Data.Set.BKTree
 Portability portable Stability Alpha quality. Interface may change without notice. Maintainer josef.svenningsson@gmail.com
Description

Burhard-Keller trees provide an implementation of sets which apart from the ordinary operations also has an approximate member search, allowing you to search for elements that are of a distance n from the element you are searching for. The distance is determined using a metric on the type of elements. Therefore all elements must implement the Metric type class, rather than the more usual Ord.

Useful metrics include the manhattan distance between two points, the Levenshtein edit distance between two strings, the number of edges in the shortest path between two nodes in a undirected graph and the Hamming distance between two binary strings. Any euclidean space also has a metric. However, in this module we use int-valued metrics and that doesn't quite with the metrics of euclidean spaces which are real-values.

The worst case complexity of many of these operations is quite bad, but the expected behavior varies greatly with the metric. For example, the discrete metric (distance x y | y == x = 0 | otherwise = 1) makes BK-trees behave abysmally. The metrics mentioned above should give good performance characteristics.

Synopsis
data BKTree a
class Eq a => Metric a where
 distance :: a -> a -> Int
null :: BKTree a -> Bool
empty :: BKTree a
fromList :: Metric a => [a] -> BKTree a
singleton :: a -> BKTree a
insert :: Metric a => a -> BKTree a -> BKTree a
member :: Metric a => a -> BKTree a -> Bool
memberDistance :: Metric a => Int -> a -> BKTree a -> Bool
delete :: Metric a => a -> BKTree a -> BKTree a
union :: Metric a => BKTree a -> BKTree a -> BKTree a
unions :: Metric a => [BKTree a] -> BKTree a
elems :: BKTree a -> [a]
elemsDistance :: Metric a => Int -> a -> BKTree a -> [a]
closest :: Metric a => a -> BKTree a -> Maybe (a, Int)
Documentation
data BKTree a
 The type of Burhard-Keller trees.
class Eq a => Metric a where

A type is Metric if is has a function distance which has the following properties:

All types of elements to BKTree must implement Metric.

This definition of a metric deviates from the mathematical one in that it returns an integer instead of a real number. The reason for choosing integers is that I wanted to avoid the rather unpredictable rounding of floating point numbers.

Methods
 distance :: a -> a -> Int Instances
 Metric Char Metric Int Metric Integer Eq a => Metric [a]
null :: BKTree a -> Bool
Test if the tree is empty.
empty :: BKTree a
The empty tree.
fromList :: Metric a => [a] -> BKTree a
Constructs a tree from a list
singleton :: a -> BKTree a
The tree with a single element
insert :: Metric a => a -> BKTree a -> BKTree a
Inserts an element into the tree. If an element is inserted several times it will be stored several times.
member :: Metric a => a -> BKTree a -> Bool
Checks whether an element is in the tree.
memberDistance :: Metric a => Int -> a -> BKTree a -> Bool
Approximate searching. memberDistance n a tree will return true if there is an element in tree which has a distance less than or equal to n from a.
delete :: Metric a => a -> BKTree a -> BKTree a
Removes an element from the tree. If an element occurs several times in the only the first occurrence will be deleted.
union :: Metric a => BKTree a -> BKTree a -> BKTree a
Merges two trees
unions :: Metric a => [BKTree a] -> BKTree a
Merges several trees
elems :: BKTree a -> [a]
Returns all the elements of the tree
elemsDistance :: Metric a => Int -> a -> BKTree a -> [a]
elemsDistance n a tree returns all the elements in tree which are at a distance less than or equal to n from the element a.
closest :: Metric a => a -> BKTree a -> Maybe (a, Int)
closest a tree returns the element in tree which is closest to a together with the distance. Returns Nothing if the tree is empty.