Tuesday, December 13, 2005

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"))

0
/ 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
1
2
3
4
5
6
7

3 comments:

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 irc.freenode.net 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 blogger.com.

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: http://darcs.complete.org/fptools/libraries/base/Data/Tree.hs

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: http://haskell.org/ghc/docs/latest/html/libraries/index.html).

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 ?

Shannon -jj Behrens said...

Sorry, no.