import Data.List
import Char

-- 5.7.1

-- > sum [x*x|x<-[1..100]]
-- 338350

-- 5.7.2

replicate' :: Int -> a -> [a]
replicate' x y = [y | _ <- [1..x]]

-- 5.7.3

pyths :: Int -> [(Int,Int,Int)]
pyths n = [ (x,y,z) | x <- [1..n], y <- [1..n], z <- [1..n], (x * x + y * y == z * z) ]

-- 5.7.4

factors :: Int -> [Int]
factors x = (\m -> nub(concat [ [x, y] | x <- [1..m], y <- [1..m], x * y == m ])) x

perfects :: Int -> [Int]
perfects x = [ n | n <- [1..x], sum ( filter (\z -> z /= n) ( factors n ) ) == n ]

-- Got there. Not gracefully ;-)

-- 5.7.5

original :: [(Int,Int)]
original = [ (x,y) | x <- [1,2,3], y <- [1,2,3] ]


new :: [(Int,Int)]
new = concat [ [ (x, y) | x <- [1..3]]  | y <- [1..3] ]

-- 5.7.6
--

positions :: Eq a => a -> [a] -> [Int]
positions x xs = [ i | (x', i) <- zip xs [0..n], x == x' ]
                 where n = length xs - 1

find' :: Eq a => a -> [(a,b)] -> [b]
find' x xs = [ i | (x', i) <- xs, x == x' ]

positions' :: Eq a => a -> [a] -> [Int]
positions' x xs = [ i | i <- find' x (zip xs [0..n])]
                 where n = length xs - 1

-- 5.7.7

scaleproduct :: [Int] -> [Int] -> Int
scaleproduct os es = sum [ a * b | (a, b) <- zip os es ]

-- 5.7.8

let2int :: Char -> Int
let2int a = Char.ord a - Char.ord 'a'

int2let :: Int -> Char
int2let a = Char.chr (a + Char.ord 'a')

shift :: Int -> Char -> Char
shift n c | isLower c = int2let((let2int c + n) `mod` 26)
          | otherwise = c

encode :: Int -> [Char] -> [Char]
encode d xs = [ shift d r | r <- xs ]

let2int' :: Char -> Int
let2int a | isLower a = Char.ord a - Char.ord 'a'
          | isUpper a = Char.ord a - Char.ord 'A'

int2let' :: Int -> Char
int2let' a | IsLower = Char.chr (a + Char.ord 'A')

shift' :: Int -> Char -> Char
shift' n c | islower c = int2let((let2int c + n) `mod` 26)
           | isupper c = int2let((let2int c + n) `mod` 26)
           | otherwise = c

encode' :: Int -> [Char] -> [Char]
encode' d xs = [ shift d r | r <- xs ]