a temple in the Far East, priests are attempting to move a stack of disks from one peg to another.
The initial stack had 64 disks threaded onto one peg and arranged from bottom to top by decreasing
size. The priests are attempting to move the stack from this peg to a second peg under the constraints
that exactly one disk is moved at a time, and at no time may a larger disk be placed above a smaller
disk. A third peg is available for temporarily holding the disks. Supposedly the world will end when
the priests complete their task, so there is little incentive for us to facilitate their efforts.
Let’s assume that the priests are attempting to move the disks from peg 1 to peg 3. We wish to
develop an algorithm that will print the precise sequence of disk-to-disk peg transfers.
If we were to approach this problem with conventional methods, we’d rapidly find ourselves
hopelessly knotted up in managing the disks. Instead, if we attack the problem with recursion in
mind, it immediately becomes tractable. Moving n disks can be viewed in terms of moving only
n – 1 disks (and hence the recursion) as follows:
a) Move n – 1 disks from peg 1 to peg 2, using peg 3 as a temporary holding area.
b) Move the last disk (the largest) from peg 1 to peg 3.
c) Move the n – 1 disks from peg 2 to peg 3, using peg 1 as a temporary holding area.
The process ends when the last task involves moving n = 1 disk, i.e., the base case. This is
accomplished by trivially moving the disk without the need for a temporary holding area.
Write a program to solve the Towers of Hanoi problem. Use a recursive function with four
parameters:
a) The number of disks to be moved
b) The peg on which these disks are initially threaded
c) The peg to which this stack of disks is to be moved
d) The peg to be used as a temporary holding area
Your program should print the precise instructions it will take to move the disks from the
starting peg to the destination peg. For example, to move a stack of three disks from peg 1 to peg 3,
your program should print the following series of moves:
1 → 3 (This means move one disk from peg 1 to peg 3.)
1 → 2
3 → 2
1 → 3
2 → 1
2 → 3
1 → 3*/

Answer 1

Code:

#include<iostream>
using namespace std;
void TOH(int n,char Sour, char Aux,char Des)
{
   if(n==1)
   {
       cout<<Sour<<"-->"<<Des<<endl;
       return;
   }
  
   TOH(n-1,Sour,Des,Aux);
   cout<<Sour<<"-->"<<Des<<endl;
   TOH(n-1,Aux,Sour,Des);
}

//main program
int main()
{
   int n;
   cout<<"TOWERS of Hanoi"<<endl;
   cout<<"Enter a number of disks to play. I'll give necessary moves."<<endl;  
   cin>>n;
   //calling the TOH
   TOH(n,'1','2','3');
   return 0;
}

Output:

Hope this helps.