2016 Update

Task/Prime-decomposition/Haskell/prime-decomposition-1.hs

@@ -1,3 +1,5 @@
-factorize n = concat [divs n p | p <- [2..n], isPrime p]
-  where
-    divs n p = if rem n p==0 then p:divs (quot n p) p else []
+factorize n = [ d | p <- [2..n], isPrime p, d <- divs n p ]
+           -- [2..n] >>= (\p-> [p|isPrime p]) >>= divs n
+    where
+    divs n p | rem n p == 0 = p : divs (quot n p) p
+             | otherwise    = []

Task/Prime-decomposition/Haskell/prime-decomposition-2.hs

@@ -1,6 +1,11 @@
-factorize n = divs n primesList
-   where
-     divs n ds@(d:t) | d*d > n    = [n | n > 1]
-                     | r == 0     =  d : divs q ds
-                     | otherwise  =      divs n t
-            where  (q,r) = quotRem n d
+import Data.Maybe (listToMaybe)
+import Data.List (unfoldr)
+
+factorize :: Integer -> [Integer]
+factorize n
+  = unfoldr (\n     -> listToMaybe [(x, div n x)      | x <- [2..n], mod n x==0]) n
+  = unfoldr (\(d,n) -> listToMaybe [(x, (x, div n x)) | x <- [d..n], mod n x==0]) (2,n)
+  = unfoldr (\(d,n) -> listToMaybe [(x, (x, div n x)) | x <-
+                    takeWhile ((<=n).(^2)) [d..] ++ [n|n>1], mod n x==0]) (2,n)
+  = unfoldr (\(ds,n) -> listToMaybe [(x, (dropWhile (< x) ds, div n x)) | n>1, x <-
+                    takeWhile ((<=n).(^2)) ds ++ [n|n>1], mod n x==0]) (primesList,n)

Task/Prime-decomposition/Haskell/prime-decomposition-3.hs

@@ -1,22 +1,6 @@
-import Test.HUnit
-import Data.List
-
-factor::Int->[Int]
-factor 1 = []
-factor n
-  | product primeDivisor == n = primeDivisor
-  | otherwise = primeDivisor ++ factor (div n $ product primeDivisor)
-  where
-    primeDivisor = filter isPrime $ filter (isDivisor n) [2 .. n]
-    isDivisor n d = (==) 0 $ mod n d
-    isPrime n = not $ any (isDivisor n) [2 .. n-1]
-
-tests = TestList[TestCase $ assertEqual "1 has no prime factors" [] $ factor 1
-                ,TestCase $ assertEqual "2 is 2" [2] $ factor 2
-                ,TestCase $ assertEqual "3 is 3" [3] $ factor 3
-                ,TestCase $ assertEqual "4 is 2*2" [2, 2] $ factor 4
-                ,TestCase $ assertEqual "5 is 5" [5] $ factor 5
-                ,TestCase $ assertEqual "6 is 2*3" [2, 3] $ factor 6
-                ,TestCase $ assertEqual "7 is 7" [7] $ factor 7
-                ,TestCase $ assertEqual "8 is 2*2*2" [2, 2, 2] $ factor 8
-                ,TestCase $ assertEqual "large number" [2, 3, 3, 5, 7, 11, 13] $ sort $ factor (2*9*5*7*11*13)]
+factorize n = divs n primesList
+     where
+     divs n ds@(d:t) | d*d > n    = [n | n > 1]
+                     | r == 0     =  d : divs q ds
+                     | otherwise  =      divs n t
+            where  (q,r) = quotRem n d