Add Collatz exploration

src/3n+1/Main.hs

@@ -0,0 +1,47 @@
+import           Control.Monad ()
+import           Debug.Trace   (trace)
+
+f' :: Integer -> Integer
+f' n = f'' 0 n
+  where
+    f'' :: Integer -> Integer -> Integer
+    f'' i n'
+      | n' == 1 = t' i
+      | even n' = t $ f'' (i + 1) (n' `div` 2)
+      | odd  n' = t $ f'' (i + 1) (3*n' + 1)
+      where t   = trace ("i: " ++ show i ++ ", number: " ++ show n')
+            t'  = t'' $ trace ("END: " ++ show n ++ ", length: " <> show i) $ t''
+            t'' = trace "\n#######################################################\n"
+
+f :: Integer -> Integer
+f n = s 0 n
+  where
+    s :: Integer -> Integer -> Integer
+    s i n
+      | n == 1 = i
+      | even n = s i' (n `div` 2)
+      | odd  n = s i' (3*n + 1)
+      where i' = i + 1
+
+main :: IO ()
+main = print $ map f [2^361..]
+
+-- collatz collect
+-- generate the collatz sequence and return it
+
+cc :: Integer -> [Integer]
+cc n = cc' [] n
+  where
+    cc' :: [Integer] -> Integer -> [Integer]
+    cc' acc n
+      | n == 1 = 1:acc
+      | even n = cc' acc' (n `div` 2)
+      | odd  n = cc' acc' (3*n + 1)
+      where acc' = acc <> [n]
+
+primes :: [Integer]
+primes = sieve [2..]
+  where
+    sieve (p:xs) = p : sieve [x|x <- xs, x `mod` p > 0]
+
+isPrime k = (k > 1) && null [ x | x <- [2..k - 1], k `mod` x == 0]

src/projectEuler/question1.hs

@@ -13,6 +13,9 @@ main = print ans
 ans :: Integer
 ans = sum $ allNumbersUnder 1000
 
+sum' :: Num a => [a] -> a
+sum' = foldl (+) 0
+
 isMultipleOf :: Integral a => a -> a -> Bool
 isMultipleOf n x = x `rem` n == 0
 

src/projectEuler/question15.hs

@@ -14,10 +14,31 @@ main = print ans
 
 ans = 42
 
-limit = 20
-points = [(x,y) | x <- [1..limit], y <- [1..limit]]
+limit = 2
+points = [ (x,y)
+  | x <- [0..limit]
+  , y <- [0..limit]
+  ]
 
 data Direction = Right | Down
 
 move Right (x,y) = (x+1, y  )
 move Down  (x,y) = (x  , y+1)
+
+-- solve :: (Int, Int) -> [[(Int, Int)]]
+{-
+λ> [(0,0)]
+[(0,0)]
+λ> [(0,0),(1,0),(2,0),(2,1),(2,2)]
+[(0,0),(1,0),(2,0),(2,1),(2,2)]
+λ> [ [(0,0),(1,0),(2,0),(2,1),(2,2)], [(0,0),(1,0),(1,1),(2,1),(2,2)]]
+[[(0,0),(1,0),(2,0),(2,1),(2,2)],[(0,0),(1,0),(1,1),(2,1),(2,2)]]
+λ>
+-}
+
+data Tree a
+  = Leaf a
+  | Branch (Tree a) (Tree a)
+  deriving (Show)
+
+

src/projectEuler/question16.hs

@@ -0,0 +1,15 @@
+{-
+https://projecteuler.net/problem=16
+
+2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.
+
+What is the sum of the digits of the number 2^1000?
+-}
+
+module Main where
+
+main :: IO ()
+main = print ans
+
+ans :: Integer
+ans = sum $ map (\c -> read [c] :: Integer) $ show (2^1000)