Week 9: Exercises

1. Drop Nth

Write a function dropNth that takes an integer N and a list. The function should return a copy of the list in which every Nth element is omitted.

> dropNth 3 "spiderman"
"spdema"

2. zipWith

zipWith is a generalized version of zip that combines corresponding elements using a function, rather than forming pairs. For example:

> zipWith (+) [1, 2, 3] [10, 11, 12]
[11,13,15]

1. What is the type of zipWith?

2. Write zipWith. For efficiency, do not call zip or otherwise form pairs of elements.

3. Alternating Map

Write a function altMap that takes two functions and a list. altMap should apply the two functions alternately to list elements. For example:

altMap (\i -> i + 1) (\i -> i - 1) [1..10] == [2, 1, 4, 3, 6, 5, 8, 7, 10, 9]

4. No Comprehension

Rewrite this function without using a list comprehension:

pairs xs ys = [(x, y) | x <- xs, y <- ys, x < y]

5. Folding Minus

What are the values of these expressions?

1. foldl (-) 0 [1, 2, 3]

2. foldr (-) 0 [1, 2, 3]

6. Types of Folds

1. What are the types of foldl and foldr?

2. Write foldl and foldr.