Twisted Tower of Hanoi Problem

The basic version of the Tower of Hanoi can be found here.
It is a twisted Tower of Hanoi problem. In which, all rules are the same with an addition of a rule:
You can not move any disk directly from the first rod to last rod i.e., If you want to move a disk from the first rod to last rod then you have to move the first rod to middle rod first and then to the last one.

Approach:

  • Base Case: If the number of disk is 1, then move it to the middle rod first and then move it to the last rod.
  • Recursive Case: In the recursive case following steps will produce the optimal solution:(All these moves are following the rules of twisted Tower of Hanoi problem)
    1. We will move first n-1 disks to the last rod first.
    2. Then move the largest disk to the middle rod.
    3. Move first n-1 disks from the last rod to the first rod.
    4. Move the largest disk at the middle rod to the last rod.
    5. Move all n-1 disks from the first rode to the last rod.

Below is the implementation of the above approach:

C++



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// C++ implementation
#include <iostream>
using namespace std;
  
// Function to print the moves
void twistedTOH(int n, char first,
                char middle, char last)
{
    // Base case
    if (n == 1) {
  
        cout << "Move disk " << n
             << " from rod " << first
             << " to " << middle
             << " and then to "
             << last << endl;
  
        return;
    }
  
    // Move n-1 disks from first to last
    twistedTOH(n - 1, first, middle, last);
  
    // Move largest disk from first to middle
    cout << "Move disk " << n
         << " from rod " << first
         << " to " << middle << endl;
  
    // Move n-1 disks from last to first
    twistedTOH(n - 1, last, middle, first);
  
    // Move nth disk from middle to last
    cout << "Move disk " << n
         << " from rod " << middle
         << " to " << last << endl;
  
    // Move n-1 disks from first to last
    twistedTOH(n - 1, first, middle, last);
}
  
// Driver's Code
int main()
{
    // Number of disks
    int n = 2;
  
    // Rods are in order
    // first(A), middle(B), last(C)
    twistedTOH(n, 'A', 'B', 'C');
  
    return 0;
}

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Java














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// Java implementation of the approach  


import java.util.*; 


  


class GFG 


{ 


  


// Function to print the moves 


static void twistedTOH(int n, char first, 


                char middle, char last) 


{ 


    // Base case 


    if (n == 1) 


    { 


  


        System.out.println("Move disk " + n + " from rod " + 


                                   first + " to " + middle +  


                                    " and then to " + last); 


  


        return; 


    } 


  


    // Move n-1 disks from first to last 


    twistedTOH(n - 1, first, middle, last); 


  


    // Move largest disk from first to middle 


    System.out.println("Move disk " + n +  


                       " from rod " + first +  


                       " to " + middle); 


  


    // Move n-1 disks from last to first 


    twistedTOH(n - 1, last, middle, first); 


  


    // Move nth disk from middle to last 


    System.out.println("Move disk " + n +  


                       " from rod " + middle +  


                       " to " + last); 


  


    // Move n-1 disks from first to last 


    twistedTOH(n - 1, first, middle, last); 


} 


  


// Driver Code 


public static void main(String[] args) 


{ 


    // Number of disks 


    int n = 2; 


  


    // Rods are in order 


    // first(A), middle(B), last(C) 


    twistedTOH(n, 'A', 'B', 'C'); 


} 


} 


  


// This code is contributed by PrinciRaj1992 



















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Python3














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# Python3 implementation of above approach 


  


# Function to print the moves  


def twistedTOH(n, first, middle, last):  


      


    # Base case  


    if (n == 1):  


  


        print("Move disk", n, "from rod", first,  


              "to", middle, "and then to", last)  


  


        return


  


    # Move n-1 disks from first to last  


    twistedTOH(n - 1, first, middle, last)  


  


    # Move largest disk from first to middle  


    print("Move disk", n, "from rod", 


                 first, "to", middle)  


  


    # Move n-1 disks from last to first  


    twistedTOH(n - 1, last, middle, first)  


  


    # Move nth disk from middle to last  


    print("Move disk", n, "from rod",  


                 middle, "to", last)  


  


    # Move n-1 disks from first to last  


    twistedTOH(n - 1, first, middle, last) 


  


# Driver Code  


  


# Number of disks  


n = 2


  


# Rods are in order  


# first(A), middle(B), last(C)  


twistedTOH(n, 'A', 'B', 'C')  


  


# This code is contributed by 


# divyamohan123 



















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C#














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// C# implementation of the approach  


using System; 


      


class GFG 


{ 


  


// Function to print the moves 


static void twistedTOH(int n, char first, 


                       char middle, char last) 


{ 


    // Base case 


    if (n == 1) 


    { 


        Console.WriteLine("Move disk " + n + " from rod " + 


                                  first + " to " + middle +  


                                   " and then to " + last); 


  


        return; 


    } 


  


    // Move n-1 disks from first to last 


    twistedTOH(n - 1, first, middle, last); 


  


    // Move largest disk from first to middle 


    Console.WriteLine("Move disk " + n +  


                      " from rod " + first +  


                      " to " + middle); 


  


    // Move n-1 disks from last to first 


    twistedTOH(n - 1, last, middle, first); 


  


    // Move nth disk from middle to last 


    Console.WriteLine("Move disk " + n +  


                      " from rod " + middle +  


                      " to " + last); 


  


    // Move n-1 disks from first to last 


    twistedTOH(n - 1, first, middle, last); 


} 


  


// Driver Code 


public static void Main(String[] args) 


{ 


    // Number of disks 


    int n = 2; 


  


    // Rods are in order 


    // first(A), middle(B), last(C) 


    twistedTOH(n, 'A', 'B', 'C'); 


} 


} 


      


// This code is contributed by PrinciRaj1992 



















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Output:


Move disk 1 from rod A to B and then to C
Move disk 2 from rod A to B
Move disk 1 from rod C to B and then to A
Move disk 2 from rod B to C
Move disk 1 from rod A to B and then to C





Recurrence formula:


T(n) = T(n-1) + 1 + T(n-1) + 1 + T(n-1)
     = 3 * T(n-1) + 2

where n is the number of disks.



By solving this recurrence the Time Complexity will be O(3n).



          
          
          

          

    

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