June 2018 Update

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-10.hs

@@ -1,44 +1 @@
-import Data.List (transpose)
-
-fib
-  :: (Integral b, Num a)
-  => b -> a
-fib 0 = 0 -- this line is necessary because "something ^ 0" returns "fromInteger 1", which unfortunately
--- in our case is not our multiplicative identity (the identity matrix) but just a 1x1 matrix of 1
-fib n = (last . head . unMat) (Mat [[1, 1], [1, 0]] ^ n)
-
--- Code adapted from Matrix exponentiation operator task ---------------------
-(<+>)
-  :: Num c
-  => [c] -> [c] -> [c]
-(<+>) = zipWith (+)
-
-(<*>)
-  :: Num a
-  => [a] -> [a] -> a
-(<*>) = (sum .) . zipWith (*)
-
-newtype Mat a = Mat
-  { unMat :: [[a]]
-  } deriving (Eq)
-
-instance Show a =>
-         Show (Mat a) where
-  show xm = "Mat " ++ show (unMat xm)
-
-instance Num a =>
-         Num (Mat a) where
-  negate xm = Mat $ map (map negate) $ unMat xm
-  xm + ym = Mat $ zipWith (<+>) (unMat xm) (unMat ym)
-  xm * ym =
-    Mat
-      [ [ xs Main.<*> ys -- to distinguish from standard applicative operator
-        | ys <- transpose $ unMat ym ]
-      | xs <- unMat xm ]
-  fromInteger n = Mat [[fromInteger n]]
-  abs = undefined
-  signum = undefined
-
--- TEST ----------------------------------------------------------------------
-main :: IO ()
-main = (print . take 10 . show . fib) (10 ^ 5)
+fib = 0 : 1 : (zipWith (+) <*> tail) fib

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-11.hs

@@ -1,35 +1 @@
-import Control.Arrow ((&&&))
-
-fibstep :: (Integer, Integer) -> (Integer, Integer)
-fibstep (a, b) = (b, a + b)
-
-fibnums :: [Integer]
-fibnums = map fst $ iterate fibstep (0, 1)
-
-fibN2 :: Integer -> (Integer, Integer)
-fibN2 m
-  | m < 10 = iterate fibstep (0, 1) !! fromIntegral m
-fibN2 m = fibN2_next (n, r) (fibN2 n)
-  where
-    (n, r) = quotRem m 3
-
-fibN2_next (n, r) (f, g)
-  | r == 0 = (a, b) -- 3n  ,3n+1
-  | r == 1 = (b, c) -- 3n+1,3n+2
-  | r == 2 = (c, d) -- 3n+2,3n+3   (*)
-  where
-    a =
-      5 * f ^ 3 +
-      if even n
-        then 3 * f
-        else (-3 * f) -- 3n
-    b = g ^ 3 + 3 * g * f ^ 2 - f ^ 3 -- 3n+1
-    c = g ^ 3 + 3 * g ^ 2 * f + f ^ 3 -- 3n+2
-    d =
-      5 * g ^ 3 +
-      if even n
-        then (-3 * g)
-        else 3 * g -- 3(n+1)   (*)
-
-main :: IO ()
-main = print $ (length &&& take 20) . show . fst $ fibN2 (10 ^ 2)
+fib = 0 : 1 : next fib where next (a: t@(b:_)) = (a+b) : next t

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-12.hs

@@ -1,2 +1 @@
- *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
-(208988,"19532821287077577316")
+fib = 0 : scanl (+) 1 fib

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-13.hs

@@ -1 +1,9 @@
-f (n,(a,b)) = (2*n,(a*a+b*b,2*a*b+b*b))     -- iterate f (1,(0,1)) ; b is nth
+import Data.List (foldl') --'
+
+fib :: Integer -> Integer
+fib n =
+  fst $
+  foldl' --'
+    (\(a, b) _ -> (b, a + b))
+    (0, 1)
+    [1 .. n]

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-14.hs

@@ -1 +1,44 @@
-g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b))     -- iterate g (1,(1,1)) ; a is nth
+import Data.List (transpose)
+
+fib
+  :: (Integral b, Num a)
+  => b -> a
+fib 0 = 0 -- this line is necessary because "something ^ 0" returns "fromInteger 1", which unfortunately
+-- in our case is not our multiplicative identity (the identity matrix) but just a 1x1 matrix of 1
+fib n = (last . head . unMat) (Mat [[1, 1], [1, 0]] ^ n)
+
+-- Code adapted from Matrix exponentiation operator task ---------------------
+(<+>)
+  :: Num c
+  => [c] -> [c] -> [c]
+(<+>) = zipWith (+)
+
+(<*>)
+  :: Num a
+  => [a] -> [a] -> a
+(<*>) = (sum .) . zipWith (*)
+
+newtype Mat a = Mat
+  { unMat :: [[a]]
+  } deriving (Eq)
+
+instance Show a =>
+         Show (Mat a) where
+  show xm = "Mat " ++ show (unMat xm)
+
+instance Num a =>
+         Num (Mat a) where
+  negate xm = Mat $ map (map negate) $ unMat xm
+  xm + ym = Mat $ zipWith (<+>) (unMat xm) (unMat ym)
+  xm * ym =
+    Mat
+      [ [ xs Main.<*> ys -- to distinguish from standard applicative operator
+        | ys <- transpose $ unMat ym ]
+      | xs <- unMat xm ]
+  fromInteger n = Mat [[fromInteger n]]
+  abs = undefined
+  signum = undefined
+
+-- TEST ----------------------------------------------------------------------
+main :: IO ()
+main = (print . take 10 . show . fib) (10 ^ 5)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-15.hs

@@ -0,0 +1,35 @@
+import Control.Arrow ((&&&))
+
+fibstep :: (Integer, Integer) -> (Integer, Integer)
+fibstep (a, b) = (b, a + b)
+
+fibnums :: [Integer]
+fibnums = map fst $ iterate fibstep (0, 1)
+
+fibN2 :: Integer -> (Integer, Integer)
+fibN2 m
+  | m < 10 = iterate fibstep (0, 1) !! fromIntegral m
+fibN2 m = fibN2_next (n, r) (fibN2 n)
+  where
+    (n, r) = quotRem m 3
+
+fibN2_next (n, r) (f, g)
+  | r == 0 = (a, b) -- 3n  ,3n+1
+  | r == 1 = (b, c) -- 3n+1,3n+2
+  | r == 2 = (c, d) -- 3n+2,3n+3   (*)
+  where
+    a =
+      5 * f ^ 3 +
+      if even n
+        then 3 * f
+        else (-3 * f) -- 3n
+    b = g ^ 3 + 3 * g * f ^ 2 - f ^ 3 -- 3n+1
+    c = g ^ 3 + 3 * g ^ 2 * f + f ^ 3 -- 3n+2
+    d =
+      5 * g ^ 3 +
+      if even n
+        then (-3 * g)
+        else 3 * g -- 3(n+1)   (*)
+
+main :: IO ()
+main = print $ (length &&& take 20) . show . fst $ fibN2 (10 ^ 2)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-16.hs

@@ -0,0 +1,2 @@
+ *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
+(208988,"19532821287077577316")

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-17.hs

@@ -0,0 +1 @@
+f (n,(a,b)) = (2*n,(a*a+b*b,2*a*b+b*b))     -- iterate f (1,(0,1)) ; b is nth

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-18.hs

@@ -0,0 +1 @@
+g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b))     -- iterate g (1,(1,1)) ; a is nth

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-4.hs

@@ -1,5 +1,6 @@
-fib n = go n 0 1
-  where
-    go n a b
-      | n == 0 = a
-      | otherwise = go (n - 1) b (a + b)
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo f where
+   f 0 = 0
+   f 1 = 1
+   f n = fib (n-1) + fib (n-2)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-5.hs

@@ -1 +1,6 @@
-fib = 0 : 1 : zipWith (+) fib (tail fib)
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \x -> case x of
+   0 -> 0
+   1 -> 1
+   n -> fib (n-1) + fib (n-2)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-6.hs

@@ -1 +1,7 @@
-fib = 0 : 1 : (zipWith (+) <*> tail) fib
+{-# Language LambdaCase #-}
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \case
+   0 -> 0
+   1 -> 1
+   n -> fib (n-1) + fib (n-2)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-7.hs

@@ -1 +1,8 @@
-fib = 0 : 1 : next fib where next (a: t@(b:_)) = (a+b) : next t
+{-# Language LambdaCase #-}
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \case
+   0 -> 0
+   1 -> 1
+   n | n>0 -> fib (n-1) + fib (n-2)
+     | otherwise -> fib (n+2) - fib (n+1)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-8.hs

@@ -1 +1,5 @@
-fib = 0 : scanl (+) 1 fib
+fib n = go n 0 1
+  where
+    go n a b
+      | n == 0 = a
+      | otherwise = go (n - 1) b (a + b)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-9.hs

@@ -1,9 +1 @@
-import Data.List (foldl') --'
-
-fib :: Integer -> Integer
-fib n =
-  fst $
-  foldl' --'
-    (\(a, b) _ -> (b, a + b))
-    (0, 1)
-    [1 .. n]
+fib = 0 : 1 : zipWith (+) fib (tail fib)