Skip to main content

Haskell: Breadth-first Tree Traversal

As an exercise, I implemented breadth-first tree traversal (instead of the much more common depth-first tree traversal) in Haskell. It took me about 3 hours, mainly because I haven't even finished reading the turorial yet. It really struck me how truly lazy Haskell is! My own language, Squeamish, had lazy evaluation, but in Haskell, you have to somewhat bend over backwards with the imperative stuff to say, "Yeah, really, I'm done defining stuff. Uh, can you actually, uh, do some evaluation or something, and, uh, maybe even print the answer?"
{- Implement breadth-first tree traversal.

Name: Shannon -jj Behrens
Date: Tue Dec 13 03:18:34 PST 2005 -}

module Main where

-- The main definition of a tree.
data Tree a = Leaf a | Branch a (Tree a) (Tree a)

-- Depth-first tree traversal.
depthFirst :: Tree a -> [a]
depthFirst (Leaf x) = [x]
depthFirst (Branch x left right) = depthFirst left ++ [x] ++
depthFirst right

-- Breadth-first tree traversal.
breadthFirst :: Tree a -> [a]
breadthFirst x = _breadthFirst [x]

_breadthFirst :: [Tree a] -> [a]
_breadthFirst [] = []
_breadthFirst xs = map treeValue xs ++
_breadthFirst (concat (map immediateChildren xs))

-- Get the value of a given tree.
treeValue :: Tree a -> a
treeValue (Leaf x) = x
treeValue (Branch x left right) = x

-- Get the immediate children of a tree.
immediateChildren :: Tree a -> [Tree a]
immediateChildren (Leaf x) = []
immediateChildren (Branch x left right) = [left, right]

-- Define some tree.
mytree = Branch "1"
(Branch "2"
(Leaf "4")
(Leaf "5"))
(Branch "3"
(Leaf "6")
(Leaf "7"))

{- 1
/ 2 3
/ \ / 4 5 6 7

Here's another.
mytree = Branch "0"
(Leaf "1")
(Branch "2"
(Branch "3"
(Leaf "4")
(Leaf "5"))
(Leaf "6"))

/ 1 2
/ 3 6
/ 4 5 -}

-- Create one "do" out of a list of things to do.
doList :: [IO ()] -> IO ()
doList = foldr (>>) (return ())

-- Main.
main :: IO ()
main = do doList (map putStrLn (breadthFirst mytree))
The result is:
$ runhugs main.hs


xerox said…
First of all, welcome to Haskell! :-)

I don't know if you're used to the IRC, but there is an active community on the #haskell channel on the network - you're very welcome to join!

Nice piece of code, buddy. I couldn't find a way to use the PRE or CODE or whatever tags in writing the comment, so, if you can, feel free to edit and fix it. Stupid

Before starting the trip, note that I just tried to write a more idiomatic (and well indented, at least to the most common taste) version of the code - for fun purposes mainly. Also, I want to show you some interesting properties emerging from your code, check them out.

Adding a 'deriving (..)' clause makes the datatype automatically instantiated in the given classes. Show and Read make values of the given type serializable via the functions 'read' and 'show'. Deriving Show is also useful for debugging purposes (if you happened to encounter any error of the type "No Show instance for (Tree a)" or something.)

data Tree a = Leaf a | Branch a (Tree a) (Tree a) deriving (Show,Read)

Right on!

depthFirst :: Tree a -> [a]
depthFirst (Leaf x) = [x]
depthFirst (Branch x l r) = depthFirst l ++ [x] ++ depthFirst r

Is it more common to hide the helper functions/values in a 'where' clause.

I don't know again how far are you on your tutorial, but keep this in mind: in the List Monad, return is \x -> [x], and bind is exactly concatMap: (>>=) = concatMap.

breadthFirst :: Tree a -> [a]
breadthFirst x = breadthFirst' [x]
where breadthFirst' :: [Tree a] -> [a]
breadthFirst' [] = []
breadthFirst' xs = map treeValue xs ++ breadthFirst' (xs >>= immediateChildren)

Pattern matching unused arguments is usually done by the means of the '_' notation. To please the eye.

treeValue :: Tree a -> a
treeValue (Leaf x) = x
treeValue (Branch x _ _) = x

immediateChildren :: Tree a -> [Tree a]
immediateChildren (Leaf _) = []
immediateChildren (Branch _ l r) = [l, r]

The next function is straightforwardly taken from the standard library,take a look around there:

levels = map (map treeValue) . takeWhile (not . null) . iterate (>>= immediateChildren) . return

Values of types instantiated in the 'Num a' typeclass (like Int, to say), along with many others (try :info Show in hugs or GHCi), are also instantiated 'Show a'; meaning that they can be feeded to the 'show' function, and by extension to 'print', latter.

Note that: print = putStrLn . show

mytree :: Tree Int
mytree = Branch 1
(Branch 2
(Leaf 4)
(Leaf 5))
(Branch 3
(Leaf 6)
(Leaf 7))

Your 'doLine' is just sequence_ from Control.Monad (the '_' means that the result of the actions in the list are discarded, take a look at the documentation:

But then, there is a simpler way:

main :: IO ()
main = mapM_ (print) (breadthFirst mytree)

Happy happy, joy joy.

-- xerox on #haskell
Anonymous said…
Dou have explanation for this ?
In OOP PHP implementation ?
jjinux said…
Sorry, no.

Popular posts from this blog

Drawing Sierpinski's Triangle in Minecraft Using Python

In his keynote at PyCon, Eben Upton, the Executive Director of the Rasberry Pi Foundation, mentioned that not only has Minecraft been ported to the Rasberry Pi, but you can even control it with Python. Since four of my kids are avid Minecraft fans, I figured this might be a good time to teach them to program using Python. So I started yesterday with the goal of programming something cool for Minecraft and then showing it off at the San Francisco Python Meetup in the evening.

The first problem that I faced was that I didn't have a Rasberry Pi. You can't hack Minecraft by just installing the Minecraft client. Speaking of which, I didn't have the Minecraft client installed either ;) My kids always play it on their Nexus 7s. I found an open source Minecraft server called Bukkit that "provides the means to extend the popular Minecraft multiplayer server." Then I found a plugin called RaspberryJuice that implements a subset of the Minecraft Pi modding API for Bukkit s…

Apple: iPad and Emacs

Someone asked my boss's buddy Art Medlar if he was going to buy an iPad. He said, "I figure as soon as it runs Emacs, that will be the sign to buy." I think he was just trying to be funny, but his statement is actually fairly profound.

It's well known that submitting iPhone and iPad applications for sale on Apple's store is a huge pain--even if they're free and open source. Apple is acting as a gatekeeper for what is and isn't allowed on your device. I heard that Apple would never allow a scripting language to be installed on your iPad because it would allow end users to run code that they hadn't verified. (I don't have a reference for this, but if you do, please post it below.) Emacs is mostly written in Emacs Lisp. Per Apple's policy, I don't think it'll ever be possible to run Emacs on the iPad.

Emacs was written by Richard Stallman, and it practically defines the Free Software movement (in a manner of speaking at least). Stal…

ERNOS: Erlang Networked Operating System

I've been reading Dreaming in Code lately, and I really like it. If you're not a dreamer, you may safely skip the rest of this post ;)

In Chapter 10, "Engineers and Artists", Alan Kay, John Backus, and Jaron Lanier really got me thinking. I've also been thinking a lot about Minix 3, Erlang, and the original Lisp machine. The ideas are beginning to synthesize into something cohesive--more than just the sum of their parts.

Now, I'm sure that many of these ideas have already been envisioned within, LLVM, Microsoft's Singularity project, or in some other place that I haven't managed to discover or fully read, but I'm going to blog them anyway.

Rather than wax philosophical, let me just dump out some ideas:Start with Minix 3. It's a new microkernel, and it's meant for real use, unlike the original Minix. "This new OS is extremely small, with the part that runs in kernel mode under 4000 lines of executable code." I bet it&…