Data.Vector.Algorithms.AmericanFlag

vector-algorithms-0.5.4.2: Efficient algorithms for vector arrays

Copyright | (c) 2011 Dan Doel
Maintainer | Dan Doel <dan.doel@gmail.com>
Stability | Experimental
Portability | Non-portable (FlexibleContexts, ScopedTypeVariables)
Safe Haskell | None
Language | Haskell98

Data.Vector.Algorithms.AmericanFlag

Description

This module implements American flag sort: an in-place, unstable, bucket sort. Also in contrast to radix sort, the values are inspected in a big endian order, and buckets are sorted via recursive splitting. This, however, makes it sensible for sorting strings in lexicographic order (provided indexing is fast).

The algorithm works as follows: at each stage, the array is looped over, counting the number of elements for each bucket. Then, starting at the beginning of the array, elements are permuted in place to reside in the proper bucket, following chains until they reach back to the current base index. Finally, each bucket is sorted recursively. This lends itself well to the aforementioned variable-length strings, and so the algorithm takes a stopping predicate, which is given a representative of the stripe, rather than running for a set number of iterations.

Synopsis

- sort :: forall e m v. (PrimMonad m, MVector v e, Lexicographic e, Ord e) => v (PrimState m) e -> m ()
- sortBy :: (PrimMonad m, MVector v e) => Comparison e -> (e -> Int -> Bool) -> Int -> (Int -> e -> Int) -> v (PrimState m) e -> m ()
- class Lexicographic e where
  - terminate :: e -> Int -> Bool
  - size :: e -> Int
  - index :: Int -> e -> Int

# Documentation

sort :: forall e m v. (PrimMonad m, MVector v e, Lexicographic e, Ord e) => v (PrimState m) e -> m ()

Sorts an array using the default ordering. Both Lexicographic and Ord are necessary because the algorithm falls back to insertion sort for sufficiently small arrays.

sortBy

Arguments

:: (PrimMonad m, MVector v e) |
=> Comparison e | a comparison for the insertion sort flalback
-> (e -> Int -> Bool) | determines whether a stripe is complete
-> Int | the number of buckets necessary
-> (Int -> e -> Int) | the big-endian radix function
-> v (PrimState m) e | the array to be sorted
-> m () |

A fully parameterized version of the sorting algorithm. Again, this function takes both radix information and a comparison, because the algorithms falls back to insertion sort for small arrays.

class Lexicographic e where

The methods of this class specify the information necessary to sort arrays using the default ordering. The name `Lexicographic` is meant to convey that index should return results in a similar way to indexing into a string.

Methods

terminate :: e -> Int -> Bool

Given a representative of a stripe and an index number, this function should determine whether to stop sorting.

size :: e -> Int

The size of the bucket array necessary for sorting es

index :: Int -> e -> Int

Determines which bucket a given element should inhabit for a particular iteration.

Instances

Lexicographic Int |
Lexicographic Int8 |
Lexicographic Int16 |
Lexicographic Int32 |
Lexicographic Int64 |
Lexicographic Word |
Lexicographic Word8 |
Lexicographic Word16 |
Lexicographic Word32 |
Lexicographic Word64 |
Lexicographic ByteString |