Joggin' the Ole Brainbox: Lists and Trees

Joggin’ the Ole Brainbox: Lists and Trees

Get your head back in the game with these warm-up problems on lists!

Question 1

Write a function which multiples every element of a list of integers by two.

Question 2

Write a function that adds together the elements of a list of doubles.

Question 3

Write a function which takes in two lists of integers, and adds each of the elements in the list pairwise to produce a new list. E.g. adder [1,2,3] [4,5,6] = [5,7,9]

Question 4

Write a function that deletes all elements in a list of integers that are even. E.g. no_evens_please [1,2,3,4,5,6] = [1,3,5]

Question 5

Write a function that inputs an integer, x, and outputs a list of integers in order from 1 to x. E.g. generate 4 = [1,2,3,4]

Question 6

Write a function which takes in a list of integers, and multiplies every element in the list based on its index in the list. Perhaps you can use the result from Question 5…. E.g. index_multiply [1,3,2,4] = [1,6,6,16]

Question 7

Write a polymorphic function which deletes every instance of an element from a list. E.g. delete True [True, False, True, False, False] = [False, False, False]

Binary Trees

Binary trees are another recursive data type that are similar to lists. Compare the two data types:

data List a = Entry (List a) | Empty --List data type
data B_Tree a = Node a (B_Tree a) (B_Tree a) | Empty --Binary tree data type

Both data types are recursive (they call themselves within their definition) and have a terminating case (Empty).

Question 8

Using the data type definition given, draw a binary tree on the whiteboard. Ask one of the PAL mentors to check your understanding.

Question 9

Write a function which inputs a binary tree of integers and add one to every node in the tree.