import System.Random
import Control.Monad.State
import Control.Applicative
 
monteCarlo :: (Random a, RandomGen g)
           => Int -> (a,a) -> (a -> Bool) -> g -> Double
monteCarlo count reg cond gen = fromIntegral hits / fromIntegral count
  where rands = take count (randomRs reg gen)
        hits  = length (filter cond rands)
 
 
instance (Random a, Random b, Random c) => Random (a,b,c) where
  random = runState (liftA3 (,,) (state random) (state random) (state random))
  randomR ((x1,y1,z1), (x2,y2,z2)) gen1 =
    let (x, gen2) = randomR (x1, x2) gen1
        (y, gen3) = randomR (y1, y2) gen2
        (z, gen4) = randomR (z1, z2) gen3
    in ((x,y,z), gen4)
 
main = do
  gen <- getStdGen
  print (monteCarlo 10000 ((0.0,0.0,0.0),(1.0,1.0,1.0)) isTriangle gen)
  where isTriangle :: (Double,Double,Double) -> Bool
        isTriangle (x,y,z) = x+y>z && y+z>x && z+x>y
 

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