Data.Vector.Algorithms.Heap

This module implements operations for working with a quaternary heap stored in an unboxed array. Most heapsorts are defined in terms of a binary heap, in which each internal node has at most two children. By contrast, a quaternary heap has internal nodes with up to four children. This reduces the number of comparisons in a heapsort slightly, and improves locality (again, slightly) by flattening out the heap.

Sorting

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

Sorts an entire array using the default ordering.

sortBy :: (PrimMonad m, MVector v e) => Comparison e -> v (PrimState m) e -> m ()

Sorts an entire array using a custom ordering.

sortByBounds

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

lower index, l

-> Int

upper index, u

-> m ()

Sorts a portion of an array [l,u) using a custom ordering

Selection

select

Arguments

:: (PrimMonad m, MVector v e, Ord e)

=> v (PrimState m) e

-> Int

number of elements to select, k

-> m ()

Moves the lowest k elements to the front of the array. The elements will be in no particular order.

selectBy

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

number of elements to select, k

-> m ()

Moves the lowest (as defined by the comparison) k elements to the front of the array. The elements will be in no particular order.

selectByBounds

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

number of elements to select, k

-> Int

lower index, l

-> Int

upper index, u

-> m ()

Moves the lowest k elements in the portion [l,u) of the array into the positions [l,k+l). The elements will be in no particular order.

Partial sorts

partialSort

Arguments

:: (PrimMonad m, MVector v e, Ord e)

=> v (PrimState m) e

-> Int

number of elements to sort, k

-> m ()

Moves the lowest k elements to the front of the array, sorted.

The remaining values of the array will be in no particular order.

partialSortBy

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

number of elements to sort, k

-> m ()

Moves the lowest k elements (as defined by the comparison) to the front of the array, sorted.

The remaining values of the array will be in no particular order.

partialSortByBounds

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

number of elements to sort, k

-> Int

lower index, l

-> Int

upper index, u

-> m ()

Moves the lowest k elements in the portion [l,u) of the array into positions [l,k+l), sorted.

The remaining values in [l,u) will be in no particular order. Values outside the range [l,u) will be unaffected.

Heap operations

heapify

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

lower index, l

-> Int

upper index, u

-> m ()

Constructs a heap in a portion of an array [l, u), using the values therein.

Note: heapify is more efficient than constructing a heap by repeated insertion. Repeated insertion has complexity O(n*log n) while heapify is able to construct a heap in O(n), where n is the number of elements in the heap.

pop

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

lower heap index, l

-> Int

upper heap index, u

-> m ()

Given a heap stored in a portion of an array [l,u), swaps the top of the heap with the element at u and rebuilds the heap.

popTo

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

lower heap index, l

-> Int

upper heap index, u

-> Int

index to pop to, t

-> m ()

Given a heap stored in a portion of an array [l,u) swaps the top of the heap with the element at position t, and rebuilds the heap.

sortHeap

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

lower heap index, l

-> Int

lower bound of final sorted portion, m

-> Int

upper heap index, u

-> m ()

Given a heap stored in a portion of an array [l,u), sorts the highest values into [m,u). The elements in [l,m) are not in any particular order.

heapInsert

Arguments

:: (PrimMonad m, MVector v e)

=> Comparison e

-> v (PrimState m) e

-> Int

lower heap index, l

-> Int

upper heap index, u

-> e

element to be inserted, e

-> m ()

Given a heap stored in a portion of an array [l,u) and an element e, inserts the element into the heap, resulting in a heap in [l,u].

Note: it is best to only use this operation when incremental construction of a heap is required. heapify is capable of building a heap in O(n) time, while repeated insertion takes O(n*log n) time.

type Comparison e = e -> e -> Ordering

A type of comparisons between two values of a given type.