praxis

Various programming exercises.
git clone git://git.jtobin.io/praxis.git
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taxicab.hs (916B)

      1 -- Spec: write a function that returns all of the ways a number can be written 
      2 -- as the sum of two non-negative cubes.
      3 
      4 {-# OPTIONS_GHC -Wall -Werror #-}
      5 
      6 import Control.Arrow
      7 import Test.QuickCheck 
      8 
      9 cubeDecomposition :: Int -> [(Int, Int)]
     10 cubeDecomposition n = 
     11     [(x, y) | x <- [1..m], y <- [x..m], x^(3 :: Int) + y^(3 :: Int) == n] 
     12   where m = truncate $ fromIntegral n ** (1/3 :: Double)
     13 
     14 main :: IO ()
     15 main = do
     16     let highConfidence = stdArgs {maxSuccess = 10000}
     17     putStrLn "running tests.." 
     18     quickCheckWith highConfidence (forAll smallInts cubedElementsSumToN)
     19 
     20 -- Tests -----------------------------------------------------------------------
     21 
     22 smallInts :: Gen Int
     23 smallInts = choose (-100000000, 100000000)
     24 
     25 cubedElementsSumToN :: Int -> Bool
     26 cubedElementsSumToN n = all (== n) d 
     27     where d = map (uncurry (+) . ((^(3 :: Int)) *** (^(3 :: Int)))) 
     28                     (cubeDecomposition n)
     29