# Haskell - Binary tree P37072

Statement html

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.

1. Write a function size :: Tree a -> Int that, given a tree, returns its size, that is, the number of node it contains.
2. Write a function height :: Tree a -> Int that, given a tree, returns its height, assuming that empty trees have zero height.
3. Write a function equal :: Eq a => Tree a -> Tree a -> Bool that, given two trees, tells whether they are the same.
4. 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.
5. Write a function preOrder :: Tree a -> [a] that, given a tree, return its pre-order traversal.
6. Write a function postOrder :: Tree a -> [a] that, given a tree, return its post-order traversal.
7. Write a function inOrder :: Tree a -> [a] that, given a tree, return its in-order traversal.
8. Write a function breadthFirst :: Tree a -> [a] that, given a tree, return its traversal by levels.
9. 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.
10. 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.

Public test cases
• Input

```let t7 = Node 7 Empty Empty
let t6 = Node 6 Empty Empty
let t5 = Node 5 Empty Empty
let t4 = Node 4 Empty Empty
let t3 = Node 3 t6 t7
let t2 = Node 2 t4 t5
let t1 = Node 1 t2 t3
let t1' = Node 1 t3 t2
size t1
height t1
equal t2 t3
isomorphic t1 t1'
preOrder t1
postOrder t1
inOrder t1
build [1,2,4,5,3] [4,2,5,1,3]
overlap (+) t2 t3
overlap (+) t1 t3
```

Output

```7
3
False
True
[1,2,4,5,3,6,7]
[4,5,2,6,7,3,1]
[4,2,5,1,6,3,7]
[1,2,3,4,5,6,7]
Node 1 (Node 2 (Node 4 Empty Empty) (Node 5 Empty Empty)) (Node 3 Empty Empty)
Node 5 (Node 10 Empty Empty) (Node 12 Empty Empty)
Node 4 (Node 8 (Node 4 Empty Empty) (Node 5 Empty Empty)) (Node 10 (Node 6 Empty Empty) (Node 7 Empty Empty))
```
• Information
Author
Jordi Petit
Language
English
Translator
Jordi Petit
Original language
Catalan
Other languages
Catalan
Official solutions