Blatt3.hs

-- Aufgabe 1 a)

rangeProduct :: Int -> Int -> Int
rangeProduct m n
        | m == n = m
        | m < n = m * rangeProduct (m+1) n
        | otherwise = 0

fac :: Int -> Int
fac 0 = 1
fac 1 = 1
fac x = rangeProduct 1 x

fac' :: Int -> Int
fac' 0 = 1
fac' n = n * fac' (n -1)

rangeProduct'::Int->Int->Int
rangeProduct' m n
        | m==n = n
        | m==0 || n==0 = 0
        | m<n = div (fac n) (fac (m-1))
        | m>n = div (fac m) (fac (n-1))

countNumberInTuple :: Int -> (Int, Int) -> Int
countNumberInTuple k (a,b)
        | a == k && b == k = 2
        | a == k || b == k = 1
        | otherwise = 0

countNumberInTriple :: Int -> (Int, Int, Int) -> Int
countNumberInTriple k (a,b,c)
        | a == k && b == k && c == k = 3
        | (a == k && b == k) || (a == k && c == k) || (b == k && b == k) = 2
        | a == k || b == k || c == k = 1
        | otherwise = 0

maxOccurs :: Int -> Int -> (Int, Int)
maxOccurs a b = (max a b, countNumberInTuple (max a b) (a,b))

{-
maxThreeOccurs :: Int -> Int -> Int -> (Int, Int)
maxThreeOccurs a b c
                | countNumberInTriple a (a,b,c) > 0 = (maxN, snd(maxOccurs b c) + 1)
                | countNumberInTriple b (a,b,c) > 0 = (maxN, snd(maxOccurs a c) + 1)
                | countNumberInTriple c (a,b,c) > 0 = (maxN, snd(maxOccurs b a) + 1)
                where maxN = max (fst (maxOccurs a b)) (fst (maxOccurs b c))
-}
-- increases value of tuple x,x at point n
increaseByOne :: Int -> (Int, Int) -> (Int, Int)
increaseByOne n (a,b)
        | n > 1 = (a, b+1)
        | n == 1 = (a+1, b)
        | n < 1 = error "Can not increase tuple at less 1"
        | otherwise = error "error while increasing tuple"

maxThreeOccurs :: Int -> Int -> Int -> (Int, Int)
maxThreeOccurs a b c
        | fst maxAB == a && a > c = maxAB 
        | fst maxAB == a && a == c = increaseByOne 2 maxAB
        | fst maxAB == b && b > c = maxAB
        | fst maxAB == b && b == c = increaseByOne 2 maxAB
        | c >= a && c >= b  = (c, 1+(countNumberInTuple c (a,b)))
        where maxAB = maxOccurs a b

matches :: Int -> [Int] -> [Int]
matches n [] = []
matches n a = [x | x <- a, x == n]

elemt :: Int -> [Int] -> Bool
elemt n a = not (null (matches n a))