# (Homework Solution): This is a modified problem about the Tower of Hanoi, where there is an extra condition while

This is a modified problem about the Tower of Hanoi, where there is an extra condition while solving the problem:

Consider the Tower of Hanoi problem with peg A, B and C. We want to transfer a tower of n disks
from peg A to peg B, if direct moves between A and B are disallowed. (Each move must be to or
from peg C. As usual, a larger disk must never appear above a smaller one.)
(a) Write a pseudocode to solve the problem recursively.
(b) Set up a recurrence equation to count the number of steps to move n disks using your method
in (a).
(c) Solve the recurrence and give the complexity of your algorithm.

A) Recursive solution

from_rod=’A’, to_rod=’B’, aux_rod=’C’, n=no of disks

def TowerOfHanoi(n ,from_rod, to_rod, aux_rod):

if n == 1:

print “Move disk 1 from rod”,from_rod,”to rod”,aux_rod

print “Move disk 1 from rod”, aux_rod, “to rod”, to_rod

return

TowerOfHanoi(n-1,from_rod, to_rod, aux_rod)

print “Move disk”,n,”from rod”,from_rod,”to rod”,aux_rod

TowerOfHanoi(n-1,from_rod, to_rod, aux_rod)

print “Move disk”,n, “from rod”, aux_rod, “to rod”, to_rod

TowerOfHanoi(n-1,from_rod, to_rod, aux_rod)

b) Recurrence equation

Consider 0 disks then we need 0 moves. So T(0)=0.

Now let’s derive T(n) for n disks.

First move n-1 disks from A to B => T(n-1) moves.

Move last disk from A to C => 1 move.

Then move n-1 disks from B to A => T(n-1) moves.

Move last disk from C to B => 1 move.

Now move n-1 disks from A to B => T(n-1) moves.

So we get T(n)=T(n-1)+1+T(n-1)+1+T(n-1).

Here recurrence relation is:

T(0)= 0

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

C) Complexity

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

T(1) = 2 = 3-1

T(2) = 3*2+2= 8 = 9-1

T(3) = 3*8+2 = 26 = 27-1

We see that

It can be easily proved using induction on n.

So it gives complexity of algorithm  .

BONUS- Python Solution

# Recursive Python function to solve tower of hanoi

def TowerOfHanoi(n ,from_rod, to_rod, aux_rod):

if n == 1:

print “Move disk 1 from rod”,from_rod,”to rod”,aux_rod

print “Move disk 1 from rod”, aux_rod, “to rod”, to_rod

return

TowerOfHanoi(n-1,from_rod, to_rod, aux_rod)

print “Move disk”,n,”from rod”,from_rod,”to rod”,aux_rod

TowerOfHanoi(n-1,from_rod, to_rod, aux_rod)

print “Move disk”,n, “from rod”, aux_rod, “to rod”, to_rod

TowerOfHanoi(n-1,from_rod, to_rod, aux_rod)

n = 3

TowerOfHanoi(n, ‘A’, ‘B’, ‘C’)

# A, C, B are the name of rods

Order NOW for a 10% Discount
Pages (550 words)
Approximate price: -

Why Us?

Top Quality and Well-Researched Papers

All ourbpapers are written from scratch. In fact, Clients who ask for paraphrasing services are highly discouraged. We have writers ready to craft any paper from scratch and deliver quality ahead of time.

Our writers keeps you posted on your papers progress - providing you with paper outline/draft. You are also at liberty to communicate directly with your writer.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time, in many cases quite ahead of time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

## Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

## Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.