On May 10, 2007, at 5:34 PM, Daniel W. wrote:
Anyway, here’s my (long) object-oriented version of the ToH. Tell me
what you think. Oh, and if you have suggestions on where someone NOT
interested in going to college can do to learn the math necessary to
start programming “for real,” please share! Thanks!
Good choice of a relatively simple problem to solve. (I’m a newbie
to Ruby, too. I enjoyed putting a solution together. Thanks!)
Three concepts come to mind in this case:
- Understanding the problem (requirements)
- Abstraction
- Recursion
Understanding the problem (requirements):
It’s important to understand what you’re trying to solve. I don’t
mean how to solve it, but what is the goal? What are the
requirements for your solution? Just saying, “solve the Towers of
Hanoi” is too vague. Do you want to just print out the list of
movements from one tower to another? Do you want to print out which
ring it is that’s moving? Do you want to ensure that the move is
legal? And what does “legal” mean anyway? (No ring may be placed on
top of a smaller ring.) In the code below, I chose to print out the
individual moves along with the ring being moved. I chose not to
verify that every move is legal.
Abstraction:
Distill things down to their essence. You don’t have to be literal
by modeling every object in the real world. In fact, many
interesting problems don’t map well (if at all) to the real world. I
mention this because you have a “hand” object in your code, and that
seemed like too much detail. An object for the game as a whole, and
objects for each tower/peg, and for each disc/ring are all
reasonable. You’ll notice in my solution below, I didn’t create a
separate class for rings/discs; all I really care about is indicating
relative size, so a number from 1 to N is good enough, which means I
can use an ordinary integer.
Recursion:
Recursion is defining a solution based on a similar, but smaller
version of the same problem. You define how the larger problem in
terms of the smaller problem, and define what the smallest problem is
(and how to solve it – which is often trivial). (There’s also
“mutual recursion” which involves defining several routines in terms
of each other. It’s a more general form of recursion. Feel free to
Google it.)
Here’s how I thought about the problem. I have a Hanoi object which
represents the entire game. Hanoi contains three Towers. Each Tower
has some rings, in a specific order. I represent rings as numbers in
the range 1 to N, with 1 being the smallest ring, and N being the
largest ring. I can remove (pop) a ring from a Tower, place (push) a
ring on a Tower, and see how many rings are on a Tower. Towers also
have names, so I can identify them in the printed output. Hanoi has
three Towers, with all of the rings starting on the left Tower, and
all of the rings in order from the largest on bottom to the smallest
on top. A fundamental operation is to move some number of rings from
one Tower to another. Solving the puzzle is as simple as moving all
of the rings from the left Tower to the right Tower.
How does recursion fit in? If I want to solve a puzzle with 5 rings,
that means I need to move 5 rings from left to right. In order to do
that, I need to temporarily move the top 4 rings from the left to the
middle, move the bottom ring from left to right, and then move the 4
rings from the middle to the right. Notice how I described solving
the 5 ring puzzle in terms of solving the 4 ring puzzle. Moving 4
rings involves moving the top 3 rings to an intermediate Tower,
moving the bottom of the 4 rings to its destination, and moving the
top 3 rings to the destination. And so on. Moving one ring is
trivial – just move it directly.
Here’s my code. Comments and critiques are welcome. Note that I
didn’t actually check to see whether a given move is legal; I’m a
trusting person. 
But if you want to do that, Tower#push would
be a good place (and Tower#pop, if you want to make sure you don’t
try to take a ring from a Tower that has no rings).
Hope this helped.
-Mark
Print out the moves to solve the Towers of Hanoi.
Supply the number of rings as the one and only command line argument.
class Tower
def initialize(name, rings)
@name = name
@rings = rings
end
def to_s
@name
end
def pop
@rings.pop
end
def push(ring)
@rings.push ring
end
def height
@rings.length
end
end
class Hanoi
def initialize(rings)
@left = Tower.new(“left”, [*(1…rings)].reverse)
@middle = Tower.new(“middle”, [])
@right = Tower.new(“right”, [])
end
def move(rings, from, to, other)
if rings == 1
ring = from.pop
puts “Move ring #{ring} from #{from} to #{to}”
to.push ring
else
move(rings-1, from, other, to)
move(1, from, to, other)
move(rings-1, other, to, from)
end
end
def solve
move(@left.height, @left, @right, @middle)
end
end
Hanoi.new(ARGV[0].to_i).solve
