mirror of https://github.com/k3s-io/k3s
952 lines
21 KiB
Go
952 lines
21 KiB
Go
// Copyright 2016 The etcd 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 adt
|
|
|
|
import (
|
|
"bytes"
|
|
"fmt"
|
|
"math"
|
|
"strings"
|
|
)
|
|
|
|
// Comparable is an interface for trichotomic comparisons.
|
|
type Comparable interface {
|
|
// Compare gives the result of a 3-way comparison
|
|
// a.Compare(b) = 1 => a > b
|
|
// a.Compare(b) = 0 => a == b
|
|
// a.Compare(b) = -1 => a < b
|
|
Compare(c Comparable) int
|
|
}
|
|
|
|
type rbcolor int
|
|
|
|
const (
|
|
black rbcolor = iota
|
|
red
|
|
)
|
|
|
|
func (c rbcolor) String() string {
|
|
switch c {
|
|
case black:
|
|
return "black"
|
|
case red:
|
|
return "black"
|
|
default:
|
|
panic(fmt.Errorf("unknown color %d", c))
|
|
}
|
|
}
|
|
|
|
// Interval implements a Comparable interval [begin, end)
|
|
// TODO: support different sorts of intervals: (a,b), [a,b], (a, b]
|
|
type Interval struct {
|
|
Begin Comparable
|
|
End Comparable
|
|
}
|
|
|
|
// Compare on an interval gives == if the interval overlaps.
|
|
func (ivl *Interval) Compare(c Comparable) int {
|
|
ivl2 := c.(*Interval)
|
|
ivbCmpBegin := ivl.Begin.Compare(ivl2.Begin)
|
|
ivbCmpEnd := ivl.Begin.Compare(ivl2.End)
|
|
iveCmpBegin := ivl.End.Compare(ivl2.Begin)
|
|
|
|
// ivl is left of ivl2
|
|
if ivbCmpBegin < 0 && iveCmpBegin <= 0 {
|
|
return -1
|
|
}
|
|
|
|
// iv is right of iv2
|
|
if ivbCmpEnd >= 0 {
|
|
return 1
|
|
}
|
|
|
|
return 0
|
|
}
|
|
|
|
type intervalNode struct {
|
|
// iv is the interval-value pair entry.
|
|
iv IntervalValue
|
|
// max endpoint of all descendent nodes.
|
|
max Comparable
|
|
// left and right are sorted by low endpoint of key interval
|
|
left, right *intervalNode
|
|
// parent is the direct ancestor of the node
|
|
parent *intervalNode
|
|
c rbcolor
|
|
}
|
|
|
|
func (x *intervalNode) color(sentinel *intervalNode) rbcolor {
|
|
if x == sentinel {
|
|
return black
|
|
}
|
|
return x.c
|
|
}
|
|
|
|
func (x *intervalNode) height(sentinel *intervalNode) int {
|
|
if x == sentinel {
|
|
return 0
|
|
}
|
|
ld := x.left.height(sentinel)
|
|
rd := x.right.height(sentinel)
|
|
if ld < rd {
|
|
return rd + 1
|
|
}
|
|
return ld + 1
|
|
}
|
|
|
|
func (x *intervalNode) min(sentinel *intervalNode) *intervalNode {
|
|
for x.left != sentinel {
|
|
x = x.left
|
|
}
|
|
return x
|
|
}
|
|
|
|
// successor is the next in-order node in the tree
|
|
func (x *intervalNode) successor(sentinel *intervalNode) *intervalNode {
|
|
if x.right != sentinel {
|
|
return x.right.min(sentinel)
|
|
}
|
|
y := x.parent
|
|
for y != sentinel && x == y.right {
|
|
x = y
|
|
y = y.parent
|
|
}
|
|
return y
|
|
}
|
|
|
|
// updateMax updates the maximum values for a node and its ancestors
|
|
func (x *intervalNode) updateMax(sentinel *intervalNode) {
|
|
for x != sentinel {
|
|
oldmax := x.max
|
|
max := x.iv.Ivl.End
|
|
if x.left != sentinel && x.left.max.Compare(max) > 0 {
|
|
max = x.left.max
|
|
}
|
|
if x.right != sentinel && x.right.max.Compare(max) > 0 {
|
|
max = x.right.max
|
|
}
|
|
if oldmax.Compare(max) == 0 {
|
|
break
|
|
}
|
|
x.max = max
|
|
x = x.parent
|
|
}
|
|
}
|
|
|
|
type nodeVisitor func(n *intervalNode) bool
|
|
|
|
// visit will call a node visitor on each node that overlaps the given interval
|
|
func (x *intervalNode) visit(iv *Interval, sentinel *intervalNode, nv nodeVisitor) bool {
|
|
if x == sentinel {
|
|
return true
|
|
}
|
|
v := iv.Compare(&x.iv.Ivl)
|
|
switch {
|
|
case v < 0:
|
|
if !x.left.visit(iv, sentinel, nv) {
|
|
return false
|
|
}
|
|
case v > 0:
|
|
maxiv := Interval{x.iv.Ivl.Begin, x.max}
|
|
if maxiv.Compare(iv) == 0 {
|
|
if !x.left.visit(iv, sentinel, nv) || !x.right.visit(iv, sentinel, nv) {
|
|
return false
|
|
}
|
|
}
|
|
default:
|
|
if !x.left.visit(iv, sentinel, nv) || !nv(x) || !x.right.visit(iv, sentinel, nv) {
|
|
return false
|
|
}
|
|
}
|
|
return true
|
|
}
|
|
|
|
// IntervalValue represents a range tree node that contains a range and a value.
|
|
type IntervalValue struct {
|
|
Ivl Interval
|
|
Val interface{}
|
|
}
|
|
|
|
// IntervalTree represents a (mostly) textbook implementation of the
|
|
// "Introduction to Algorithms" (Cormen et al, 3rd ed.) chapter 13 red-black tree
|
|
// and chapter 14.3 interval tree with search supporting "stabbing queries".
|
|
type IntervalTree interface {
|
|
// Insert adds a node with the given interval into the tree.
|
|
Insert(ivl Interval, val interface{})
|
|
// Delete removes the node with the given interval from the tree, returning
|
|
// true if a node is in fact removed.
|
|
Delete(ivl Interval) bool
|
|
// Len gives the number of elements in the tree.
|
|
Len() int
|
|
// Height is the number of levels in the tree; one node has height 1.
|
|
Height() int
|
|
// MaxHeight is the expected maximum tree height given the number of nodes.
|
|
MaxHeight() int
|
|
// Visit calls a visitor function on every tree node intersecting the given interval.
|
|
// It will visit each interval [x, y) in ascending order sorted on x.
|
|
Visit(ivl Interval, ivv IntervalVisitor)
|
|
// Find gets the IntervalValue for the node matching the given interval
|
|
Find(ivl Interval) *IntervalValue
|
|
// Intersects returns true if there is some tree node intersecting the given interval.
|
|
Intersects(iv Interval) bool
|
|
// Contains returns true if the interval tree's keys cover the entire given interval.
|
|
Contains(ivl Interval) bool
|
|
// Stab returns a slice with all elements in the tree intersecting the interval.
|
|
Stab(iv Interval) []*IntervalValue
|
|
// Union merges a given interval tree into the receiver.
|
|
Union(inIvt IntervalTree, ivl Interval)
|
|
}
|
|
|
|
// NewIntervalTree returns a new interval tree.
|
|
func NewIntervalTree() IntervalTree {
|
|
sentinel := &intervalNode{
|
|
iv: IntervalValue{},
|
|
max: nil,
|
|
left: nil,
|
|
right: nil,
|
|
parent: nil,
|
|
c: black,
|
|
}
|
|
return &intervalTree{
|
|
root: sentinel,
|
|
count: 0,
|
|
sentinel: sentinel,
|
|
}
|
|
}
|
|
|
|
type intervalTree struct {
|
|
root *intervalNode
|
|
count int
|
|
|
|
// red-black NIL node
|
|
// use 'sentinel' as a dummy object to simplify boundary conditions
|
|
// use the sentinel to treat a nil child of a node x as an ordinary node whose parent is x
|
|
// use one shared sentinel to represent all nil leaves and the root's parent
|
|
sentinel *intervalNode
|
|
}
|
|
|
|
// TODO: make this consistent with textbook implementation
|
|
//
|
|
// "Introduction to Algorithms" (Cormen et al, 3rd ed.), chapter 13.4, p324
|
|
//
|
|
// 0. RB-DELETE(T, z)
|
|
// 1.
|
|
// 2. y = z
|
|
// 3. y-original-color = y.color
|
|
// 4.
|
|
// 5. if z.left == T.nil
|
|
// 6. x = z.right
|
|
// 7. RB-TRANSPLANT(T, z, z.right)
|
|
// 8. else if z.right == T.nil
|
|
// 9. x = z.left
|
|
// 10. RB-TRANSPLANT(T, z, z.left)
|
|
// 11. else
|
|
// 12. y = TREE-MINIMUM(z.right)
|
|
// 13. y-original-color = y.color
|
|
// 14. x = y.right
|
|
// 15. if y.p == z
|
|
// 16. x.p = y
|
|
// 17. else
|
|
// 18. RB-TRANSPLANT(T, y, y.right)
|
|
// 19. y.right = z.right
|
|
// 20. y.right.p = y
|
|
// 21. RB-TRANSPLANT(T, z, y)
|
|
// 22. y.left = z.left
|
|
// 23. y.left.p = y
|
|
// 24. y.color = z.color
|
|
// 25.
|
|
// 26. if y-original-color == BLACK
|
|
// 27. RB-DELETE-FIXUP(T, x)
|
|
|
|
// Delete removes the node with the given interval from the tree, returning
|
|
// true if a node is in fact removed.
|
|
func (ivt *intervalTree) Delete(ivl Interval) bool {
|
|
z := ivt.find(ivl)
|
|
if z == ivt.sentinel {
|
|
return false
|
|
}
|
|
|
|
y := z
|
|
if z.left != ivt.sentinel && z.right != ivt.sentinel {
|
|
y = z.successor(ivt.sentinel)
|
|
}
|
|
|
|
x := ivt.sentinel
|
|
if y.left != ivt.sentinel {
|
|
x = y.left
|
|
} else if y.right != ivt.sentinel {
|
|
x = y.right
|
|
}
|
|
|
|
x.parent = y.parent
|
|
|
|
if y.parent == ivt.sentinel {
|
|
ivt.root = x
|
|
} else {
|
|
if y == y.parent.left {
|
|
y.parent.left = x
|
|
} else {
|
|
y.parent.right = x
|
|
}
|
|
y.parent.updateMax(ivt.sentinel)
|
|
}
|
|
if y != z {
|
|
z.iv = y.iv
|
|
z.updateMax(ivt.sentinel)
|
|
}
|
|
|
|
if y.color(ivt.sentinel) == black {
|
|
ivt.deleteFixup(x)
|
|
}
|
|
|
|
ivt.count--
|
|
return true
|
|
}
|
|
|
|
// "Introduction to Algorithms" (Cormen et al, 3rd ed.), chapter 13.4, p326
|
|
//
|
|
// 0. RB-DELETE-FIXUP(T, z)
|
|
// 1.
|
|
// 2. while x ≠ T.root and x.color == BLACK
|
|
// 3. if x == x.p.left
|
|
// 4. w = x.p.right
|
|
// 5. if w.color == RED
|
|
// 6. w.color = BLACK
|
|
// 7. x.p.color = RED
|
|
// 8. LEFT-ROTATE(T, x, p)
|
|
// 9. if w.left.color == BLACK and w.right.color == BLACK
|
|
// 10. w.color = RED
|
|
// 11. x = x.p
|
|
// 12. else if w.right.color == BLACK
|
|
// 13. w.left.color = BLACK
|
|
// 14. w.color = RED
|
|
// 15. RIGHT-ROTATE(T, w)
|
|
// 16. w = w.p.right
|
|
// 17. w.color = x.p.color
|
|
// 18. x.p.color = BLACK
|
|
// 19. LEFT-ROTATE(T, w.p)
|
|
// 20. x = T.root
|
|
// 21. else
|
|
// 22. w = x.p.left
|
|
// 23. if w.color == RED
|
|
// 24. w.color = BLACK
|
|
// 25. x.p.color = RED
|
|
// 26. RIGHT-ROTATE(T, x, p)
|
|
// 27. if w.right.color == BLACK and w.left.color == BLACK
|
|
// 28. w.color = RED
|
|
// 29. x = x.p
|
|
// 30. else if w.left.color == BLACK
|
|
// 31. w.right.color = BLACK
|
|
// 32. w.color = RED
|
|
// 33. LEFT-ROTATE(T, w)
|
|
// 34. w = w.p.left
|
|
// 35. w.color = x.p.color
|
|
// 36. x.p.color = BLACK
|
|
// 37. RIGHT-ROTATE(T, w.p)
|
|
// 38. x = T.root
|
|
// 39.
|
|
// 40. x.color = BLACK
|
|
//
|
|
func (ivt *intervalTree) deleteFixup(x *intervalNode) {
|
|
for x != ivt.root && x.color(ivt.sentinel) == black {
|
|
if x == x.parent.left { // line 3-20
|
|
w := x.parent.right
|
|
if w.color(ivt.sentinel) == red {
|
|
w.c = black
|
|
x.parent.c = red
|
|
ivt.rotateLeft(x.parent)
|
|
w = x.parent.right
|
|
}
|
|
if w == nil {
|
|
break
|
|
}
|
|
if w.left.color(ivt.sentinel) == black && w.right.color(ivt.sentinel) == black {
|
|
w.c = red
|
|
x = x.parent
|
|
} else {
|
|
if w.right.color(ivt.sentinel) == black {
|
|
w.left.c = black
|
|
w.c = red
|
|
ivt.rotateRight(w)
|
|
w = x.parent.right
|
|
}
|
|
w.c = x.parent.color(ivt.sentinel)
|
|
x.parent.c = black
|
|
w.right.c = black
|
|
ivt.rotateLeft(x.parent)
|
|
x = ivt.root
|
|
}
|
|
} else { // line 22-38
|
|
// same as above but with left and right exchanged
|
|
w := x.parent.left
|
|
if w.color(ivt.sentinel) == red {
|
|
w.c = black
|
|
x.parent.c = red
|
|
ivt.rotateRight(x.parent)
|
|
w = x.parent.left
|
|
}
|
|
if w == nil {
|
|
break
|
|
}
|
|
if w.left.color(ivt.sentinel) == black && w.right.color(ivt.sentinel) == black {
|
|
w.c = red
|
|
x = x.parent
|
|
} else {
|
|
if w.left.color(ivt.sentinel) == black {
|
|
w.right.c = black
|
|
w.c = red
|
|
ivt.rotateLeft(w)
|
|
w = x.parent.left
|
|
}
|
|
w.c = x.parent.color(ivt.sentinel)
|
|
x.parent.c = black
|
|
w.left.c = black
|
|
ivt.rotateRight(x.parent)
|
|
x = ivt.root
|
|
}
|
|
}
|
|
}
|
|
|
|
if x != nil {
|
|
x.c = black
|
|
}
|
|
}
|
|
|
|
func (ivt *intervalTree) createIntervalNode(ivl Interval, val interface{}) *intervalNode {
|
|
return &intervalNode{
|
|
iv: IntervalValue{ivl, val},
|
|
max: ivl.End,
|
|
c: red,
|
|
left: ivt.sentinel,
|
|
right: ivt.sentinel,
|
|
parent: ivt.sentinel,
|
|
}
|
|
}
|
|
|
|
// TODO: make this consistent with textbook implementation
|
|
//
|
|
// "Introduction to Algorithms" (Cormen et al, 3rd ed.), chapter 13.3, p315
|
|
//
|
|
// 0. RB-INSERT(T, z)
|
|
// 1.
|
|
// 2. y = T.nil
|
|
// 3. x = T.root
|
|
// 4.
|
|
// 5. while x ≠ T.nil
|
|
// 6. y = x
|
|
// 7. if z.key < x.key
|
|
// 8. x = x.left
|
|
// 9. else
|
|
// 10. x = x.right
|
|
// 11.
|
|
// 12. z.p = y
|
|
// 13.
|
|
// 14. if y == T.nil
|
|
// 15. T.root = z
|
|
// 16. else if z.key < y.key
|
|
// 17. y.left = z
|
|
// 18. else
|
|
// 19. y.right = z
|
|
// 20.
|
|
// 21. z.left = T.nil
|
|
// 22. z.right = T.nil
|
|
// 23. z.color = RED
|
|
// 24.
|
|
// 25. RB-INSERT-FIXUP(T, z)
|
|
|
|
// Insert adds a node with the given interval into the tree.
|
|
func (ivt *intervalTree) Insert(ivl Interval, val interface{}) {
|
|
y := ivt.sentinel
|
|
z := ivt.createIntervalNode(ivl, val)
|
|
x := ivt.root
|
|
for x != ivt.sentinel {
|
|
y = x
|
|
if z.iv.Ivl.Begin.Compare(x.iv.Ivl.Begin) < 0 {
|
|
x = x.left
|
|
} else {
|
|
x = x.right
|
|
}
|
|
}
|
|
|
|
z.parent = y
|
|
if y == ivt.sentinel {
|
|
ivt.root = z
|
|
} else {
|
|
if z.iv.Ivl.Begin.Compare(y.iv.Ivl.Begin) < 0 {
|
|
y.left = z
|
|
} else {
|
|
y.right = z
|
|
}
|
|
y.updateMax(ivt.sentinel)
|
|
}
|
|
z.c = red
|
|
|
|
ivt.insertFixup(z)
|
|
ivt.count++
|
|
}
|
|
|
|
// "Introduction to Algorithms" (Cormen et al, 3rd ed.), chapter 13.3, p316
|
|
//
|
|
// 0. RB-INSERT-FIXUP(T, z)
|
|
// 1.
|
|
// 2. while z.p.color == RED
|
|
// 3. if z.p == z.p.p.left
|
|
// 4. y = z.p.p.right
|
|
// 5. if y.color == RED
|
|
// 6. z.p.color = BLACK
|
|
// 7. y.color = BLACK
|
|
// 8. z.p.p.color = RED
|
|
// 9. z = z.p.p
|
|
// 10. else if z == z.p.right
|
|
// 11. z = z.p
|
|
// 12. LEFT-ROTATE(T, z)
|
|
// 13. z.p.color = BLACK
|
|
// 14. z.p.p.color = RED
|
|
// 15. RIGHT-ROTATE(T, z.p.p)
|
|
// 16. else
|
|
// 17. y = z.p.p.left
|
|
// 18. if y.color == RED
|
|
// 19. z.p.color = BLACK
|
|
// 20. y.color = BLACK
|
|
// 21. z.p.p.color = RED
|
|
// 22. z = z.p.p
|
|
// 23. else if z == z.p.right
|
|
// 24. z = z.p
|
|
// 25. RIGHT-ROTATE(T, z)
|
|
// 26. z.p.color = BLACK
|
|
// 27. z.p.p.color = RED
|
|
// 28. LEFT-ROTATE(T, z.p.p)
|
|
// 29.
|
|
// 30. T.root.color = BLACK
|
|
//
|
|
func (ivt *intervalTree) insertFixup(z *intervalNode) {
|
|
for z.parent.color(ivt.sentinel) == red {
|
|
if z.parent == z.parent.parent.left { // line 3-15
|
|
|
|
y := z.parent.parent.right
|
|
if y.color(ivt.sentinel) == red {
|
|
y.c = black
|
|
z.parent.c = black
|
|
z.parent.parent.c = red
|
|
z = z.parent.parent
|
|
} else {
|
|
if z == z.parent.right {
|
|
z = z.parent
|
|
ivt.rotateLeft(z)
|
|
}
|
|
z.parent.c = black
|
|
z.parent.parent.c = red
|
|
ivt.rotateRight(z.parent.parent)
|
|
}
|
|
} else { // line 16-28
|
|
// same as then with left/right exchanged
|
|
y := z.parent.parent.left
|
|
if y.color(ivt.sentinel) == red {
|
|
y.c = black
|
|
z.parent.c = black
|
|
z.parent.parent.c = red
|
|
z = z.parent.parent
|
|
} else {
|
|
if z == z.parent.left {
|
|
z = z.parent
|
|
ivt.rotateRight(z)
|
|
}
|
|
z.parent.c = black
|
|
z.parent.parent.c = red
|
|
ivt.rotateLeft(z.parent.parent)
|
|
}
|
|
}
|
|
}
|
|
|
|
// line 30
|
|
ivt.root.c = black
|
|
}
|
|
|
|
// rotateLeft moves x so it is left of its right child
|
|
//
|
|
// "Introduction to Algorithms" (Cormen et al, 3rd ed.), chapter 13.2, p313
|
|
//
|
|
// 0. LEFT-ROTATE(T, x)
|
|
// 1.
|
|
// 2. y = x.right
|
|
// 3. x.right = y.left
|
|
// 4.
|
|
// 5. if y.left ≠ T.nil
|
|
// 6. y.left.p = x
|
|
// 7.
|
|
// 8. y.p = x.p
|
|
// 9.
|
|
// 10. if x.p == T.nil
|
|
// 11. T.root = y
|
|
// 12. else if x == x.p.left
|
|
// 13. x.p.left = y
|
|
// 14. else
|
|
// 15. x.p.right = y
|
|
// 16.
|
|
// 17. y.left = x
|
|
// 18. x.p = y
|
|
//
|
|
func (ivt *intervalTree) rotateLeft(x *intervalNode) {
|
|
// rotateLeft x must have right child
|
|
if x.right == ivt.sentinel {
|
|
return
|
|
}
|
|
|
|
// line 2-3
|
|
y := x.right
|
|
x.right = y.left
|
|
|
|
// line 5-6
|
|
if y.left != ivt.sentinel {
|
|
y.left.parent = x
|
|
}
|
|
x.updateMax(ivt.sentinel)
|
|
|
|
// line 10-15, 18
|
|
ivt.replaceParent(x, y)
|
|
|
|
// line 17
|
|
y.left = x
|
|
y.updateMax(ivt.sentinel)
|
|
}
|
|
|
|
// rotateRight moves x so it is right of its left child
|
|
//
|
|
// 0. RIGHT-ROTATE(T, x)
|
|
// 1.
|
|
// 2. y = x.left
|
|
// 3. x.left = y.right
|
|
// 4.
|
|
// 5. if y.right ≠ T.nil
|
|
// 6. y.right.p = x
|
|
// 7.
|
|
// 8. y.p = x.p
|
|
// 9.
|
|
// 10. if x.p == T.nil
|
|
// 11. T.root = y
|
|
// 12. else if x == x.p.right
|
|
// 13. x.p.right = y
|
|
// 14. else
|
|
// 15. x.p.left = y
|
|
// 16.
|
|
// 17. y.right = x
|
|
// 18. x.p = y
|
|
//
|
|
func (ivt *intervalTree) rotateRight(x *intervalNode) {
|
|
// rotateRight x must have left child
|
|
if x.left == ivt.sentinel {
|
|
return
|
|
}
|
|
|
|
// line 2-3
|
|
y := x.left
|
|
x.left = y.right
|
|
|
|
// line 5-6
|
|
if y.right != ivt.sentinel {
|
|
y.right.parent = x
|
|
}
|
|
x.updateMax(ivt.sentinel)
|
|
|
|
// line 10-15, 18
|
|
ivt.replaceParent(x, y)
|
|
|
|
// line 17
|
|
y.right = x
|
|
y.updateMax(ivt.sentinel)
|
|
}
|
|
|
|
// replaceParent replaces x's parent with y
|
|
func (ivt *intervalTree) replaceParent(x *intervalNode, y *intervalNode) {
|
|
y.parent = x.parent
|
|
if x.parent == ivt.sentinel {
|
|
ivt.root = y
|
|
} else {
|
|
if x == x.parent.left {
|
|
x.parent.left = y
|
|
} else {
|
|
x.parent.right = y
|
|
}
|
|
x.parent.updateMax(ivt.sentinel)
|
|
}
|
|
x.parent = y
|
|
}
|
|
|
|
// Len gives the number of elements in the tree
|
|
func (ivt *intervalTree) Len() int { return ivt.count }
|
|
|
|
// Height is the number of levels in the tree; one node has height 1.
|
|
func (ivt *intervalTree) Height() int { return ivt.root.height(ivt.sentinel) }
|
|
|
|
// MaxHeight is the expected maximum tree height given the number of nodes
|
|
func (ivt *intervalTree) MaxHeight() int {
|
|
return int((2 * math.Log2(float64(ivt.Len()+1))) + 0.5)
|
|
}
|
|
|
|
// IntervalVisitor is used on tree searches; return false to stop searching.
|
|
type IntervalVisitor func(n *IntervalValue) bool
|
|
|
|
// Visit calls a visitor function on every tree node intersecting the given interval.
|
|
// It will visit each interval [x, y) in ascending order sorted on x.
|
|
func (ivt *intervalTree) Visit(ivl Interval, ivv IntervalVisitor) {
|
|
ivt.root.visit(&ivl, ivt.sentinel, func(n *intervalNode) bool { return ivv(&n.iv) })
|
|
}
|
|
|
|
// find the exact node for a given interval
|
|
func (ivt *intervalTree) find(ivl Interval) *intervalNode {
|
|
ret := ivt.sentinel
|
|
f := func(n *intervalNode) bool {
|
|
if n.iv.Ivl != ivl {
|
|
return true
|
|
}
|
|
ret = n
|
|
return false
|
|
}
|
|
ivt.root.visit(&ivl, ivt.sentinel, f)
|
|
return ret
|
|
}
|
|
|
|
// Find gets the IntervalValue for the node matching the given interval
|
|
func (ivt *intervalTree) Find(ivl Interval) (ret *IntervalValue) {
|
|
n := ivt.find(ivl)
|
|
if n == ivt.sentinel {
|
|
return nil
|
|
}
|
|
return &n.iv
|
|
}
|
|
|
|
// Intersects returns true if there is some tree node intersecting the given interval.
|
|
func (ivt *intervalTree) Intersects(iv Interval) bool {
|
|
x := ivt.root
|
|
for x != ivt.sentinel && iv.Compare(&x.iv.Ivl) != 0 {
|
|
if x.left != ivt.sentinel && x.left.max.Compare(iv.Begin) > 0 {
|
|
x = x.left
|
|
} else {
|
|
x = x.right
|
|
}
|
|
}
|
|
return x != ivt.sentinel
|
|
}
|
|
|
|
// Contains returns true if the interval tree's keys cover the entire given interval.
|
|
func (ivt *intervalTree) Contains(ivl Interval) bool {
|
|
var maxEnd, minBegin Comparable
|
|
|
|
isContiguous := true
|
|
ivt.Visit(ivl, func(n *IntervalValue) bool {
|
|
if minBegin == nil {
|
|
minBegin = n.Ivl.Begin
|
|
maxEnd = n.Ivl.End
|
|
return true
|
|
}
|
|
if maxEnd.Compare(n.Ivl.Begin) < 0 {
|
|
isContiguous = false
|
|
return false
|
|
}
|
|
if n.Ivl.End.Compare(maxEnd) > 0 {
|
|
maxEnd = n.Ivl.End
|
|
}
|
|
return true
|
|
})
|
|
|
|
return isContiguous && minBegin != nil && maxEnd.Compare(ivl.End) >= 0 && minBegin.Compare(ivl.Begin) <= 0
|
|
}
|
|
|
|
// Stab returns a slice with all elements in the tree intersecting the interval.
|
|
func (ivt *intervalTree) Stab(iv Interval) (ivs []*IntervalValue) {
|
|
if ivt.count == 0 {
|
|
return nil
|
|
}
|
|
f := func(n *IntervalValue) bool { ivs = append(ivs, n); return true }
|
|
ivt.Visit(iv, f)
|
|
return ivs
|
|
}
|
|
|
|
// Union merges a given interval tree into the receiver.
|
|
func (ivt *intervalTree) Union(inIvt IntervalTree, ivl Interval) {
|
|
f := func(n *IntervalValue) bool {
|
|
ivt.Insert(n.Ivl, n.Val)
|
|
return true
|
|
}
|
|
inIvt.Visit(ivl, f)
|
|
}
|
|
|
|
type visitedInterval struct {
|
|
root Interval
|
|
left Interval
|
|
right Interval
|
|
color rbcolor
|
|
depth int
|
|
}
|
|
|
|
func (vi visitedInterval) String() string {
|
|
bd := new(strings.Builder)
|
|
bd.WriteString(fmt.Sprintf("root [%v,%v,%v], left [%v,%v], right [%v,%v], depth %d",
|
|
vi.root.Begin, vi.root.End, vi.color,
|
|
vi.left.Begin, vi.left.End,
|
|
vi.right.Begin, vi.right.End,
|
|
vi.depth,
|
|
))
|
|
return bd.String()
|
|
}
|
|
|
|
// visitLevel traverses tree in level order.
|
|
// used for testing
|
|
func (ivt *intervalTree) visitLevel() []visitedInterval {
|
|
if ivt.root == ivt.sentinel {
|
|
return nil
|
|
}
|
|
|
|
rs := make([]visitedInterval, 0, ivt.Len())
|
|
|
|
type pair struct {
|
|
node *intervalNode
|
|
depth int
|
|
}
|
|
queue := []pair{{ivt.root, 0}}
|
|
for len(queue) > 0 {
|
|
f := queue[0]
|
|
queue = queue[1:]
|
|
|
|
vi := visitedInterval{
|
|
root: f.node.iv.Ivl,
|
|
color: f.node.color(ivt.sentinel),
|
|
depth: f.depth,
|
|
}
|
|
if f.node.left != ivt.sentinel {
|
|
vi.left = f.node.left.iv.Ivl
|
|
queue = append(queue, pair{f.node.left, f.depth + 1})
|
|
}
|
|
if f.node.right != ivt.sentinel {
|
|
vi.right = f.node.right.iv.Ivl
|
|
queue = append(queue, pair{f.node.right, f.depth + 1})
|
|
}
|
|
|
|
rs = append(rs, vi)
|
|
}
|
|
|
|
return rs
|
|
}
|
|
|
|
type StringComparable string
|
|
|
|
func (s StringComparable) Compare(c Comparable) int {
|
|
sc := c.(StringComparable)
|
|
if s < sc {
|
|
return -1
|
|
}
|
|
if s > sc {
|
|
return 1
|
|
}
|
|
return 0
|
|
}
|
|
|
|
func NewStringInterval(begin, end string) Interval {
|
|
return Interval{StringComparable(begin), StringComparable(end)}
|
|
}
|
|
|
|
func NewStringPoint(s string) Interval {
|
|
return Interval{StringComparable(s), StringComparable(s + "\x00")}
|
|
}
|
|
|
|
// StringAffineComparable treats "" as > all other strings
|
|
type StringAffineComparable string
|
|
|
|
func (s StringAffineComparable) Compare(c Comparable) int {
|
|
sc := c.(StringAffineComparable)
|
|
|
|
if len(s) == 0 {
|
|
if len(sc) == 0 {
|
|
return 0
|
|
}
|
|
return 1
|
|
}
|
|
if len(sc) == 0 {
|
|
return -1
|
|
}
|
|
|
|
if s < sc {
|
|
return -1
|
|
}
|
|
if s > sc {
|
|
return 1
|
|
}
|
|
return 0
|
|
}
|
|
|
|
func NewStringAffineInterval(begin, end string) Interval {
|
|
return Interval{StringAffineComparable(begin), StringAffineComparable(end)}
|
|
}
|
|
|
|
func NewStringAffinePoint(s string) Interval {
|
|
return NewStringAffineInterval(s, s+"\x00")
|
|
}
|
|
|
|
func NewInt64Interval(a int64, b int64) Interval {
|
|
return Interval{Int64Comparable(a), Int64Comparable(b)}
|
|
}
|
|
|
|
func newInt64EmptyInterval() Interval {
|
|
return Interval{Begin: nil, End: nil}
|
|
}
|
|
|
|
func NewInt64Point(a int64) Interval {
|
|
return Interval{Int64Comparable(a), Int64Comparable(a + 1)}
|
|
}
|
|
|
|
type Int64Comparable int64
|
|
|
|
func (v Int64Comparable) Compare(c Comparable) int {
|
|
vc := c.(Int64Comparable)
|
|
cmp := v - vc
|
|
if cmp < 0 {
|
|
return -1
|
|
}
|
|
if cmp > 0 {
|
|
return 1
|
|
}
|
|
return 0
|
|
}
|
|
|
|
// BytesAffineComparable treats empty byte arrays as > all other byte arrays
|
|
type BytesAffineComparable []byte
|
|
|
|
func (b BytesAffineComparable) Compare(c Comparable) int {
|
|
bc := c.(BytesAffineComparable)
|
|
|
|
if len(b) == 0 {
|
|
if len(bc) == 0 {
|
|
return 0
|
|
}
|
|
return 1
|
|
}
|
|
if len(bc) == 0 {
|
|
return -1
|
|
}
|
|
|
|
return bytes.Compare(b, bc)
|
|
}
|
|
|
|
func NewBytesAffineInterval(begin, end []byte) Interval {
|
|
return Interval{BytesAffineComparable(begin), BytesAffineComparable(end)}
|
|
}
|
|
|
|
func NewBytesAffinePoint(b []byte) Interval {
|
|
be := make([]byte, len(b)+1)
|
|
copy(be, b)
|
|
be[len(b)] = 0
|
|
return NewBytesAffineInterval(b, be)
|
|
}
|