Documentation
¶
Overview ¶
Package interval provides two implementations for an interval tree. One is based on an augmented Left-Leaning Red Black tree. The other is based on an augmented BTree.
Index ¶
Constants ¶
const ( // DefaultBTreeMinimumDegree is the default B-tree minimum degree. Benchmarks // show that the interval tree performs best with this minimum degree. DefaultBTreeMinimumDegree = 32 // DefaultBTreeFreeListSize is the default size of a B-tree's freelist. DefaultBTreeFreeListSize = 32 )
const ( TD234 = iota BU23 )
Operation LLRBMode of the underlying LLRB tree.
const LLRBMode = BU23
LLRBMode .
Variables ¶
var ErrEmptyRange = errors.Newf("interval: empty range")
ErrEmptyRange is returned if an interval is used where the start value is equal to the end value.
var ErrInvertedRange = errors.Newf("interval: inverted range")
ErrInvertedRange is returned if an interval is used where the start value is greater than the end value.
var ErrNilRange = errors.Newf("interval: nil range")
ErrNilRange is returned if an interval is used where both the start value and the end value are nil. This is a specialization of ErrEmptyRange.
var ExclusiveOverlapper = exclusiveOverlapper{}
ExclusiveOverlapper defines overlapping as a pair of ranges that share a segment of the keyspace in the exclusive. "exclusive" means that the start keys are treated as inclusive and the end keys are treated as exclusive.
var InclusiveOverlapper = inclusiveOverlapper{}
InclusiveOverlapper defines overlapping as a pair of ranges that share a segment of the keyspace in the inclusive way. "inclusive" means that both start and end keys treated as inclusive values.
Functions ¶
func Compare ¶
Compare returns a value indicating the sort order relationship between a and b. The comparison is performed lexicographically on (a.Range().Start, a.ID()) and (b.Range().Start, b.ID()) tuples where Range().Start is more significant that ID().
Given c = Compare(a, b):
c == -1 if (a.Range().Start, a.ID()) < (b.Range().Start, b.ID()); c == 0 if (a.Range().Start, a.ID()) == (b.Range().Start, b.ID()); and c == 1 if (a.Range().Start, a.ID()) > (b.Range().Start, b.ID()).
"c == 0" is equivalent to "Equal(a, b) == true".
func Equal ¶
Equal returns a boolean indicating whether the given Interfaces are equal to each other. If "Equal(a, b) == true", "a.Range().End == b.Range().End" must hold. Otherwise, the interval tree behavior is undefined. "Equal(a, b) == true" is equivalent to "Compare(a, b) == 0". But the former has measurably better performance than the latter. So Equal should be used when only equality state is needed.
func RangeGroupsOverlap ¶
func RangeGroupsOverlap(rg1, rg2 RangeGroup) bool
RangeGroupsOverlap determines if two RangeGroups contain any overlapping Ranges or if they are fully disjoint. It does so by iterating over the RangeGroups together and comparing subsequent ranges.
Types ¶
type Comparable ¶
type Comparable []byte
A Comparable is a type that describes the ends of a Range.
func (Comparable) Compare ¶
func (c Comparable) Compare(o Comparable) int
Compare returns a value indicating the sort order relationship between the receiver and the parameter.
Given c = a.Compare(b):
c == -1 if a < b; c == 0 if a == b; and c == 1 if a > b.
func (Comparable) Equal ¶
func (c Comparable) Equal(o Comparable) bool
Equal returns a boolean indicating if the given comparables are equal to each other. Note that this has measurably better performance than Compare() == 0, so it should be used when only equality state is needed.
type FreeList ¶
type FreeList struct {
// contains filtered or unexported fields
}
FreeList represents a free list of btree nodes. By default each BTree has its own FreeList, but multiple BTrees can share the same FreeList. Two Btrees using the same freelist are safe for concurrent write access.
func NewFreeList ¶
NewFreeList creates a new free list. size is the maximum size of the returned free list.
type Interface ¶
type Interface interface {
Range() Range
// Returns a unique ID for the element.
// TODO(nvanbenschoten): Should this be changed to an int64?
ID() uintptr
}
An Interface is a type that can be inserted into an interval tree.
type Operation ¶
An Operation is a function that operates on an Interface. If done is returned true, the Operation is indicating that no further work needs to be done and so the DoMatching function should traverse no further.
type Overlapper ¶
type Overlapper interface {
// Overlap checks whether two ranges overlap.
Overlap(Range, Range) bool
}
Overlapper specifies the overlapping relationship.
type Range ¶
type Range struct {
Start, End Comparable
}
A Range is a type that describes the basic characteristics of an interval.
type RangeGroup ¶
type RangeGroup interface {
// Add will attempt to add the provided Range to the RangeGroup,
// returning whether the addition increased the range of the group
// or not.
Add(Range) bool
// Sub will attempt to remove the provided Range from the RangeGroup,
// returning whether the subtraction reduced the range of the group
// or not.
Sub(Range) bool
// Clear clears all ranges from the RangeGroup, resetting it to be
// used again.
Clear()
// Overlaps returns whether the provided Range is partially contained
// within the group of Ranges in the RangeGroup.
Overlaps(Range) bool
// Encloses returns whether the provided Range is fully contained
// within the group of Ranges in the RangeGroup.
Encloses(Range) bool
// ForEach calls the provided function with each Range stored in
// the group. An error is returned indicating whether the callback
// function saw an error, whereupon the Range iteration will halt
// (potentially prematurely) and the error will be returned from ForEach
// itself. If no error is returned from the callback, the method
// will visit all Ranges in the group before returning a nil error.
ForEach(func(Range) error) error
// Iterator returns an iterator to visit each Range stored in the
// group, in-order. It is not safe to mutate the RangeGroup while
// iteration is being performed.
Iterator() RangeGroupIterator
// Len returns the number of Ranges currently within the RangeGroup.
// This will always be equal to or less than the number of ranges added,
// as ranges that overlap will merge to produce a single larger range.
Len() int
fmt.Stringer
}
RangeGroup represents a set of possibly disjointed Ranges. The interface exposes methods to manipulate the group by adding and subtracting Ranges. All methods requiring a Range will panic if the provided range is inverted or empty.
One use case of the interface is to add ranges to the group and observe whether the addition increases the size of the group or not, indicating whether the new range's interval is redundant, or if it is needed for the full composition of the group. Because the RangeGroup builds as more ranges are added, insertion order of the ranges is critical. For instance, if two identical ranges are added, only the first to be added with Add will return true, as it will be the only one to expand the group.
Another use case of the interface is to add and subtract ranges as needed to the group, allowing the internals of the implementation to coalesce and split ranges when needed to factor the group to its minimum number of disjoint ranges.
func NewRangeList ¶
func NewRangeList() RangeGroup
NewRangeList constructs a linked-list backed RangeGroup.
func NewRangeTree ¶
func NewRangeTree() RangeGroup
NewRangeTree constructs an interval tree backed RangeGroup.
type RangeGroupIterator ¶
type RangeGroupIterator interface {
// Next returns the next Range in the RangeGroup. It returns false
// if there are no more Ranges.
Next() (Range, bool)
}
RangeGroupIterator is an iterator that walks in-order over a RangeGroup.
type Tree ¶
type Tree interface {
// AdjustRanges fixes range fields for all nodes in the tree. This must be
// called before Get, Do or DoMatching* is used if fast insertion or deletion
// has been performed.
AdjustRanges()
// Len returns the number of intervals stored in the Tree.
Len() int
// Get returns a slice of Interfaces that overlap r in the tree. The slice is
// sorted nondecreasingly by interval start.
Get(r Range) []Interface
// GetWithOverlapper returns a slice of Interfaces that overlap r in the tree
// using the provided overlapper function. The slice is sorted nondecreasingly
// by interval start.
GetWithOverlapper(r Range, overlapper Overlapper) []Interface
// Insert inserts the Interface e into the tree. Insertions may replace an
// existing Interface which is equal to the Interface e.
Insert(e Interface, fast bool) error
// Delete deletes the Interface e if it exists in the tree. The deleted
// Interface is equal to the Interface e.
Delete(e Interface, fast bool) error
// Do performs fn on all intervals stored in the tree. The traversal is done
// in the nondecreasing order of interval start. A boolean is returned
// indicating whether the traversal was interrupted by an Operation returning
// true. If fn alters stored intervals' sort relationships, future tree
// operation behaviors are undefined.
Do(fn Operation) bool
// DoMatching performs fn on all intervals stored in the tree that overlaps r.
// The traversal is done in the nondecreasing order of interval start. A
// boolean is returned indicating whether the traversal was interrupted by an
// Operation returning true. If fn alters stored intervals' sort
// relationships, future tree operation behaviors are undefined.
DoMatching(fn Operation, r Range) bool
// Iterator creates an iterator to iterate over all intervals stored in the
// tree, in-order.
Iterator() TreeIterator
// Clear this tree.
Clear()
// Clone clones the tree, returning a copy.
Clone() Tree
}
Tree is an interval tree. For all the functions which have a fast argument, fast being true means a fast operation which does not adjust node ranges. If fast is false, node ranges are adjusted.
func NewTree ¶
func NewTree(overlapper Overlapper) Tree
NewTree creates a new interval tree with the given overlapper function. It uses the augmented Left-Leaning Red Black tree implementation.
type TreeIterator ¶
type TreeIterator interface {
// Next returns the current interval stored in the interval tree and moves
// the iterator to the next interval. The method returns false if no intervals
// remain in the interval tree.
Next() (Interface, bool)
}
TreeIterator iterates over all intervals stored in the interval tree, in-order.
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