FP Laboratory 4

Functions working with lists

Implement following functions:

• Create a function that takes first n elements of the list.

take' :: Int -> [a] -> [a]

• Create a function that takes the remaining list after the first n elements.

drop' :: Int -> [a] -> [a]

• Create a function that find the smallest element in the list. Consider input restrictions.

minimum' :: [a] -> a -- Is this right?

• Find all prime divisors of a given number.

divisors :: a -> [a]

Functions working with lists and tuples

Implement following functions:

• Create a function that merge two lists into one list of tuples.

zipThem:: [a] -> [b] -> [(a,b)]

• Create a function that compute Cartesian product of two vectors.

dotProduct :: [a] -> [b] -> [(a,b)]

• Create a function that computes n-th number in the Fibonacci sequence. The function should be use n bigger then 50 and get the result in less then a second).

fibonacci :: Int -> Int

High-order functions

• Create a function that takes a string and converts all characters to upper case letters.

allToUpper :: String -> String

• Implement the quicksort algorithm. As a pivot use always the first element in the list. For dividing the list, use the function filter.

quicksort :: (Ord a) => [a] -> [a]

*Main> filter (<5) [1..10]
[1,2,3,4]