From c0b06a7a32fd48e2f922e31bd4dc7e9a8d2c557c Mon Sep 17 00:00:00 2001
From: Anthony Romano <anthony.romano@coreos.com>
Date: Sun, 28 Feb 2016 22:11:26 -0800
Subject: [PATCH] pkg/adt: interval tree
---
pkg/adt/interval_tree.go | 526 ++++++++++++++++++++++++++++++++++
pkg/adt/interval_tree_test.go | 138 +++++++++
2 files changed, 664 insertions(+)
create mode 100644 pkg/adt/interval_tree.go
create mode 100644 pkg/adt/interval_tree_test.go
diff --git a/pkg/adt/interval_tree.go b/pkg/adt/interval_tree.go
new file mode 100644
index 000000000..465c6200c
--- /dev/null
+++ b/pkg/adt/interval_tree.go
@@ -0,0 +1,526 @@
+// Copyright 2016 CoreOS, Inc.
+//
+// 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 (
+ "math"
+)
+
+// 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 bool
+
+const black = true
+const red = false
+
+// 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() rbcolor {
+ if x == nil {
+ return black
+ }
+ return x.c
+}
+
+func (n *intervalNode) height() int {
+ if n == nil {
+ return 0
+ }
+ ld := n.left.height()
+ rd := n.right.height()
+ if ld < rd {
+ return rd + 1
+ }
+ return ld + 1
+}
+
+func (x *intervalNode) min() *intervalNode {
+ for x.left != nil {
+ x = x.left
+ }
+ return x
+}
+
+// successor is the next in-order node in the tree
+func (x *intervalNode) successor() *intervalNode {
+ if x.right != nil {
+ return x.right.min()
+ }
+ y := x.parent
+ for y != nil && 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() {
+ for x != nil {
+ oldmax := x.max
+ max := x.iv.Ivl.End
+ if x.left != nil && x.left.max.Compare(max) > 0 {
+ max = x.left.max
+ }
+ if x.right != nil && 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, nv nodeVisitor) {
+ if x == nil {
+ return
+ }
+ v := iv.Compare(&x.iv.Ivl)
+ switch {
+ case v < 0:
+ x.left.visit(iv, nv)
+ case v > 0:
+ maxiv := Interval{x.iv.Ivl.Begin, x.max}
+ if maxiv.Compare(iv) == 0 {
+ x.left.visit(iv, nv)
+ x.right.visit(iv, nv)
+ }
+ default:
+ nv(x)
+ x.left.visit(iv, nv)
+ x.right.visit(iv, nv)
+ }
+}
+
+type IntervalValue struct {
+ Ivl Interval
+ Val interface{}
+}
+
+// IntervalTree represents a (mostly) textbook implementation of the
+// "Introduction to Algorithms" (Cormen et al, 2nd ed.) chapter 13 red-black tree
+// and chapter 14.3 interval tree with search supporting "stabbing queries".
+type IntervalTree struct {
+ root *intervalNode
+ count int
+}
+
+// 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 == nil {
+ return false
+ }
+
+ y := z
+ if z.left != nil && z.right != nil {
+ y = z.successor()
+ }
+
+ x := y.left
+ if x == nil {
+ x = y.right
+ }
+ if x != nil {
+ x.parent = y.parent
+ }
+
+ if y.parent == nil {
+ ivt.root = x
+ } else {
+ if y == y.parent.left {
+ y.parent.left = x
+ } else {
+ y.parent.right = x
+ }
+ y.parent.updateMax()
+ }
+ if y != z {
+ z.iv = y.iv
+ z.updateMax()
+ }
+
+ if y.color() == black && x != nil {
+ ivt.deleteFixup(x)
+ }
+
+ ivt.count--
+ return true
+}
+
+func (ivt *IntervalTree) deleteFixup(x *intervalNode) {
+ for x != ivt.root && x.color() == black && x.parent != nil {
+ if x == x.parent.left {
+ w := x.parent.right
+ if w.color() == red {
+ w.c = black
+ x.parent.c = red
+ ivt.rotateLeft(x.parent)
+ w = x.parent.right
+ }
+ if w == nil {
+ break
+ }
+ if w.left.color() == black && w.right.color() == black {
+ w.c = red
+ x = x.parent
+ } else {
+ if w.right.color() == black {
+ w.left.c = black
+ w.c = red
+ ivt.rotateRight(w)
+ w = x.parent.right
+ }
+ w.c = x.parent.color()
+ x.parent.c = black
+ w.right.c = black
+ ivt.rotateLeft(x.parent)
+ x = ivt.root
+ }
+ } else {
+ // same as above but with left and right exchanged
+ w := x.parent.left
+ if w.color() == red {
+ w.c = black
+ x.parent.c = red
+ ivt.rotateRight(x.parent)
+ w = x.parent.left
+ }
+ if w == nil {
+ break
+ }
+ if w.left.color() == black && w.right.color() == black {
+ w.c = red
+ x = x.parent
+ } else {
+ if w.left.color() == black {
+ w.right.c = black
+ w.c = red
+ ivt.rotateLeft(w)
+ w = x.parent.left
+ }
+ w.c = x.parent.color()
+ x.parent.c = black
+ w.left.c = black
+ ivt.rotateRight(x.parent)
+ x = ivt.root
+ }
+ }
+ }
+ if x != nil {
+ x.c = black
+ }
+}
+
+// Insert adds a node with the given interval into the tree.
+func (ivt *IntervalTree) Insert(ivl Interval, val interface{}) {
+ var y *intervalNode
+ z := &intervalNode{iv: IntervalValue{ivl, val}, max: ivl.End, c: red}
+ x := ivt.root
+ for x != nil {
+ 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 == nil {
+ ivt.root = z
+ } else {
+ if z.iv.Ivl.Begin.Compare(y.iv.Ivl.Begin) < 0 {
+ y.left = z
+ } else {
+ y.right = z
+ }
+ y.updateMax()
+ }
+ z.c = red
+ ivt.insertFixup(z)
+ ivt.count++
+}
+
+func (ivt *IntervalTree) insertFixup(z *intervalNode) {
+ for z.parent != nil && z.parent.parent != nil && z.parent.color() == red {
+ if z.parent == z.parent.parent.left {
+ y := z.parent.parent.right
+ if y.color() == 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 {
+ // same as then with left/right exchanged
+ y := z.parent.parent.left
+ if y.color() == 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)
+ }
+ }
+ }
+ ivt.root.c = black
+}
+
+// rotateLeft moves x so it is left of its right child
+func (ivt *IntervalTree) rotateLeft(x *intervalNode) {
+ y := x.right
+ x.right = y.left
+ if y.left != nil {
+ y.left.parent = x
+ }
+ x.updateMax()
+ ivt.replaceParent(x, y)
+ y.left = x
+ y.updateMax()
+}
+
+// rotateLeft moves x so it is right of its left child
+func (ivt *IntervalTree) rotateRight(x *intervalNode) {
+ if x == nil {
+ return
+ }
+ y := x.left
+ x.left = y.right
+ if y.right != nil {
+ y.right.parent = x
+ }
+ x.updateMax()
+ ivt.replaceParent(x, y)
+ y.right = x
+ y.updateMax()
+}
+
+// replaceParent replaces x's parent with y
+func (ivt *IntervalTree) replaceParent(x *intervalNode, y *intervalNode) {
+ y.parent = x.parent
+ if x.parent == nil {
+ ivt.root = y
+ } else {
+ if x == x.parent.left {
+ x.parent.left = y
+ } else {
+ x.parent.right = y
+ }
+ x.parent.updateMax()
+ }
+ 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() }
+
+// 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)
+}
+
+// InternalVisitor is used on tree searchs; return false to stop searching.
+type IntervalVisitor func(n *IntervalValue) bool
+
+// Visit calls a visitor function on every tree node intersecting the given interval.
+func (ivt *IntervalTree) Visit(ivl Interval, ivv IntervalVisitor) {
+ ivt.root.visit(&ivl, func(n *intervalNode) bool { return ivv(&n.iv) })
+}
+
+// find the exact node for a given interval
+func (ivt *IntervalTree) find(ivl Interval) (ret *intervalNode) {
+ f := func(n *intervalNode) bool {
+ if n.iv.Ivl != ivl {
+ return true
+ }
+ ret = n
+ return false
+ }
+ ivt.root.visit(&ivl, 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 == nil {
+ return nil
+ }
+ return &n.iv
+}
+
+// Contains returns true if there is some tree node intersecting the given interval.
+func (ivt *IntervalTree) Contains(iv Interval) bool {
+ x := ivt.root
+ for x != nil && iv.Compare(&x.iv.Ivl) != 0 {
+ if x.left != nil && x.left.max.Compare(iv.Begin) > 0 {
+ x = x.left
+ } else {
+ x = x.right
+ }
+ }
+ return x != nil
+}
+
+// Stab returns a slice with all elements in the tree intersecting the interval.
+func (ivt *IntervalTree) Stab(iv Interval) (ivs []*IntervalValue) {
+ f := func(n *IntervalValue) bool { ivs = append(ivs, n); return true }
+ ivt.Visit(iv, f)
+ return ivs
+}
+
+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 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
+}
diff --git a/pkg/adt/interval_tree_test.go b/pkg/adt/interval_tree_test.go
new file mode 100644
index 000000000..6cc540265
--- /dev/null
+++ b/pkg/adt/interval_tree_test.go
@@ -0,0 +1,138 @@
+// Copyright 2016 CoreOS, Inc.
+//
+// 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 (
+ "math/rand"
+ "testing"
+ "time"
+)
+
+func TestIntervalTreeContains(t *testing.T) {
+ ivt := &IntervalTree{}
+ ivt.Insert(NewStringInterval("1", "3"), 123)
+
+ if ivt.Contains(NewStringPoint("0")) {
+ t.Errorf("contains 0")
+ }
+ if !ivt.Contains(NewStringPoint("1")) {
+ t.Errorf("missing 1")
+ }
+ if !ivt.Contains(NewStringPoint("11")) {
+ t.Errorf("missing 11")
+ }
+ if !ivt.Contains(NewStringPoint("2")) {
+ t.Errorf("missing 2")
+ }
+ if ivt.Contains(NewStringPoint("3")) {
+ t.Errorf("contains 3")
+ }
+}
+
+func TestIntervalTreeStringAffine(t *testing.T) {
+ ivt := &IntervalTree{}
+ ivt.Insert(NewStringAffineInterval("8", ""), 123)
+ if !ivt.Contains(NewStringAffinePoint("9")) {
+ t.Errorf("missing 9")
+ }
+ if ivt.Contains(NewStringAffinePoint("7")) {
+ t.Errorf("contains 7")
+ }
+}
+
+func TestIntervalTreeStab(t *testing.T) {
+ ivt := &IntervalTree{}
+ ivt.Insert(NewStringInterval("0", "1"), 123)
+ ivt.Insert(NewStringInterval("0", "2"), 456)
+ ivt.Insert(NewStringInterval("5", "6"), 789)
+ ivt.Insert(NewStringInterval("6", "8"), 999)
+ ivt.Insert(NewStringInterval("0", "3"), 0)
+
+ if ivt.root.max.Compare(StringComparable("8")) != 0 {
+ t.Fatalf("wrong root max got %v, expected 8", ivt.root.max)
+ }
+ if x := len(ivt.Stab(NewStringPoint("0"))); x != 3 {
+ t.Errorf("got %d, expected 3", x)
+ }
+ if x := len(ivt.Stab(NewStringPoint("1"))); x != 2 {
+ t.Errorf("got %d, expected 2", x)
+ }
+ if x := len(ivt.Stab(NewStringPoint("2"))); x != 1 {
+ t.Errorf("got %d, expected 1", x)
+ }
+ if x := len(ivt.Stab(NewStringPoint("3"))); x != 0 {
+ t.Errorf("got %d, expected 0", x)
+ }
+ if x := len(ivt.Stab(NewStringPoint("5"))); x != 1 {
+ t.Errorf("got %d, expected 1", x)
+ }
+ if x := len(ivt.Stab(NewStringPoint("55"))); x != 1 {
+ t.Errorf("got %d, expected 1", x)
+ }
+ if x := len(ivt.Stab(NewStringPoint("6"))); x != 1 {
+ t.Errorf("got %d, expected 1", x)
+ }
+}
+
+type xy struct {
+ x int64
+ y int64
+}
+
+func TestIntervalTreeRandom(t *testing.T) {
+ // generate unique intervals
+ ivs := make(map[xy]struct{})
+ ivt := &IntervalTree{}
+ maxv := 128
+ rand.Seed(time.Now().UnixNano())
+
+ for i := rand.Intn(maxv) + 1; i != 0; i-- {
+ x, y := int64(rand.Intn(maxv)), int64(rand.Intn(maxv))
+ if x > y {
+ t := x
+ x = y
+ y = t
+ } else if x == y {
+ y++
+ }
+ iv := xy{x, y}
+ if _, ok := ivs[iv]; ok {
+ // don't double insert
+ continue
+ }
+ ivt.Insert(NewInt64Interval(x, y), 123)
+ ivs[iv] = struct{}{}
+ }
+
+ for ab := range ivs {
+ for xy := range ivs {
+ v := xy.x + int64(rand.Intn(int(xy.y-xy.x)))
+ if slen := len(ivt.Stab(NewInt64Point(v))); slen == 0 {
+ t.Fatalf("expected %v stab non-zero for [%+v)", v, xy)
+ }
+ if !ivt.Contains(NewInt64Point(v)) {
+ t.Fatalf("did not get %d as expected for [%+v)", v, xy)
+ }
+ }
+ if !ivt.Delete(NewInt64Interval(ab.x, ab.y)) {
+ t.Errorf("did not delete %v as expected", ab)
+ }
+ delete(ivs, ab)
+ }
+
+ if ivt.Len() != 0 {
+ t.Errorf("got ivt.Len() = %v, expected 0", ivt.Len())
+ }
+}