I'm trying to construct a function
all_trees :: [Int] -> [Tree]
such that all_trees [1,2,3] will yield
[
Leaf 1,
Leaf 2,
Leaf 3,
Branch (Leaf 1) (Leaf 2),
Branch (Leaf 1) (Leaf 3),
Branch (Leaf 2) (Leaf 1),
Branch (Leaf 2) (Leaf 3),
Branch (Leaf 3) (Leaf 1),
Branch (Leaf 3) (Leaf 2),
Branch (Branch (Leaf 1) (Leaf 2)) (Leaf 3),
Branch (Branch (Leaf 1) (Leaf 3)) (Leaf 1),
Branch (Branch (Leaf 2) (Leaf 1)) (Leaf 3),
Branch (Branch (Leaf 2) (Leaf 3)) (Leaf 1),
Branch (Branch (Leaf 3) (Leaf 1)) (Leaf 2),
Branch (Branch (Leaf 3) (Leaf 2)) (Leaf 1),
Branch (Leaf 1) (Branch (Leaf 2) (Leaf 3)),
Branch (Leaf 1) (Branch (Leaf 3) (Leaf 2)),
Branch (Leaf 2) (Branch (Leaf 1) (Leaf 3)),
Branch (Leaf 2) (Branch (Leaf 3) (Leaf 2)),
Branch (Leaf 3) (Branch (Leaf 1) (Leaf 2)),
Branch (Leaf 3) (Branch (Leaf 2) (Leaf 1))
]
So far I'm not doing too well. Here's what I've got:
data Tree = Leaf Int | Branch Tree Tree
pick :: [x] -> [(x,[x])]
pick = pick_from []
pick_from :: [x] -> [x] -> [(x,[x])]
pick_from ks [] = []
pick_from ks [x] = []
pick_from ks xs = (head xs, ks ++ tail xs) : pick_from (ks ++ [head xs])
(tail xs)
setup :: [Int] -> [Tree]
setup = map Leaf
tree2 :: [Tree] -> [Tree]
tree2 xs = do
(x0,xs0) <- pick xs
(x1,xs1) <- pick xs0
return (Branch x0 x1)
all_trees ns = (setup ns) ++ (tree2 $ setup ns)
Clearly I need another layer of recursion here. (The input list is of
arbitrary length.) However, I need to somehow avoid creating duplicate
subtrees...
(BTW, I'm really impressed with how useful the list monad is for
constructing tree2...)
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