Week 3 exercises

week3/Homework3.hs

@@ -1,21 +0,0 @@
--- setting the "warn-incomplete-patterns" flag asks GHC to warn you
--- about possible missing cases in pattern-matching definitions
-{-# OPTIONS_GHC -fwarn-incomplete-patterns #-}
-
--- see https://wiki.haskell.org/Safe_Haskell
-{-# LANGUAGE Safe #-}
-
-
-module Homework3 (gasUsage , luhnDouble , luhn) where
-
-import Types
-
-gasUsage :: (Fractional a, Ord a) => a -> Classification
-gasUsage = undefined
-
-luhnDouble :: Int -> Int
-luhnDouble = undefined
-
-luhn :: Int -> Int -> Int -> Int -> Bool
-luhn = undefined
-

week3/homework.hs

@@ -0,0 +1,29 @@
+-- setting the "warn-incomplete-patterns" flag asks GHC to warn you
+-- about possible missing cases in pattern-matching definitions
+{-# OPTIONS_GHC -fwarn-incomplete-patterns #-}
+
+-- see https://wiki.haskell.org/Safe_Haskell
+{-# LANGUAGE Safe #-}
+
+
+module Homework3 (gasUsage , luhnDouble , luhn) where
+
+import Types
+
+gasUsage :: (Fractional a, Ord a) => a -> Classification
+gasUsage g | g < 3 = Low
+           | 3 <= g && g < 5 = Medium
+           | 5 <= g && g < 7 = High
+           | otherwise = SuperHigh
+
+luhnDouble :: Int -> Int
+luhnDouble x = let y = x * 2 in
+                if y > 9 then y - 9 else y
+
+luhn :: Int -> Int -> Int -> Int -> Bool
+luhn a b c d = let x = [a, b, c, d] in
+               sum (
+                    map
+                        (\(i, y) -> if i `mod` 2 == 0 then luhnDouble y else y)
+                        (zip [1..4] (reverse x))
+               ) `mod` 10 == 0

week3/problems.hs

@@ -0,0 +1,47 @@
+aand :: [Bool] -> Bool
+aand x = aandImpl x True
+
+aandImpl :: [Bool] -> Bool -> Bool
+aandImpl (x:xs) cursor = aandImpl xs (cursor && x)
+aandImpl _ cursor = cursor
+
+cconcat :: [[a]] -> [a]
+cconcat [] = []
+cconcat (x:xs) = x ++ (cconcat xs)
+
+rreplicate :: Int -> a -> [a]
+rreplicate 1 t = [t]
+rreplicate n t = [t] ++ (rreplicate (n-1) t)
+
+(!!!) :: [a] -> Int -> a
+(!!!) (x:_) 0 = x
+(!!!) (x:xs) n = xs !!! (n-1)
+
+isElem :: Eq a => a -> [a] -> Bool
+isElem y [x] = x == y
+isElem y (x:xs) = x == y || (isElem y xs)
+
+merge :: Ord a => [a] -> [a] -> [a]
+merge [a] [b] | a < b = [a, b]
+              | otherwise = [b, a]
+merge [a] (b:bs) | a < b = [a] ++ ([b] ++ bs)
+                 | otherwise = [b] ++ (merge [a] bs)
+merge (a:as) [b] | a < b = [a] ++ (merge as [b])
+                 | otherwise = [b] ++ ([a] ++ as)
+merge (a:as) (b:bs) | a < b = [a] ++ (merge as ([b] ++ bs))
+                    | otherwise = [b] ++ (merge ([a] ++ as) bs)
+
+isPythTriple :: (Int, Int, Int) -> Bool
+isPythTriple (x, y, z) = x^2 + y^2 == z^2
+
+pyths :: Int -> [(Int, Int, Int)]
+pyths n = [(x, y, z) | x <- [1..n], y <- [1..n], z <- [1..n], isPythTriple (x, y, z)]
+
+factors :: Int -> [Int]
+factors n = [x | x <- [1..n], n `mod` x == 0]
+
+perfects :: Int -> [Int]
+perfects n = [x | x <- [1..n], (sum (tail (reverse (factors x)))) == x]
+
+scalarProduct :: [Int] -> [Int] -> Int -> Int
+scalarProduct a b n = sum ([(a!!i)*(b!!i) | i <- [0..n-1]])