Python Program for Tower of Hanoi
The Tower of Hanoi is a classic mathematical puzzle that involves moving a set of disks from one rod to another, adhering to specific rules. In this Python program, we’ll explore how to solve the Tower of Hanoi using recursion, a fundamental programming technique that allows us to break down this complex problem into simpler, manageable sub-problems. The program will demonstrate the sequence of moves required to transfer the disks between the rods efficiently, providing a clear example of recursive problem-solving in action. This educational example not only enhances understanding of recursion but also offers insight into algorithmic thinking for solving puzzles.
What are the rules of the Tower of Hanoi?
Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:
- Only one disk can be moved at a time.
- Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e. a disk can only be moved if it is the uppermost disk on a stack.
- No disk may be placed on top of a smaller disk.
Note: Transferring the top n-1 disks from the source rod to the Auxiliary rod can again be thought of as a fresh problem and can be solved in the same manner.
Tower of Hanoi Using Recursion
The function recursively breaks down the problem of moving n disks into smaller problems of moving n-1 disks. It alternates the roles of the rods (source, destination, auxiliary) in each recursive call to facilitate the step-by-step transfer of disks according to the rules of the Tower of Hanoi puzzle. The rules are that you can only move one disk at a time and a larger disk may not be placed on top of a smaller disk.
# Recursive Python function to solve the tower of hanoi
def TowerOfHanoi(n , source, destination, auxiliary):
if n==1:
print ("Move disk 1 from source",source,"to destination",destination)
return
TowerOfHanoi(n-1, source, auxiliary, destination)
print ("Move disk",n,"from source",source,"to destination",destination)
TowerOfHanoi(n-1, auxiliary, destination, source)
# Driver code
n = 4
TowerOfHanoi(n,'A','B','C')
# A, C, B are the name of rods
Output
Move disk 1 from source A to destination C Move disk 2 from source A to destination B Move disk 1 from source C to destination B Move disk 3 from source A to destination C Move disk 1 from source B to destination A Move disk 2 from source B to destination C Move disk 1 from source A to destination C Move disk 4 from source A to destination B Move disk 1 from source C to destination B Move disk 2 from source C to destination A Move disk 1 from source B to destination A Move disk 3 from source C to destination B Move disk 1 from source A to destination C Move disk 2 from source A to destination B Move disk 1 from source C to destination B
Time Complexity: O(2n)
Auxiliary Space: O(n)
Practice Tower of Hanoi Problem Yourself
