FP Cvičení 5
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Generátory seznamů
Implementujte následující funkce s využitím genrátoru seznamu:
- Vytvořte funkci, která vygeneruje seznam všech lichých čísel v daném intervalu.
oddList :: Int -> Int -> [Int]
*Main> oddList 1 10
[1,3,5,7,9]
- Vztvořte funkci která odstraní všechna velká písmena z řetězce.
removeAllUpper :: String -> String
*Main> removeAllUpper "ABCabcABC"
"abc"
import Data.Char
removeAllUpper :: String -> String
removeAllUpper xs = [ x |x<-xs, not (isUpper x)]
- Vytvořte funkci která spočítá sjednocení a průnik dvou množin.
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]
Komplexnější funkce
- 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]
- Goldbach's conjecture says that every positive even number greater than 2 is the sum of two prime numbers. Example: 28 = 5 + 23. It is one of the most famous facts in number theory that has not been proved to be correct in the general case yet. Create a function, that computes for a given even integer number the list of pairs of primes, that satisfies the rule of Goldbach's conjecture.
goldbach :: Int-> [(Int, Int)]
*Main>goldbach 28
[(5, 23),(11,17)]
isPrime :: Int -> Bool
isPrime n = null [x |x<-[2..ceiling (sqrt (fromIntegral n)::Double)], n `mod` x == 0]
goldbach :: Int-> [(Int, Int)]
goldbach n = let primes = [x |x<-[2..(n `div` 2)], isPrime x]
in [(x,n-x) |x<-primes, isPrime (n-x)]
- In most cases, if an even number is written as the sum of two prime numbers, one of them is very small. We will be searching for cases that violates this rule. Create a function, that has three parameters. First two defines an interval, where we will be searching for Goldbach numbers. The last parameter is the limit. For each number in this interval, find Goldbach's pair with smallest prime number. If this smallest number is bigger than given limit, the corresponding pair will be in the result.
goldbachList :: Int -> Int-> Int -> [(Int, Int)]
*Main>goldbachList 4 2000 50
[(73,919),(61,1321),(67,1789),(61,1867)]
isPrime :: Int -> Bool
isPrime n = null [x |x<-[2..ceiling (sqrt (fromIntegral n)::Double)], n `mod` x == 0]
goldbach :: Int-> [(Int, Int)]
goldbach n = let primes = [x |x<-[2..(n `div` 2)+1], isPrime x]
in [(x,n-x) |x<-primes, isPrime (n-x)]
goldbachList :: Int -> Int-> Int -> [(Int, Int)]
goldbachList a b limit = filter (\(x,_)-> x>limit) [head (goldbach x) | x<-[a..b], even x]
- 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",...]