Difference between revisions of "PFP Laboratory 4"
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+ | == List comprehension == | ||
+ | Using the list comprehension implement following functions: | ||
+ | |||
+ | * Create a function that generates a list of all odd numbers in given interval. | ||
+ | <syntaxhighlight lang="Haskell">oddList :: Int -> Int -> [Int]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> oddList 1 10 | ||
+ | [1,3,5,7,9] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | oddList :: Int -> Int -> [Int] | ||
+ | oddList a b = [ x |x<-[a..b], odd x] | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/TXOOI93332]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | * Create a function that removes all upper case letters from a string. | ||
+ | <syntaxhighlight lang="Haskell">removeAllUpper :: String -> String</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> removeAllUpper "ABCabcABC" | ||
+ | "abc" | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | import Data.Char | ||
+ | |||
+ | removeAllUpper :: String -> String | ||
+ | removeAllUpper xs = [ x |x<-xs, not (isUpper x)] | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/TXOOI93332]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | * Create functions that computes union and intersection of two sets. | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | union :: Eq a => [a] -> [a] -> [a] | ||
+ | intersection :: Eq a => [a] -> [a] -> [a] | ||
+ | </syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> union [1..5] [3..10] | ||
+ | [1,2,3,4,5,6,7,8,9,10] | ||
+ | *Main> intersection [1..5] [3..10] | ||
+ | [3,4,5] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | union :: Eq a => [a] -> [a] -> [a] | ||
+ | union xs ys = xs ++ [y| y<-ys, not (elem y xs)] | ||
+ | |||
+ | intersection :: Eq a => [a] -> [a] -> [a] | ||
+ | intersection xs ys = [y| y<-ys, elem y xs] | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/TXOOI93332]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | == More complex functions == | ||
+ | * Create a function that count the number of occurrences of all characters from a given string. | ||
+ | |||
+ | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/B2LFNJfC-TU]]</div> | ||
+ | <syntaxhighlight lang="Haskell">countThem :: String -> [(Char, Int)]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main>countThem "hello hello hello" | ||
+ | [('h',3),('e',3),('l',6),('o',3),(' ',2)] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | unique :: String -> String | ||
+ | unique n = reverse(tmp n "") where | ||
+ | tmp [] store = store | ||
+ | tmp (x:xs) store | x `elem` store = tmp xs store | ||
+ | | otherwise = tmp xs (x:store) | ||
+ | |||
+ | unique' :: String -> String | ||
+ | unique' [] = [] | ||
+ | unique' (x:xs) = x: unique' (filter (/=x)xs) | ||
+ | |||
+ | countThem :: String -> [(Char, Int)] | ||
+ | countThem xs = let u = unique xs | ||
+ | in [(x, length (filter (==x) xs)) |x<-u] | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/UVITE26792]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
+ | * Create a function that generates all combinations of given length from the characters from given string. You can assume, that all character are unique and the given length is not bigger then the length of this string. | ||
+ | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/-muPoJucLyI]]</div> | ||
+ | <syntaxhighlight lang="Haskell">combinations :: Int -> String -> [String]</syntaxhighlight> | ||
+ | <syntaxhighlight lang="Haskell" class="myDark"> | ||
+ | *Main> combinations 3 "abcdef" | ||
+ | ["abc","abd","abe",...] | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution"> | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | combinations :: Int -> String -> [String] | ||
+ | combinations 1 xs = [[x]| x<-xs] | ||
+ | combinations n (x:xs) | n == length (x:xs) = [(x:xs)] | ||
+ | |otherwise = [[x] ++ y |y<-combinations (n-1) xs ] | ||
+ | ++ (combinations n xs) | ||
+ | </syntaxhighlight> | ||
+ | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/RTRV90066]] | ||
+ | </div> | ||
+ | <div style="clear:both"></div> | ||
+ | |||
== List of lists == | == List of lists == | ||
<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/voiTk64SaQM]]</div> | <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/voiTk64SaQM]]</div> | ||
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</syntaxhighlight> | </syntaxhighlight> | ||
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/JXX12735]] | [[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/JXX12735]] | ||
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</div> | </div> | ||
<div style="clear:both"></div> | <div style="clear:both"></div> |
Latest revision as of 10:58, 29 September 2022
List comprehension
Using the list comprehension implement following functions:
- Create a function that generates a list of all odd numbers in given interval.
oddList :: Int -> Int -> [Int]
*Main> oddList 1 10
[1,3,5,7,9]
- Create a function that removes all upper case letters from a string.
removeAllUpper :: String -> String
*Main> removeAllUpper "ABCabcABC"
"abc"
import Data.Char
removeAllUpper :: String -> String
removeAllUpper xs = [ x |x<-xs, not (isUpper x)]
- Create functions that computes union and intersection of two sets.
union :: Eq a => [a] -> [a] -> [a]
intersection :: Eq a => [a] -> [a] -> [a]
*Main> union [1..5] [3..10]
[1,2,3,4,5,6,7,8,9,10]
*Main> intersection [1..5] [3..10]
[3,4,5]
union :: Eq a => [a] -> [a] -> [a]
union xs ys = xs ++ [y| y<-ys, not (elem y xs)]
intersection :: Eq a => [a] -> [a] -> [a]
intersection xs ys = [y| y<-ys, elem y xs]
More complex functions
- Create a function that count the number of occurrences of all characters from a given string.
countThem :: String -> [(Char, Int)]
*Main>countThem "hello hello hello"
[('h',3),('e',3),('l',6),('o',3),(' ',2)]
unique :: String -> String
unique n = reverse(tmp n "") where
tmp [] store = store
tmp (x:xs) store | x `elem` store = tmp xs store
| otherwise = tmp xs (x:store)
unique' :: String -> String
unique' [] = []
unique' (x:xs) = x: unique' (filter (/=x)xs)
countThem :: String -> [(Char, Int)]
countThem xs = let u = unique xs
in [(x, length (filter (==x) xs)) |x<-u]
- Create a function that generates all combinations of given length from the characters from given string. You can assume, that all character are unique and the given length is not bigger then the length of this string.
combinations :: Int -> String -> [String]
*Main> combinations 3 "abcdef"
["abc","abd","abe",...]
combinations :: Int -> String -> [String]
combinations 1 xs = [[x]| x<-xs]
combinations n (x:xs) | n == length (x:xs) = [(x:xs)]
|otherwise = [[x] ++ y |y<-combinations (n-1) xs ]
++ (combinations n xs)
List of lists
Consider following type representing picture:
type Pic = [String]
If you want to print this picture you can use:
pp :: Pic -> IO ()
pp x = putStr (concat (map (++"\n") x))
Picture example:
pic :: Pic
pic = [ "....#....",
"...###...",
"..#.#.#..",
".#..#..#.",
"....#....",
"....#....",
"....#####"]
*Main> pp pic
....#....
...###...
..#.#.#..
.#..#..#.
....#....
....#....
....#####
Create functions that:
- Flips picture veriticaly and horizontally.
flipV :: Pic -> Pic
flipH :: Pic -> Pic
*Main> pp(flipV pic)
....#....
...###...
..#.#.#..
.#..#..#.
....#....
....#....
#####....
*Main> pp(flipH pic)
....#####
....#....
....#....
.#..#..#.
..#.#.#..
...###...
....#....
flipV :: Pic -> Pic
flipV = map reverse
flipV' :: Pic -> Pic
flipV' xs = [reverse x|x<-xs]
flipH :: Pic -> Pic
flipH = reverse
- Place one picture above another.
above :: Pic -> Pic -> Pic
*Main> pp(above pic pic)
....#....
...###...
..#.#.#..
.#..#..#.
....#....
....#....
....#####
....#....
...###...
..#.#.#..
.#..#..#.
....#....
....#....
....#####
- Place two pictures side by side (consider, that they have the same height).
sideBySide :: Pic -> Pic -> Pic
*Main> pp(sideBySide pic pic)
....#........#....
...###......###...
..#.#.#....#.#.#..
.#..#..#..#..#..#.
....#........#....
....#........#....
....#####....#####
sideBySide :: Pic -> Pic -> Pic
sideBySide xs ys = map (\(x,y) -> x ++ y)(zip xs ys)
sideBySide':: Pic -> Pic -> Pic
sideBySide' (x:xs) (y:ys) = (x ++ y) : sideBySide' xs ys
sideBySide' _ _ = []
sideBySide'' :: Pic -> Pic -> Pic
sideBySide'' = zipWith (++)
- Rotate picture to the left and to the right.
rotateR :: Pic -> Pic
rotateL :: Pic -> Pic
*Main> pp(rotateR pic)
.......
...#...
....#..
.....#.
#######
#....#.
#...#..
#..#...
#......
*Main> pp(rotateL pic)
......#
...#..#
..#...#
.#....#
#######
.#.....
..#....
...#...
.......
toRow :: String -> Pic
toRow xs = map (\x -> [x]) xs -- [[x]|x<-xs]
rotateR :: Pic -> Pic
rotateR [x] = toRow x
rotateR (x:xs) = (rotateR xs) `sideBySide` (toRow x)
rotateR' :: Pic -> Pic
rotateR' x = foldl1 sideBySide (reverse (map toRow x))
rotateL :: Pic -> Pic
rotateL [x] = reverse(toRow x)
rotateL (x:xs) = reverse(toRow x) `sideBySide` (rotateL xs)
rotateL' :: Pic -> Pic
rotateL' x = foldl1 sideBySide (map (reverse.toRow) x)