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range_group.go
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// Copyright 2016 The Cockroach Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
// implied. See the License for the specific language governing
// permissions and limitations under the License.
package interval
import (
"bytes"
"container/list"
"fmt"
)
// 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.
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
}
// RangeGroupIterator is an iterator that walks in-order over a RangeGroup.
type RangeGroupIterator interface {
// Next returns the next Range in the RangeGroup. It returns false
// if there are no more Ranges.
Next() (Range, bool)
}
// rangeList is an implementation of a RangeGroup using a linked
// list to sequentially order non-overlapping ranges.
//
// rangeList is not safe for concurrent use by multiple goroutines.
type rangeList struct {
ll list.List
}
// NewRangeList constructs a linked-list backed RangeGroup.
func NewRangeList() RangeGroup {
var rl rangeList
rl.ll.Init()
return &rl
}
// Add implements RangeGroup. It iterates over the current ranges in the
// rangeList to find which overlap with the new range. If there is no
// overlap, the new range will be added and the function will return true.
// If there is some overlap, the function will return true if the new
// range increases the range of the rangeList, in which case it will be
// added to the list, and false if it does not increase the range, in which
// case it won't be added. If the range is added, the function will also attempt
// to merge any ranges within the list that now overlap.
func (rl *rangeList) Add(r Range) bool {
if err := rangeError(r); err != nil {
panic(err)
}
for e := rl.ll.Front(); e != nil; e = e.Next() {
er := e.Value.(Range)
switch {
case InclusiveOverlapper.Overlap(er, r):
// If a current range fully contains the new range, no
// need to add it.
if contains(er, r) {
return false
}
// Merge as many ranges as possible, and replace old range.
newR := merge(er, r)
for p := e.Next(); p != nil; {
pr := p.Value.(Range)
if InclusiveOverlapper.Overlap(newR, pr) {
newR = merge(newR, pr)
nextP := p.Next()
rl.ll.Remove(p)
p = nextP
} else {
break
}
}
e.Value = newR
return true
case r.End.Compare(er.Start) < 0:
// Past where inclusive overlapping ranges would be.
rl.ll.InsertBefore(r, e)
return true
}
}
rl.ll.PushBack(r)
return true
}
// Sub implements RangeGroup. It iterates over the current ranges in the
// rangeList to find which overlap with the range to subtract. For all
// ranges that overlap with the provided range, the overlapping segment of
// the range is removed. If the provided range fully contains a range in
// the rangeList, the range in the rangeList will be removed. The method
// returns whether the subtraction resulted in any decrease to the size
// of the RangeGroup.
func (rl *rangeList) Sub(r Range) bool {
if err := rangeError(r); err != nil {
panic(err)
}
dec := false
for e := rl.ll.Front(); e != nil; {
er := e.Value.(Range)
switch {
case ExclusiveOverlapper.Overlap(er, r):
sCmp := er.Start.Compare(r.Start)
eCmp := er.End.Compare(r.End)
delStart := sCmp >= 0
delEnd := eCmp <= 0
cont := eCmp < 0
switch {
case delStart && delEnd:
// Remove the entire range.
nextE := e.Next()
rl.ll.Remove(e)
e = nextE
case delStart:
// Remove the start of the range by truncating.
er.Start = r.End
e.Value = er
e = e.Next()
case delEnd:
// Remove the end of the range by truncating.
er.End = r.Start
e.Value = er
e = e.Next()
default:
// Remove the middle of the range by splitting and truncating.
oldEnd := er.End
er.End = r.Start
e.Value = er
rSplit := Range{Start: r.End, End: oldEnd}
newE := rl.ll.InsertAfter(rSplit, e)
e = newE.Next()
}
dec = true
if !cont {
return dec
}
case r.End.Compare(er.Start) <= 0:
// Past where exclusive overlapping ranges would be.
return dec
default:
e = e.Next()
}
}
return dec
}
// Clear implements RangeGroup. It clears all ranges from the
// rangeList.
func (rl *rangeList) Clear() {
rl.ll.Init()
}
// Overlaps implements RangeGroup. It returns whether the provided
// Range is partially contained within the group of Ranges in the rangeList.
func (rl *rangeList) Overlaps(r Range) bool {
if err := rangeError(r); err != nil {
panic(err)
}
for e := rl.ll.Front(); e != nil; e = e.Next() {
er := e.Value.(Range)
switch {
case ExclusiveOverlapper.Overlap(er, r):
return true
case r.End.Compare(er.Start) <= 0:
// Past where exclusive overlapping ranges would be.
return false
}
}
return false
}
// Encloses implements RangeGroup. It returns whether the provided
// Range is fully contained within the group of Ranges in the rangeList.
func (rl *rangeList) Encloses(r Range) bool {
if err := rangeError(r); err != nil {
panic(err)
}
for e := rl.ll.Front(); e != nil; e = e.Next() {
er := e.Value.(Range)
switch {
case contains(er, r):
return true
case r.End.Compare(er.Start) <= 0:
// Past where exclusive overlapping ranges would be.
return false
}
}
return false
}
// ForEach implements RangeGroup. It calls the provided function f
// with each Range stored in the rangeList.
func (rl *rangeList) ForEach(f func(Range) error) error {
it := rangeListIterator{e: rl.ll.Front()}
for r, ok := it.Next(); ok; r, ok = it.Next() {
if err := f(r); err != nil {
return err
}
}
return nil
}
// rangeListIterator is an in-order iterator operating over a rangeList.
type rangeListIterator struct {
e *list.Element
}
// Next implements RangeGroupIterator. It returns the next Range in the
// rangeList, or false.
func (rli *rangeListIterator) Next() (r Range, ok bool) {
if rli.e != nil {
r = rli.e.Value.(Range)
ok = true
rli.e = rli.e.Next()
}
return r, ok
}
// Iterator implements RangeGroup. It returns an iterator to iterate over
// the group of ranges.
func (rl *rangeList) Iterator() RangeGroupIterator {
return &rangeListIterator{e: rl.ll.Front()}
}
// Len implements RangeGroup. It returns the number of ranges in
// the rangeList.
func (rl *rangeList) Len() int {
return rl.ll.Len()
}
func (rl *rangeList) String() string {
return rgString(rl)
}
// rangeTree is an implementation of a RangeGroup using an interval
// tree to efficiently store and search for non-overlapping ranges.
//
// rangeTree is not safe for concurrent use by multiple goroutines.
type rangeTree struct {
t Tree
idCount uintptr
}
// NewRangeTree constructs an interval tree backed RangeGroup.
func NewRangeTree() RangeGroup {
return &rangeTree{
t: NewTree(InclusiveOverlapper),
}
}
// rangeKey implements Interface and can be inserted into a Tree. It
// provides uniqueness as well as a key interval.
type rangeKey struct {
r Range
id uintptr
}
var _ Interface = rangeKey{}
// makeKey creates a new rangeKey defined by the provided range.
func (rt *rangeTree) makeKey(r Range) rangeKey {
rt.idCount++
return rangeKey{
r: r,
id: rt.idCount,
}
}
// Range implements Interface.
func (rk rangeKey) Range() Range {
return rk.r
}
// ID implements Interface.
func (rk rangeKey) ID() uintptr {
return rk.id
}
func (rk rangeKey) String() string {
return fmt.Sprintf("%d: %q-%q", rk.id, rk.r.Start, rk.r.End)
}
// Add implements RangeGroup. It first uses the interval tree to lookup
// the current ranges which overlap with the new range. If there is no
// overlap, the new range will be added and the function will return true.
// If there is some overlap, the function will return true if the new
// range increases the range of the rangeTree, in which case it will be
// added to the tree, and false if it does not increase the range, in which
// case it won't be added. If the range is added, the function will also attempt
// to merge any ranges within the tree that now overlap.
func (rt *rangeTree) Add(r Range) bool {
if err := rangeError(r); err != nil {
panic(err)
}
overlaps := rt.t.Get(r)
if len(overlaps) == 0 {
key := rt.makeKey(r)
if err := rt.t.Insert(&key, false /* !fast */); err != nil {
panic(err)
}
return true
}
first := overlaps[0].(*rangeKey)
// If a current range fully contains the new range, no
// need to add it.
if contains(first.r, r) {
return false
}
// Merge as many ranges as possible, and replace old range.
first.r = merge(first.r, r)
for _, o := range overlaps[1:] {
other := o.(*rangeKey)
first.r = merge(first.r, other.r)
if err := rt.t.Delete(o, true /* fast */); err != nil {
panic(err)
}
}
rt.t.AdjustRanges()
return true
}
// Sub implements RangeGroup. It first uses the interval tree to lookup
// the current ranges which overlap with the range to subtract. For all
// ranges that overlap with the provided range, the overlapping segment of
// the range is removed. If the provided range fully contains a range in
// the rangeTree, the range in the rangeTree will be removed. The method
// returns whether the subtraction resulted in any decrease to the size
// of the RangeGroup.
func (rt *rangeTree) Sub(r Range) bool {
if err := rangeError(r); err != nil {
panic(err)
}
overlaps := rt.t.GetWithOverlapper(r, ExclusiveOverlapper)
if len(overlaps) == 0 {
return false
}
for _, o := range overlaps {
rk := o.(*rangeKey)
sCmp := rk.r.Start.Compare(r.Start)
eCmp := rk.r.End.Compare(r.End)
delStart := sCmp >= 0
delEnd := eCmp <= 0
switch {
case delStart && delEnd:
// Remove the entire range.
if err := rt.t.Delete(o, true /* fast */); err != nil {
panic(err)
}
case delStart:
// Remove the start of the range by truncating.
rk.r.Start = r.End
case delEnd:
// Remove the end of the range by truncating.
rk.r.End = r.Start
default:
// Remove the middle of the range by splitting.
oldEnd := rk.r.End
rk.r.End = r.Start
rSplit := Range{Start: r.End, End: oldEnd}
rKey := rt.makeKey(rSplit)
if err := rt.t.Insert(&rKey, true /* fast */); err != nil {
panic(err)
}
}
}
rt.t.AdjustRanges()
return true
}
// Clear implements RangeGroup. It clears all rangeKeys from the rangeTree.
func (rt *rangeTree) Clear() {
rt.t = NewTree(InclusiveOverlapper)
}
// Overlaps implements RangeGroup. It returns whether the provided
// Range is partially contained within the group of Ranges in the rangeTree.
func (rt *rangeTree) Overlaps(r Range) bool {
if err := rangeError(r); err != nil {
panic(err)
}
overlaps := rt.t.GetWithOverlapper(r, ExclusiveOverlapper)
return len(overlaps) > 0
}
// Encloses implements RangeGroup. It returns whether the provided
// Range is fully contained within the group of Ranges in the rangeTree.
func (rt *rangeTree) Encloses(r Range) bool {
if err := rangeError(r); err != nil {
panic(err)
}
overlaps := rt.t.GetWithOverlapper(r, ExclusiveOverlapper)
if len(overlaps) != 1 {
return false
}
first := overlaps[0].(*rangeKey)
return contains(first.r, r)
}
// ForEach implements RangeGroup. It calls the provided function f
// with each Range stored in the rangeTree.
func (rt *rangeTree) ForEach(f func(Range) error) error {
var err error
rt.t.Do(func(i Interface) bool {
err = f(i.Range())
return err != nil
})
return err
}
// rangeListIterator is an in-order iterator operating over a rangeTree.
type rangeTreeIterator struct {
it TreeIterator
}
// Next implements RangeGroupIterator. It returns the next Range in the
// rangeTree, or false.
func (rti *rangeTreeIterator) Next() (r Range, ok bool) {
i, ok := rti.it.Next()
if !ok {
return Range{}, false
}
return i.Range(), true
}
// Iterator implements RangeGroup. It returns an iterator to iterate over
// the group of ranges.
func (rt *rangeTree) Iterator() RangeGroupIterator {
return &rangeTreeIterator{it: rt.t.Iterator()}
}
// Len implements RangeGroup. It returns the number of rangeKeys in
// the rangeTree.
func (rt *rangeTree) Len() int {
return rt.t.Len()
}
func (rt *rangeTree) String() string {
return rgString(rt)
}
// contains returns if the range in the out range fully contains the
// in range.
func contains(out, in Range) bool {
return in.Start.Compare(out.Start) >= 0 && out.End.Compare(in.End) >= 0
}
// merge merges the provided ranges together into their union range. The
// ranges must overlap or the function will not produce the correct output.
func merge(l, r Range) Range {
start := l.Start
if r.Start.Compare(start) < 0 {
start = r.Start
}
end := l.End
if r.End.Compare(end) > 0 {
end = r.End
}
return Range{Start: start, End: end}
}
// rgString returns a string representation of the ranges in a RangeGroup.
func rgString(rg RangeGroup) string {
var buffer bytes.Buffer
buffer.WriteRune('[')
space := false
if err := rg.ForEach(func(r Range) error {
if space {
buffer.WriteRune(' ')
}
buffer.WriteString(r.String())
space = true
return nil
}); err != nil {
panic(err)
}
buffer.WriteRune(']')
return buffer.String()
}
// 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.
func RangeGroupsOverlap(rg1, rg2 RangeGroup) bool {
it1, it2 := rg1.Iterator(), rg2.Iterator()
r1, ok1 := it1.Next()
r2, ok2 := it2.Next()
if !ok1 || !ok2 {
return false
}
for {
// Check if the current pair of Ranges overlap.
if ExclusiveOverlapper.Overlap(r1, r2) {
return true
}
// If not, advance the Range further behind.
var ok bool
if r1.Start.Compare(r2.Start) < 0 {
r1, ok = it1.Next()
} else {
r2, ok = it2.Next()
}
if !ok {
return false
}
}
}