Created
January 30, 2012 12:10
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module IntervalTree (interval, toList, delete, deleteRange) | |
where | |
data IntervalTree = Empty | Range Int Int | Split Int Int Int IntervalTree IntervalTree deriving Show | |
interval :: Int -> Int -> IntervalTree | |
interval x y | y < x = Empty | |
interval x y = Range x y | |
toList :: IntervalTree -> [Int] | |
toList Empty = [] | |
toList (Range x y) = [x..y] | |
toList (Split _ _ _ x y) = toList x ++ toList y | |
delete :: Int -> IntervalTree -> IntervalTree | |
delete i x | not (x `couldPossiblyContain` i) = x | |
delete i (Range x y) | i == x = interval (x + 1) y | |
delete i (Range x y) | i == y = interval x (y - 1) | |
delete i (Range x y) = delete i (newsplit x y) | |
delete i (Split m _ _ x y) | i <= m = join m (delete i x) y | |
delete i (Split m _ _ x y) = join m x (delete i y) | |
deleteRange :: Int -> Int -> IntervalTree -> IntervalTree | |
deleteRange _ _ Empty = Empty | |
deleteRange _ y t | y < lowerBound t = t | |
deleteRange x _ t | x > upperBound t = t | |
deleteRange x y t | x <= lowerBound t && y >= upperBound t = Empty | |
deleteRange x y (Range m n) | x <= m = interval (y + 1) n | |
deleteRange x y (Range m n) | y >= n = interval m (x - 1) | |
deleteRange x y (Range m n) = deleteRange x y (newsplit m n) | |
deleteRange x y (Split k _ _ l r) = join k (deleteRange x y l) (deleteRange x y r) | |
newsplit :: Int -> Int -> IntervalTree | |
newsplit x y = Split m x y (interval x m) (interval (m + 1) y) | |
where m = (x + y) `div` 2 | |
join :: Int -> IntervalTree -> IntervalTree -> IntervalTree | |
join m Empty y = y | |
join m x Empty = x | |
join m x y = Split m (lowerBound x) (upperBound y) x y | |
couldPossiblyContain :: IntervalTree -> Int -> Bool | |
couldPossiblyContain Empty _ = False | |
couldPossiblyContain x i = (lowerBound x <= i) && (upperBound x >= i) | |
lowerBound :: IntervalTree -> Int | |
lowerBound (Range x _) = x | |
lowerBound (Split _ lb _ _ _) = lb | |
upperBound :: IntervalTree -> Int | |
upperBound (Range _ y) = y | |
upperBound (Split _ _ ub _ _) = ub |
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