Haskell 2-3-4 Tree

问题

We've been asked to create a 2-3-4 tree in Haskell, as in write the data type, the insert function, and a display function.

I'm finding it very difficult to get information on this kind of tree, even in a language I'm comfortable with (Java, C++).

What I have so far -

data Tree t = Empty 
    | Two t (Tree t)(Tree t) 
    | Three t t (Tree t)(Tree t)(Tree t) 
    | Four t t t (Tree t)(Tree t)(Tree t)(Tree t) deriving (Eq, Ord, Show)


leaf2 a = Two a Empty Empty
leaf3 a b = Three a b Empty Empty Empty
leaf4 a b c = Four a b c Empty Empty Empty Empty

addNode::(Ord t) => t ->  Tree t -> Tree t
addNode t Empty = leaf2 t
addNode x (Two t left right)
    | x < t = Two t (addNode x left) right
    | otherwise = Two t left (addNode x right)

This compiles but I'm not sure if it's correct, but not sure how to start writing the insert into a three node or four node.

The assignment also says that "deriving show" for the display function is not enough, that it should print out the tree in the format normally seen in diagrams. Again, unsure on the way to go with this.

Any help or direction appreciated.

回答1:

I know nothing about 2-3-4 trees, but for the Three node, you would start with something like this:

addNode t (Three x y left mid right)
  | cond1 = expr1
  | cond2 = expr2
  (etc)

What cond1, cond2, expr1, and expr2 are, exactly, is dependent on the definition of what a 2-3-4 tree is.

As for a show method, the general outline would be this:

instance (Show t) => Show (Tree t) where
  show Empty = ...
  show (Two x l r) = ...show x...show l...show r...
  show (Three x y l m r) = ...
  show (Four x y z l m n r) = ...

The implementation depends on how you want it to look, but for the non-Empty cases, you will probably invoke show on all of the components of the tree being shown. If you want to indent the nested parts of the tree, then perhaps you should create a separate method:

instance (Show t) => Show (Tree t) where
  show = showTree 0

showTree :: Show t => Int -> Tree t -> String
showTree n = indent . go
  where indent = (replicate n ' ' ++)
        go Empty = "Empty"
        go (Two x l r) = (...show x...showTree (n+1) l...showTree (n+1) r...)
        (etc)

回答2:

We've been asked to create a 2-3-4 tree

My condolences. I myself once had to implement one for homework. A 2-3-4 tree is a B-tree with all the disadvantages of the B-tree and none of the advantages, because writing the cases separately for each number of children as you do is as cumbersome as having a list of only 2-4 elements.

Point being: B-tree insertion algorithms should work, just fix the size. Cormen et al. have pseudocode for one in their book Introduction to algorithms (heavy imperativeness warning!).

It might still be better to have lists of data elements and children instead of the four-case algebraic data type, even if the type wouldn't enforce the size of the nodes then. At least it would make it easier to expand the node size.

来源：https://stackoverflow.com/questions/8549057/haskell-2-3-4-tree