Haskell — Binary tree

In this problem you have to write several functions for generic binary trees. The definition of the trees is given by:

    data Tree a = Node a (Tree a) (Tree a) | Empty deriving (Show)

That is, a tree with elements of type $a$ is, either an empty tree, either a node with an element (of type $a$ ) and two other trees of the same type. The deriving (Show) statement simply enables an visualization of trees.

Write a function size :: Tree a -> Int that, given a tree, returns its size, that is, the number of node it contains.
Write a function height :: Tree a -> Int that, given a tree, returns its height, assuming that empty trees have zero height.
Write a function equal :: Eq a => Tree a -> Tree a -> Bool that, given two trees, tells whether they are the same.
Write a function isomorphic :: Eq a => Tree a -> Tree a -> Bool that, given two trees, tells whether they are isomorphic, that is, if one can obtain one from the other flipping some of its descendants.
Write a function preOrder :: Tree a -> [a] that, given a tree, return its pre-order traversal.
Write a function postOrder :: Tree a -> [a] that, given a tree, return its post-order traversal.
Write a function inOrder :: Tree a -> [a] that, given a tree, return its in-order traversal.
Write a function breadthFirst :: Tree a -> [a] that, given a tree, return its traversal by levels.
Write a function build :: Eq a => [a] -> [a] -> Tree a that, given a pre-order traversal of a tree and an in-order traversal of the same tree, returns the original tree. You can assume that the three has no repeated elements.
Write a function overlap :: (a -> a -> a) -> Tree a -> Tree a -> Tree a that, given two trees, returns its overlapping using a function. Overlapping two trees with a function consists in placing the two trees one on the other and combine the double nodes using the given function.

Scoring

Each function scores 10 points.

Problem information

Author: Unknown
Translator: Jordi Petit

Generation: 2026-02-03T17:09:41.885Z