Finding max & sum of a tree in Haskell with map

Resume

I found an interesting algorithm to find the max and sum of a tree in Haskell using map. This algorithm is pretty short and useful for me.

Type definition

data Tree = Leaf Int | Node [Tree]

In the definition above, we defined a tree. In the tree, we will have either a

Leaf Int

or a

Node [Tree]

.

Attention: this is not a binary tree. It can have many sub-nodes within a node.

Sum

sum' :: Tree -> Int
sum' (Leaf l) = l
sum' (Node node) = sum (map sum' node)

We use a

map

to calculate every value of a

Leaf

in the tree, then construct a list with these values. Finally, we can figure out the sum of the tree.

Max

max' :: Tree -> Int
max' (Leaf l) = l
max' (Node node) = maximum (map max' node)

Like

sum

above, we can reuse it without major modification. Just replace

sum

with

maximum

. Then this function will figure out the maximum value of this tree recursively.

Test

let tree = Node [Node [Leaf 4, Leaf 5], Leaf 6]
*Main> let tree = Node [Node [Leaf 4, Leaf 5], Leaf 6]
*Main> sum' tree
15
*Main> max' tree
6