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import qualified Data.Set as Set
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data Ord a => Range a = Single !a | Range !a !a
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instance (Ord a, Show a) => Show (Range a) where
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show (Single x) = concat ["(", show x, ")"]
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show (Range x y) = concat ["(", show x, "–", show y, ")"]
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newtype Ord a => Ranges a = Ranges [Range a] deriving Show
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-- | A rather hacked-up instance.
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-- This is to support fast lookups using 'Data.Set' (see 'toSet').
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instance (Ord a) => Eq (Range a) where
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(Single x) == (Single y) = x == y
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(Single a) == (Range x y) = x <= a && a <= y
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(Range x y) == (Single a) = x <= a && a <= y
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(Range lx ux) == (Range ly uy) = (lx <= uy && ux >= ly) || (ly <= ux && uy >= lx)
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instance (Ord a) => Ord (Range a) where
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(Single x) <= (Single y) = x <= y
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(Single x) <= (Range y _) = x <= y
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(Range _ x) <= (Single y) = x <= y
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(Range _ x) <= (Range y _) = x <= y
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-- | A range consisting of a single value.
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single :: (Ord a) => a -> Range a
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-- | Construct a 'Range' from a lower and upper bound.
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range :: (Ord a) => a -> a -> Range a
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| otherwise = error "lower bound must be smaller than upper bound"
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-- | Construct a 'Ranges' from a list of lower and upper bounds.
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ranges :: (Ord a) => [Range a] -> Ranges a
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ranges = Ranges . foldr (flip mergeRanges) []
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-- | Tests if a given range contains a particular value.
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inRange :: (Ord a) => a -> Range a -> Bool
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inRange x y = Single x == y
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-- | Tests if any of the ranges contains a particular value.
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inRanges :: (Ord a) => a -> Ranges a -> Bool
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inRanges x (Ranges xs) = or . map (x `inRange`) $ xs
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mergeRange :: (Ord a) => Range a -> Range a -> Either (Range a) (Range a)
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then Right $ minMax x y
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minMax :: (Ord a) => Range a -> Range a -> Range a
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minMax (Range lx ux) (Range ly uy) = Range (min lx ly) (max ux uy)
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minMax (Single _) y = y
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minMax x@(Range _ _) (Single _) = x
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-- | Allows quick lookups using ranges.
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toSet :: (Ord a) => Ranges a -> Set (Range a)
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toSet (Ranges x) = Set.fromList x
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addRange :: (Ord a) => Ranges a -> Range a -> Ranges a
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addRange (Ranges x) = Ranges . mergeRanges x
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mergeRanges :: (Ord a) => [Range a] -> Range a -> [Range a]
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mergeRanges [] y = [y]
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mergeRanges (x:xs) y = case mergeRange x y of
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Right z -> mergeRanges xs z
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Left x -> x : (mergeRanges xs y)