Difference between revisions of "FP Laboratory 4"
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*Main> insertOnIndex [4,5,6,7,8,9,10] 100 6 | *Main> insertOnIndex [4,5,6,7,8,9,10] 100 6 | ||
[4,5,6,7,8,9,100,10] | [4,5,6,7,8,9,100,10] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <translate> | ||
+ | * Create a function that joins the list of lists into one list using a separator. | ||
+ | </translate> | ||
+ | |||
+ | <syntaxhighlight lang="Haskell">join :: [[a]] -> a -> [a]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> join ["I","love","functional","programming"] ' ' | ||
+ | "I love functional programming" | ||
+ | *Main> join [[1,2,3],[4,5],[6,7,8],[9]] 0 | ||
+ | [1,2,3,0,4,5,0,6,7,8,0,9] | ||
</syntaxhighlight> | </syntaxhighlight> |
Revision as of 11:50, 28 August 2023
Contents
Functions working with lists
Implement following functions:
- Create a function that takes first n elements of the list.
take' :: Int -> [a] -> [a]
*Main> take' 2 [1,2,3]
[1,2]
- Create a function that takes the remaining list after the first n elements.
drop' :: Int -> [a] -> [a]
*Main> drop' 2 [1,2,3]
[3]
- Create a function that find the smallest element in the list. Consider input restrictions.
minimum' :: [a] -> a -- Is this right?
*Main> minimum' [1,3,4,0]
0
minimum' :: Ord a => [a] -> a
minimum' [x] = x
minimum' (x:y:z) | x < y = minimum' (x:z)
| otherwise = minimum' (y:z)
- Find all integer divisors of a given number.
divisors :: Int -> [Int]
*Main> divisors 32
[1,2,4,8,16,32]
divisors :: Int -> [Int]
divisors n = tmp n where
tmp 0 = []
tmp x | n `mod` x == 0 = x: tmp (x-1)
| otherwise = tmp (x-1)
divisors' :: Int -> [Int]
divisors' n = filter (\x -> n `mod` x == 0) [1..n]
divisors'' :: Int -> [Int]
divisors'' n = [x | x<-[1..n], n `mod` x == 0]
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)]
*Main> zipThem [1,2,3] "ABCD"
[(1,'A'),(2,'B'),(3,'C')]
- Create a function that compute Cartesian product of two vectors.
dotProduct :: [a] -> [b] -> [(a,b)]
*Main> dotProduct [1..4] "ABC"
[(1,'A'),(1,'B'),(1,'C'),(2,'A'),(2,'B'),(2,'C'),(3,'A'),(3,'B'),(3,'C'),(4,'A'),(4,'B'),(4,'C')]
dotProduct :: [a] -> [b] -> [(a,b)]
dotProduct [] _ = []
dotProduct (x:xs) ys = tmp ys ++ dotProduct xs ys where
tmp [] = []
tmp (b:bs) = (x,b) : tmp bs
dotProduct' :: [a] -> [b] -> [(a,b)]
dotProduct' xs ys = [(x,y)|x<-xs, y<-ys]
dotProduct'' :: [a] -> [b] -> [(a,b)]
dotProduct'' x y =
zip (concat (map (replicate (length y)) x))
(concat (replicate (length x) y))
- Create a function that computes n-th number in the Fibonacci sequence. The function should use tuples in the solution.
fibonacci :: Int -> Int
*Main> fibonacci 12
144
fibonacci :: Int -> Int
fibonacci n = fst (tmp n) where
fibStep (a,b) = (b,a+b)
tmp 0 = (0,1)
tmp x = fibStep (tmp (x-1))
High-order functions
- Create a function that takes a string and converts all characters to upper case letters.
allToUpper :: String -> String
*Main> allToUpper "aAbc"
"AABC"
import Data.Char
allToUpper :: String -> String
allToUpper xs = [toUpper x |x<-xs]
allToUpper' :: String -> String
allToUpper' xs = map toUpper xs
- Implement the
quicksort
algorithm. As a pivot use always the first element in the list. For dividing the list, use the functionfilter
.
quicksort :: (Ord a) => [a] -> [a]
*Main> filter (<5) [1..10]
[1,2,3,4]
*Main> quicksort [1,5,3,7,9,5,2,1]
[1,1,2,3,5,5,7,9]
quicksort :: (Ord a) => [a] -> [a]
quicksort [] = []
quicksort (x:xs) = let lp = filter (< x) xs
rp = filter (>= x) xs
in quicksort lp ++ [x] ++ quicksort rp
Additional exercises
- Create a function that removes the first occurrence of a given element from a list.
removeOne :: Eq a => [a] -> [a]
*Main> removeOne 4 [1,4,6,8,4,5,4,7]
[1,6,8,4,5,4,7]
*Main> removeOne 'e' "Ahoj"
"Ahoj"
- Create a function that removes all occurrences of a given element from a list.
removeAll :: Eq a => [a] -> [a]
*Main> removeAll 4 [1,4,6,8,4,5,4,7]
[1,6,8,5,7]
*Main> removeAll 'e' "Ahoj"
"Ahoj"
- Create your own implementation of the
replicate
function.
replicate' :: Int -> a -> [a]
*Main> replicate' 4 8
[8,8,8,8]
- Create a function that realizes the left rotation of a list by n elements. Function
iterate
might be helpful.
rotateLeftN :: [a] -> Int -> [a]
*Main> rotateLeftN [1,2,3,4,5] 2
[3,4,5,1,2]
*Main> rotateLeftN [1,2,3,4,5] 6
[2,3,4,5,1]
- Create a function that realizes the right rotation of a list by n elements.
rotateRightN :: [a] -> Int -> [a]
*Main> rotateRightN [1,2,3,4,5] 2
[4,5,1,2,3]
*Main> rotateRightN [1,2,3,4,5] 6
[5,1,2,3,4]
- Create function alternate, which interleaves two lists into one, alternating between elements taken from the first list and elements from the second.
alternate :: [a] -> [a] -> [a]
*Main> alternate [1,2,3] [4,5,6]
[1,4,2,5,3,6]
*Main> alternate [1,2] [4,5,6]
[1,4,2,5,6]
*Main> alternate [1,2,3] [4]
[1,4,2,3]
*Main> alternate [1,2,3] []
[1,2,3]
- Use filter to create a non-recursive function that takes a list of integers as input and returns a list of those that are even and greater than 7.
filterEvenGt7 :: [Int] -> [Int]
*Main> filterEvenGt7 [1,2,6,9,10,3,12,8]
[10,12,8]
*Main> filterEvenGt7 [5,2,6,19,129]
[]
- Create a function that splits a list of numbers into a list of triples. Extra elements should be forgotten.
makeTriples :: [Int] -> [(Int,Int,Int)]
*Main> makeTriples [1,2,3,4,5,6,7,8,9]
[(1,2,3),(4,5,6),(7,8,9)]
*Main> makeTriples [1,2,3,4,5,6,7,8,9,10,11]
[(1,2,3),(4,5,6),(7,8,9)]
- Create a function that inserts an element into a list on the specific index.
insertOnIndex :: [a] -> a -> Int -> [a]
*Main> insertOnIndex [4,5,6,7,8,9,10] 100 0
[100,4,5,6,7,8,9,10]
*Main> insertOnIndex [4,5,6,7,8,9,10] 100 3
[4,5,6,100,7,8,9,10]
*Main> insertOnIndex [4,5,6,7,8,9,10] 100 6
[4,5,6,7,8,9,100,10]
- Create a function that joins the list of lists into one list using a separator.
join :: [[a]] -> a -> [a]
*Main> join ["I","love","functional","programming"] ' '
"I love functional programming"
*Main> join [[1,2,3],[4,5],[6,7,8],[9]] 0
[1,2,3,0,4,5,0,6,7,8,0,9]