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 the last rod then you have to move the first rod to the middle rod first and then to the last one.
Approach:
- Base Case: If the number of disks is 1, then move it to the middle rod first and then move it to the last rod.
- Recursive Case: In the recursive case, the following steps will produce the optimal solution:(All these moves follow the rules of the twisted Tower of Hanoi problem)
- We will move the first n-1 disks to the last rod first.
- Then move the largest disk to the middle rod.
- Move the first n-1 disk from the last rod to the first rod.
- Move the largest disk from the middle rod to the last rod.
- Move all n-1 disks from the first rod to the last rod.
Below is the implementation of the above approach:
C++
// C++ implementation#include <iostream>using namespace std;// Function to print the movesvoid 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 Codeint main(){ // Number of disks int n = 2; // Rods are in order // first(A), middle(B), last(C) twistedTOH(n, 'A', 'B', 'C'); return 0;} |
Java
// Java implementation of the approach import java.util.*;class GFG{// Function to print the movesstatic 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 Codepublic 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 |
Python3
# 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 |
C#
// C# implementation of the approach using System; class GFG{// Function to print the movesstatic 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 Codepublic 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 |
Javascript
<script>// Javascript program // Function to print the movesfunction twistedTOH(n, first, middle, last){ // Base case if (n == 1) { document.write("Move disk " + n + " from rod " + first + " to " + middle + " and then to " + last + "<br>"); return; } // Move n-1 disks from first to last twistedTOH(n - 1, first, middle, last); // Move largest disk from first to middle document.write("Move disk " + n + " from rod " + first + " to " + middle + "<br>"); // Move n-1 disks from last to first twistedTOH(n - 1, last, middle, first); // Move nth disk from middle to last document.write("Move disk " + n + " from rod " + middle + " to " + last + "<br>"); // Move n-1 disks from first to last twistedTOH(n - 1, first, middle, last);}// driver code// Number of disksvar n = 2;// Rods are in order// first(A), middle(B), last(C)twistedTOH(n, 'A', 'B', 'C');// This code contributed by shivani</script> |
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).
Auxiliary Space: O(n).
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
… [Trackback]
[…] There you will find 10417 more Information to that Topic: geeksforgeeks.org/twisted-tower-of-hanoi-problem/ […]