module Work1 where

import Data.Char


--------------------------------------------------------------------------------
-- Operating on *all* elements in a list

-- Examples of using list comprehension

-- sumSquares n gives the sum of the squares of the numbers from 1 to n
sumSquares :: Integer -> Integer
sumSquares n = sum [i*i | i <- [1..n]]

-- allCAPS s changes each character to upper case
allCAPS :: String -> String
allCAPS str = [toUpper c | c <- str]

-- takeWords n s returns the first n words of s
takeWords :: Int -> String -> String
takeWords n str = unwords $ take n $ words str

-- capitalize s capitalizes all words in s
capitalize :: String -> String
capitalize str = unwords [cap w | w <- words str]
  where
    cap :: String -> String
    cap (c:str) = toUpper c : str

-- Socrative (later)
-- toNorwegian a sentence to Norwegian
  -- "inte" -> "ikke"
  -- "jag"  -> "jeg"



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-- Operating on *some* elements in a list (filtering)

-- keepPositives as delete all negative numbers from as
keepPositives :: [Integer] -> [Integer]
keepPositives as = [a | a <- as, a > 0]

-- divisors n lists the (positive) divisors of n
divisors :: Integer -> [Integer]
divisors n = [f | f <- [1..n], n `mod` f == 0]

-- isPrime n checks if n is a (positive) prime number
isPrime :: Integer -> Bool
isPrime n = length (divisors n) == 2

-- censor s deletes all lines in s which contain the word "money"



--------------------------------------------------------------------------------
-- Multiple list generators

-- dices n returns the ways that a pair of dices can result in the sum n
dices :: Integer -> [(Integer,Integer)]
dices n = [(d1,d2) | d1 <- [1..6], d2 <- [1..6], d1+d2 == n]

-- check_max n checks that the max function is correct for all arguments from 0
-- to n
check_max :: Integer -> Bool
check_max n = and
    [max a b >= a && max a b >= b | a <- [0..n], b <- [0..n]]

-- closestPoints ps gives the distance between the closest (non-equal) points in
-- the list ps
  -- @ patterns