Data.LCA.Online

Provides online calculation of the the lowest common ancestor in O(log h) by compressing the spine of the paths using a skew-binary random access list.

Algorithms used here assume that the key values chosen for k are globally unique.

Documentation

data Path a

Compressed paths using skew binary random access lists

Instances

Functor Path

Foldable Path

Traversable Path

Read a => Read (Path a)

Show a => Show (Path a)

lca :: Path a -> Path b -> Path a

O(log h) Compute the lowest common ancestor

empty :: Path a

The empty path

cons :: Int -> a -> Path a -> Path a

O(1) Invariant: most operations assume that the keys k are globally unique

uncons :: Path a -> Maybe (Int, a, Path a)

O(1)

view :: Path a -> View Path a

O(1)

null :: Path a -> Bool

O(1)

length :: Path a -> Int

O(1)

isAncestorOf :: Path a -> Path b -> Bool

O(log h) xs isAncestorOf ys holds when xs is a prefix starting at the root of path ys.

keep :: Int -> Path a -> Path a

O(log (h - k)) to keep k elements of path of height h

drop :: Int -> Path a -> Path a

O(log k) to drop k elements from a path

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

O(1) Compare to see if two trees have the same leaf key