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| 1 | +{-# LANGUAGE FlexibleInstances #-} |
| 2 | +module Data.Ranges |
| 3 | +(range, ranges, Range, Ranges, inRange, inRanges, toSet, single, addRange, diffRanges) |
| 4 | +where |
| 5 | + |
| 6 | +import Data.Set (Set) |
| 7 | +import qualified Data.Set as Set |
| 8 | + |
| 9 | +-- Why do we need a Single instead of Range (a, a)? |
| 10 | +data Ord a => Range a = Single !a | Range !a !a | Empty |
| 11 | +instance (Ord a, Show a) => Show (Range a) where |
| 12 | + show (Single x) = concat ["(", show x, ")"] |
| 13 | + show (Range x y) = concat ["(", show x, ", ", show y, ")"] |
| 14 | + show Empty = "(Empty)" |
| 15 | + |
| 16 | +newtype Ord a => Ranges a = Ranges [Range a] deriving Show |
| 17 | + |
| 18 | +-- | A rather hacked-up instance. |
| 19 | +-- This is to support fast lookups using 'Data.Set' (see 'toSet'). |
| 20 | +-- Ranges are equal if one is contained in the other?! |
| 21 | +instance (Ord a) => Eq (Range a) where |
| 22 | + (Single x) == (Single y) = x == y |
| 23 | + (Single a) == (Range x y) = x <= a && a <= y |
| 24 | + (Range x y) == (Single a) = x <= a && a <= y |
| 25 | + (Range lx ux) == (Range ly uy) = (lx <= uy && ux >= ly) || (ly <= ux && uy >= lx) |
| 26 | + |
| 27 | +instance (Ord a) => Ord (Range a) where |
| 28 | + (Single x) <= (Single y) = x <= y |
| 29 | + (Single x) <= (Range y _) = x <= y |
| 30 | + (Range _ x) <= (Single y) = x <= y |
| 31 | + (Range _ x) <= (Range y _) = x <= y |
| 32 | + |
| 33 | +-- | A range consisting of a single value. |
| 34 | +single :: (Ord a) => a -> Range a |
| 35 | +single x = Single x |
| 36 | + |
| 37 | +-- | Construct a 'Range' from a lower and upper bound. |
| 38 | +range :: (Ord a) => a -> a -> Range a |
| 39 | +range l u |
| 40 | + | l <= u = Range l u |
| 41 | + | otherwise = Range u l |
| 42 | + |
| 43 | +-- | Construct a 'Ranges' from a list of lower and upper bounds. |
| 44 | +ranges :: (Ord a) => [Range a] -> Ranges a |
| 45 | +ranges = Ranges . foldr (flip mergeRanges) [] |
| 46 | + |
| 47 | +-- | Tests if a given range contains a particular value. |
| 48 | +inRange :: (Ord a) => a -> Range a -> Bool |
| 49 | +inRange x y = Single x == y |
| 50 | + |
| 51 | +-- | Tests if any of the ranges contains a particular value. |
| 52 | +inRanges :: (Ord a) => a -> Ranges a -> Bool |
| 53 | +inRanges x (Ranges xs) = or . map (x `inRange`) $ xs |
| 54 | + |
| 55 | +mergeRange :: (Ord a) => Range a -> Range a -> Either (Range a) (Range a) |
| 56 | +mergeRange x y = |
| 57 | + if x == y |
| 58 | + then Right $ minMax x y |
| 59 | + else Left $ x |
| 60 | + |
| 61 | +minMax :: (Ord a) => Range a -> Range a -> Range a |
| 62 | +minMax (Range lx ux) (Range ly uy) = Range (min lx ly) (max ux uy) |
| 63 | +minMax (Single _) y = y |
| 64 | +minMax x@(Range _ _) (Single _) = x |
| 65 | + |
| 66 | +-- | Allows quick lookups using ranges. |
| 67 | +toSet :: (Ord a) => Ranges a -> Set (Range a) |
| 68 | +toSet (Ranges x) = Set.fromList x |
| 69 | + |
| 70 | +addRange :: (Ord a) => Ranges a -> Range a -> Ranges a |
| 71 | +addRange (Ranges x) = Ranges . mergeRanges x |
| 72 | + |
| 73 | +mergeRanges :: (Ord a) => [Range a] -> Range a -> [Range a] |
| 74 | +mergeRanges [] y = [y] |
| 75 | +mergeRanges (x:xs) y = case mergeRange x y of |
| 76 | + Right z -> mergeRanges xs z |
| 77 | + Left x -> x : (mergeRanges xs y) |
| 78 | + |
| 79 | +-- Remove all elements from A that are a member of B |
| 80 | +diffRange :: (Ord a) => Range a -> Range a -> [Range a] |
| 81 | +diffRange Empty b = [Empty] |
| 82 | +diffRange a Empty = [a] |
| 83 | +diffRange (Single a) (Single b) = if (a == b) |
| 84 | + then [Empty] |
| 85 | + else [(Single a)] |
| 86 | +diffRange (Single b) (Range l u) = if (l < b) && (b < u) |
| 87 | + then [Empty] |
| 88 | + else [(Single b)] |
| 89 | +diffRange (Range l u) (Single b) = if (l < b) && (b < u) |
| 90 | + then [(Range l b), (Range b u)] |
| 91 | + else [(Range l u)] |
| 92 | +diffRange (Range al au) (Range bl bu) = |
| 93 | + if (bu <= al) || (au <= bl) then -- B is before or after A |
| 94 | + [(Range al au)] |
| 95 | + else if (bl <= al) && (bu < au) then -- B is to the left of A |
| 96 | + [(Range bu au)] |
| 97 | + else if (bl > al) && (bu < au) then -- B is inside A |
| 98 | + [(Range al bl), (Range bu au)] |
| 99 | + else if (bl < al) && (bu > au) then -- A is inside B |
| 100 | + [Empty] |
| 101 | + else if (bl > al) && (bu >= au) then -- B is to the right of A |
| 102 | + [(Range al bl)] |
| 103 | + else -- A is equal to B |
| 104 | + [Empty] |
| 105 | + |
| 106 | +diffRanges :: (Ord a) => Range a -> Ranges a -> Ranges a |
| 107 | +diffRanges r (Ranges d) = Ranges (diffRanges' r d) where |
| 108 | + diffRanges' r [] = [r] |
| 109 | + diffRanges' r (s:rest) = case (diffRange r s) of |
| 110 | + [r'] -> diffRanges' r' rest |
| 111 | + [b, r'] -> b:(diffRanges' r' rest) |
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