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instance Fractional Fraction where
  (/) f             = (*) f . recip
  recip (Frac a b)  = Frac b a
  fromRational r    = Frac (numerator r) (denominator r)

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instance Eq Fraction where
  (/=) f    = not . (==) f
  (==) f f' = (x == x') && (y == y')
      where (Frac x y) = simplify f
            (Frac x' y') = simplify f'
  
instance Ord Fraction where
  compare (Frac a b) (Frac c d) = compare (a `quot` b) (c `quot` d)
  (<)  f    = (==) LT . compare f
  (>)  f    = (==) GT . compare f

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instance Monoid Fraction where
  mempty  = 0
  mappend = (+)
  mconcat = foldr mappend mempty

(%) :: Integer -> Integer -> Fraction
(%) a = simplify . Frac a

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import Fraction

main = return . length . filter moreInNum . map sqrtTwo $ [1..1000]
  where moreInNum f = length ( (show . num) f ) > length ( (show . denom) f)
        sqrtTwo = simplify . (+) 1 . sqrtTwo'
          where sqrtTwo' 1 = 1 % 2
                sqrtTwo' n = 1 / ( 2 + sqrtTwo' (pred n) )

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module Fraction 
  (
    Fraction,
    (%),
    simplify,
    num,
    denom
  ) where

import Data.Monoid

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tsort :: (Eq a) => Graph a -> [a]
tsort graph  = tsort' [] (noInbound graph) graph
  where noInbound (Graph v e) = filter (flip notElem $ map snd e) v
        tsort' l []    (Graph _ []) = reverse l
        tsort' l []    _            = error "There is at least one cycle in this graph."
        tsort' l (n:s) g            = tsort' (n:l) s' g'
          where outEdges = outbound n g
                outNodes = map snd outEdges
                g'       = foldr removeEdge g outEdges
                s'       = s ++ filter (null . flip inbound g') outNodes

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danceOutcome = graphFromFile "people.txt" >>= \f -> return $ tsort f

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module Graph(
  Graph(Graph),
  removeEdge,
  outbound,
  inbound
)where

data Graph a = Graph{ vertices :: [a], edges :: [(a, a)] } deriving Show

removeEdge :: (Eq a) => (a, a) -> Graph a -> Graph a

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import Data.List --for later
import System.Environment --for later
import Graph

data Letter = A | B | C | D | E | F deriving (Show, Eq, Enum)

sample :: Graph Letter
sample = Graph [A,B,C,D,E,F] [(A, B), (A, C), (B, D), (C, D), (D, E), (D, F), (B, C), (F, E)]

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Leslie Andy
April Andy
Ron Ann
Ron April
Ann Jerry
Ann Andy
Leslie April
Ron Andy
Leslie Ron
Andy Jerry