[Haskell-cafe] Trees

[Adrian Neumann]

Good morning,

as an exercise for my Algorithms and Programming course I have to  
program a couple of simple functions over trees. Until now everything  
we did in Java could be done in Haskell (usually much nicer too)  
using the naive

 > data Tree a = Leaf a | Node a [Tree a]

But now the assignments require more than a simple top-down  
traversal. For example: given a tree t and two nodes u,v, find the  
first common ancestor.
In Java this is really simple, because each node has a "parent"  
reference. That way I only need to follow those references until I  
find the first common ancestor. This should take something like O(log  
n) in the average case.

In Haskell however the best way I've come up with so far is doing a  
BFS and looking for the last common node in the paths to u and v.  
This is neither fast, nor particularly elegant.
So how would you smart guys do it? With a Zipper? It would be nice if  
there was an elegant solution without monads.

--Adrian
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