Module

Data.Sequence.Ordered

This module defines a sequence where elements are always kept in order. This enables constant time access to the least and greatest elements, in addition to logarithmic time partitioning.

The module is intended to be imported qualified, to avoid ambiguity or name clashes. For example:

import Data.Sequence.Ordered (OrdSeq)
import Data.Sequence.Ordered as OrdSeq

#OrdSeq 

newtype OrdSeq a

An ordered sequence. The Semigroup instance uses the merge function.

Instances

#empty 

empty :: forall a. OrdSeq a

#fromFoldable 

fromFoldable :: forall f a. Foldable f => Ord a => f a -> OrdSeq a

Probably O(n*log(n)), but depends on the Foldable instance. Consruct an ordered sequence from any any Foldable.

#insert 

insert :: forall a. Ord a => a -> OrdSeq a -> OrdSeq a

O(log(n)). Insert the given value into the correct place in the sequence.

#null 

null :: forall a. OrdSeq a -> Boolean

O(1). Returns true if the given sequence is empty, false otherwise.

#length 

length :: forall a. OrdSeq a -> Int

O(n). Return the length of the sequence.

#least 

least :: forall a. Ord a => OrdSeq a -> Maybe a

O(1). Access the least element of the sequence, or Nothing if the sequence is empty.

#greatest 

greatest :: forall a. Ord a => OrdSeq a -> Maybe a

O(1). Access the greatest element of the sequence, or Nothing if the sequence is empty.

#popLeast 

popLeast :: forall a. Ord a => OrdSeq a -> Maybe (Tuple a (OrdSeq a))

O(1). Remove the least element of the sequence, returning that element and the remainder of the sequence. If the sequence is empty, return Nothing.

#popGreatest 

popGreatest :: forall a. Ord a => OrdSeq a -> Maybe (Tuple a (OrdSeq a))

O(1). Remove the greatest element of the sequence, returning that element and the remainder of the sequence. If the sequence is empty, return Nothing.

#partition 

partition :: forall a. Ord a => a -> OrdSeq a -> Tuple (OrdSeq a) (OrdSeq a)

O(log(n)). Split an ordered sequence into two halves. The first element of the returned tuple contains all elements which compared less than or equal to the argument; the second element contains the rest.

#merge 

merge :: forall a. Ord a => OrdSeq a -> OrdSeq a -> OrdSeq a

O(m*log(n/m)), where m and n are the lengths of the longer and shorter sequences respectively. Create a new sequence containing every element in both of the given sequences.

#intersection 

intersection :: forall a. Ord a => OrdSeq a -> OrdSeq a -> OrdSeq a

O(n*log(n)), where n is the length of the longer sequence. Create a new sequence containing only elements which are common to both sequences.

#deleteAll 

deleteAll :: forall a. Ord a => a -> OrdSeq a -> OrdSeq a

O(log(n)). Delete all elements from the sequence which compare EQ to the given value.

#toUnfoldable 

toUnfoldable :: forall f. Functor f => Unfoldable f => OrdSeq ~> f

Probably O(n), but depends on the Unfoldable instance. Unfold an ordered sequence in ascending order.

#toUnfoldableDescending 

toUnfoldableDescending :: forall f a. Functor f => Unfoldable f => OrdSeq a -> f a

Probably O(n), but depends on the Unfoldable instance. Unfold an ordered sequence in descending order.

#sort 

sort :: forall f a. Functor f => Foldable f => Unfoldable f => Ord a => f a -> f a

Sort any structure (which has Foldable, Unfoldable, and Functor instances) by converting to an OrdSeq and back again. I am fairly sure this is usually O(n*log(n)), although of course this depends on the Unfoldable and Foldable instances.

Modules