查找树中的所有部分路径

Question

I am trying to create a Haskell function that generates a list containing all the partial paths of a tree, given the tree implementation data Tree a = Empty | Node a (Tree a) (Tree a) data Tree a = Empty | Node a (Tree a) (Tree a) . For example, if I have a tree

tree = Node 5 (Node 3 Empty Empty ) (Node 2 Empty Empty )

I want to get

[[],[5],[5,3],[5,2]]

How could I make such a function?

Answer 1

First let us consider the type of this function, it must be Tree a -> [[a]] .

So what can we do given a node Node x left right ? We have the path that is just the node itself - this is just [x] , as well as the paths that go through this node to the left- and right sub tree. The paths going throu the left and right sub tree are just what we get if we apply our function to left and right respectively. We now just need to add x to the start of each of those paths and we do that by calling map(x:) paths . (And for an empty one we should get an empty list as there is no path.)

data Tree a = Empty | Node a (Tree a) (Tree a)
tree = Node 5 (Node 3 Empty Empty ) (Node 2 Empty Empty )

pp :: Tree a -> [[a]]
pp (Node x left right) = [[x]] ++ map(x:)(pp left) ++ map(x:)(pp right)
pp Empty = []

Now this has one flaw that the empty path is not considered as a partial path by this function. But we can easily amend that by adding it and wrapping it in another function:

partialPaths :: Tree a -> [[a]]
partialPaths t = [[]] ++ pp t

main = print $ partialPaths tree

Try it online!