| Copyright | (c) Luke Palmer, 2013 |
|---|---|
| License | BSD3 |
| Maintainer | Luke Palmer <lrpalmer@gmail.com> |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Safe-Inferred |
| Language | Haskell98 |
Data.Partition
Description
Disjoint set data structure -- Partition a maintains a collection of disjoint sets of type a, with the ability to find which set a particular item belongs to and the ability to merge any two such sets into one.
- data Partition a
- discrete :: Partition a
- empty :: Partition a
- fromSets :: Ord a => [Set a] -> Partition a
- fromDisjointSets :: Ord a => [Set a] -> Partition a
- nontrivialSets :: Partition a -> [Set a]
- joinElems :: Ord a => a -> a -> Partition a -> Partition a
- find :: Ord a => Partition a -> a -> Set a
- rep :: Ord a => Partition a -> a -> a
Documentation
A Partition of a: represents a collection of disjoint sets of a whose union includes every element of a. Semantics: [[Partition a]] = P(P(a)) where P is the power set operation.
discrete :: Partition a Source
A partition in which every element of a is in its own set. Semantics: [[discrete]] = { { x } | x in a }
fromSets :: Ord a => [Set a] -> Partition a Source
Takes a list of (not necessarily disjoint) sets and constructs a partition that associates all elements shared in any of the sets.
O (n k log n), where k is the maximum set-size and n = l k is the total number of non-discrete elements.
fromDisjointSets :: Ord a => [Set a] -> Partition a Source
Takes a list of disjoint sets and constructs a partition containing those sets, with every remaining element being given its own set. The precondition is not checked.
O (n log n), where n is the total number of elements in the given sets.
nontrivialSets :: Partition a -> [Set a] Source
Returns a list of all nontrivial sets (sets with more than one element) in the partition.
joinElems :: Ord a => a -> a -> Partition a -> Partition a Source
joinElems x y merges the two sets containing x and y into a single set. Semantics: [[joinElems x y p]] = (p `minus` find x `minus` find y) `union` { find x `union` find y }.
O (max(k log n, k log k)), where k is the size of nontrivial subsets and n is the total number of elements in such sets.