Copyright | (C) 2011-2015 Edward Kmett |
---|---|
License | BSD-style (see the file LICENSE) |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Stability | experimental |
Portability | portable |
Safe Haskell | Safe-Inferred |
Language | Haskell2010 |
Provides online calculation of the the lowest common ancestor in O(log h)
by compressing the spine of a Path
using a skew-binary random access
list.
This library implements the technique described in my talk
http://www.slideshare.net/ekmett/skewbinary-online-lowest-common-ancestor-search
to improve the known asymptotic bounds on both online lowest common ancestor search
http://en.wikipedia.org/wiki/Lowest_common_ancestor
and the online level ancestor problem:
http://en.wikipedia.org/wiki/Level_ancestor_problem
Algorithms used here assume that the key values chosen for k
are
globally unique.
Synopsis
- data Path a
- lca :: Path a -> Path b -> Path a
- empty :: Path a
- cons :: Int -> a -> Path a -> Path a
- uncons :: Path a -> Maybe (Int, a, Path a)
- view :: Path a -> View Path a
- null :: Path a -> Bool
- length :: Path a -> Int
- isAncestorOf :: Path a -> Path b -> Bool
- keep :: Int -> Path a -> Path a
- drop :: Int -> Path a -> Path a
- traverseWithKey :: Applicative f => (Int -> a -> f b) -> Path a -> f (Path b)
- toList :: Path a -> [(Int, a)]
- fromList :: [(Int, a)] -> Path a
- (~=) :: Path a -> Path b -> Bool
Documentation
Compressed paths using skew binary random access lists
Instances
Functor Path Source # | |
Foldable Path Source # | |
Defined in Data.LCA.Online fold :: Monoid m => Path m -> m # foldMap :: Monoid m => (a -> m) -> Path a -> m # foldMap' :: Monoid m => (a -> m) -> Path a -> m # foldr :: (a -> b -> b) -> b -> Path a -> b # foldr' :: (a -> b -> b) -> b -> Path a -> b # foldl :: (b -> a -> b) -> b -> Path a -> b # foldl' :: (b -> a -> b) -> b -> Path a -> b # foldr1 :: (a -> a -> a) -> Path a -> a # foldl1 :: (a -> a -> a) -> Path a -> a # elem :: Eq a => a -> Path a -> Bool # maximum :: Ord a => Path a -> a # | |
Traversable Path Source # | |
Read a => Read (Path a) Source # | |
Show a => Show (Path a) Source # | |
lca :: Path a -> Path b -> Path a Source #
O(log h) Compute the lowest common ancestor of two paths.
>>>
let fromList' = fromList . map (flip (,) ())
>>>
length (lca (fromList' [1, 2, 3, 4, 5, 6]) (fromList' [7, 8, 3, 4, 5, 6]))
4
cons :: Int -> a -> Path a -> Path a Source #
O(1) Invariant: most operations assume that the keys k
are globally unique
Extend the Path
with a new node ID and value.
uncons :: Path a -> Maybe (Int, a, Path a) Source #
O(1) Extract the node ID and value from the newest node on the Path
.
isAncestorOf :: Path a -> Path b -> Bool Source #
O(log h) xs
holds when isAncestorOf
ysxs
is a prefix starting at the root of Path
ys
.
traverseWithKey :: Applicative f => (Int -> a -> f b) -> Path a -> f (Path b) Source #
Traverse a Path
with access to the node IDs.