chapter4, 5

problems/mshibatatt/chapter4/1.hs

@@ -0,0 +1,3 @@
+halve :: [a] -> ([a], [a])
+halve xs = (take n xs, drop n xs) 
+    where n = (length xs) `div` 2

problems/mshibatatt/chapter4/2.hs

@@ -0,0 +1,11 @@
+-- using head and tail
+third_a :: [a] -> a
+third_a xs = head (tail (tail xs))
+
+-- using index
+third_b :: [a] -> a
+third_b xs = xs !! 2
+
+-- using pattern match
+third_c :: [a] -> a
+third_c (_:_:x:_) = x

problems/mshibatatt/chapter4/3.hs

@@ -0,0 +1,13 @@
+-- condition 
+safetail_a :: [a] -> [a]
+safetail_a xs = if null xs then [] else tail xs
+
+-- equation with guard 
+safetail_b :: [a] -> [a]
+safetail_b xs | null xs = [] 
+              | otherwise = tail xs
+
+-- pattern match 
+safetail_c :: [a] -> [a]
+safetail_c [] = []
+safetail_c (_:xs) = xs

problems/mshibatatt/chapter4/7.hs

@@ -0,0 +1,2 @@
+mult :: Int -> Int -> Int -> Int
+mult = \x -> (\y -> (\z -> x*y*z))

problems/mshibatatt/chapter4/8.hs

@@ -0,0 +1,7 @@
+luhnDouble :: Int -> Int
+luhnDouble x = if x2 > 9 then x2 - 9 else x2 where x2 = x*2
+
+luhn :: Int -> Int -> Int -> Int -> Bool
+luhn x y z w = (luhnDouble x + y + luhnDouble z + w) `mod` 10 == 0
+
+

problems/mshibatatt/chapter5/1.hs

@@ -0,0 +1 @@
+sum [x^2 | x <- [1..100]]

problems/mshibatatt/chapter5/10.hs

@@ -0,0 +1,35 @@
+import Data.Char
+alphas xs = length [x | x <- xs, (x >= 'a' && x <= 'z') || (x >= 'A' && x <= 'Z')]
+count x xs = length [x' | x' <- xs, x == x']
+count_2 x y xs = length [x' | x' <- xs, x == x' || y == x']
+
+let2int_lower c = ord c - ord 'a'
+int2let_lower n = chr (ord 'a' + n)
+let2int_upper c = ord c - ord 'A'
+int2let_upper n = chr (ord 'A' + n)
+
+shift n c | isLower c = int2let_lower ((let2int_lower c + n) `mod` 26)
+          | isUpper c = int2let_upper ((let2int_upper c + n) `mod` 26)
+          | otherwise = c 
+
+encode n xs = [shift n x | x <- xs]
+
+positions x xs = [i | (x', i) <- zip xs [0..], x == x']
+
+percent n m = (fromIntegral n) / (fromIntegral m) * 100
+freqs xs = [percent (count_2 x y xs) n | (x, y) <- zip ['a'..'z'] ['A'..'Z']]
+    where n = alphas xs
+
+chisqr os es = sum [((o-e)^2)/e | (o,e) <- zip os es]
+rotate n xs = drop n xs ++ take n xs
+
+table :: [Float]
+table = [8.1, 1.5, 2.8, 4.2, 12.7, 2.2, 2.0, 6.1, 7.0,
+         0.2, 0.8, 4.0, 2.4, 6.7, 7.5, 1.9, 0.1, 6.0,
+         6.3, 9.0, 2.8, 1.0, 2.4, 0.2, 2.0, 0.1]
+
+crack xs = encode (-factor) xs
+  where
+    factor = head (positions (minimum chitab) chitab)
+    chitab = [chisqr (rotate n table') table | n <- [0..26]]
+    table' = freqs xs

problems/mshibatatt/chapter5/2.hs

@@ -0,0 +1,2 @@
+grid :: Int -> Int -> [(Int, Int)]
+grid x y = [(a, b) | a <- [0..x], b <- [0..y]]

problems/mshibatatt/chapter5/3.hs

@@ -0,0 +1,2 @@
+square :: Int -> [(Int, Int)]
+square n = [(x, y) | x <- [0..n], y <- [0..n], x /= y]

problems/mshibatatt/chapter5/4.hs

@@ -0,0 +1,2 @@
+replicate_c :: Int -> a -> [a]
+replicate_c n x = [x | _ <- [1..n]]

problems/mshibatatt/chapter5/5.hs

@@ -0,0 +1,2 @@
+pyths :: Int -> [(Int, Int, Int)]
+pyths n = [(x, y, z) | x <- [1..n], y <- [1..n], z <- [1..n], x^2 + y^2 == z^2]

problems/mshibatatt/chapter5/6.hs

@@ -0,0 +1,2 @@
+perfects :: Int -> [Int]
+perfects n = [x | x <- [1..n], sum [y | y <- [1..x-1], x `mod` y == 0] == x]

problems/mshibatatt/chapter5/7.hs

@@ -0,0 +1,3 @@
+[(x, y) | x <- [1, 2, 3], y <- [4, 5, 6]]
+-- ?
+[(z, y) | z <- [x | x <- [1, 2, 3]], y <- [4, 5, 6]]

problems/mshibatatt/chapter5/8.hs

@@ -0,0 +1,8 @@
+find :: Eq a => a -> [(a, b)] -> [b]
+find k t = [v | (k', v) <- t, k == k']
+
+positions :: Eq a => a -> [a] -> [Int]
+positions x xs = [i | (x', i) <- zip xs [0..], x == x']
+
+positions_find :: Eq a => a -> [a] -> [Int]
+positions_find x xs = find x [xs' | xs' <- zip xs [0..]]

problems/mshibatatt/chapter5/9.hs

@@ -0,0 +1,2 @@
+scalarproduct :: [Int] -> [Int] -> Int
+scalarproduct xs ys = sum [x*y |(x, y) <- zip xs ys]

problems/mshibatatt/chapter6/1.hs

@@ -0,0 +1,3 @@
+fac :: Int -> Int
+fac 0 = 1
+fac n | n > 0 = n * fac(n-1)

problems/mshibatatt/chapter6/2.hs

@@ -0,0 +1,3 @@
+sumdown :: Int -> Int
+sumdown 0  = 0
+sumdown n | n > 0 = n + sumdown(n-1)

problems/mshibatatt/chapter6/3.hs

@@ -0,0 +1,3 @@
+(^) :: Int -> Int -> Int
+m ^ 0 = 1
+m ^ n | n > 0 = m * (m Main.^ (n-1))

problems/mshibatatt/chapter6/4.hs

@@ -0,0 +1,4 @@
+euclid :: Int -> Int -> Int
+euclid m n | m == n = m
+           | m < n = euclid m (n-m)
+           | n < m = euclid (m-n) n

problems/mshibatatt/chapter6/6.hs

@@ -0,0 +1,20 @@
+and_ :: [Bool] -> Bool
+and_ [] = True
+and_ (x:xs) = x && and_ xs
+
+concat_ :: [[a]] -> [a]
+concat_ [[]] = []
+concat_ [x:[xs]] = [x] ++ concat_ [[xs]]
+
+replicate_ :: Int -> a -> [a]
+replicate_ 0 a = []
+replicate_ n a | n > 0 = [a] ++ (replicate_ (n-1) a) 
+
+index :: [a] -> Int -> a
+index (x:xs) 0 = x
+index (x:xs) n | n > 0 = index xs (n-1)
+
+elem_ :: Eq a => a -> [a] -> Bool
+elem_ a [] = False
+elem_ a (x:xs) | a == x = True
+               | otherwise = elem_ a xs

problems/mshibatatt/chapter6/7.hs

@@ -0,0 +1,6 @@
+merge :: Ord a => [a] -> [a] -> [a]
+merge xs [] = xs
+merge xs (y:ys) = merge (small ++ [y] ++ large) ys 
+    where 
+        small = [x | x <- xs, x <= y]
+        large = [x | x <- xs, x > y]

problems/mshibatatt/chapter6/8.hs

@@ -0,0 +1,15 @@
+merge :: Ord a => [a] -> [a] -> [a]
+merge xs [] = xs
+merge xs (y:ys) = merge (small ++ [y] ++ large) ys 
+    where 
+        small = [x | x <- xs, x <= y]
+        large = [x | x <- xs, x > y]
+
+halve :: [a] -> ([a], [a])
+halve xs = (take n xs, drop n xs) 
+    where n = (length xs) `div` 2
+
+msort :: Ord a => [a] -> [a]
+msort x | length x == 1 = x
+        | otherwise = merge (msort a) (msort b)
+            where (a, b) = halve x

problems/mshibatatt/chapter6/9.hs

@@ -0,0 +1,11 @@
+sum_a :: [Int] -> Int
+sum_a [] = 0
+sum_a (x:xs) = x + sum_a xs
+
+take_b :: Int -> [a] -> [a]
+take_b 0 xs = []
+take_b n (x:xs) = [x] ++ take_b (n-1) xs
+
+last_c :: [a] -> a
+last_c [x] = x
+last_c (x:xs) = last_c xs

problems/mshibatatt/chapter7/10.hs

@@ -0,0 +1,9 @@
+luhnDouble :: Int -> Int
+luhnDouble x = if x2 > 9 then x2 - 9 else x2 where x2 = x*2
+
+altMap :: (a -> b) -> (a -> b) -> [a] -> [b]
+altMap _ _ [] = []
+altMap f g (x:xs) = [f x] ++ altMap g f xs 
+
+luhn :: [Int] -> Bool
+luhn x = (sum (altMap luhnDouble (\y -> y) x)) `mod` 10 == 0

problems/mshibatatt/chapter7/2.hs

@@ -0,0 +1,19 @@
+all_a :: (a -> Bool) -> [a] -> Bool
+all_a _ [] = True
+all_a p (x:xs) = (p x) && (all_a p xs)
+
+any_b :: (a -> Bool) -> [a] -> Bool
+any_b _ [] = False
+any_b p (x:xs) = (p x) || (any_b p xs) 
+
+takewhile_c :: (a -> Bool) -> [a] -> [a]
+takewhile_c _ [] = []
+takewhile_c p (x:xs) | p x = [x] ++ takewhile_c p xs
+                     | otherwise = []
+
+dropwhile_d :: (a -> Bool) -> [a] -> [a]
+dropwhile_d _ [] = []
+dropwhile_d p (x:xs) | p x = dropwhile_d p xs
+                     | otherwise = x:xs
+
+

problems/mshibatatt/chapter7/3.hs

@@ -0,0 +1,2 @@
+map_ f = foldr (\x xs -> f x : xs) [] 
+filter_ p = foldr (\x xs -> if p x then x:xs else xs) []

problems/mshibatatt/chapter7/4.hs

@@ -0,0 +1,2 @@
+dec2int :: [Int] -> Int
+dec2int = foldl (\x y -> 10*x+y) 0

problems/mshibatatt/chapter7/5.hs

@@ -0,0 +1,5 @@
+curry :: ((a, b) -> c) -> (a -> b -> c)
+curry f = \x y -> f (x, y)
+
+uncurry :: (a -> b -> c) -> ((a, b) -> c)
+uncurry f = \(x, y) -> f x y

problems/mshibatatt/chapter7/9.hs

@@ -0,0 +1,3 @@
+altMap :: (a -> b) -> (a -> b) -> [a] -> [b]
+altMap _ _ [] = []
+altMap f g (x:xs) = [f x] ++ altMap g f xs