FP Laboratory 4

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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 integer 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]