| // 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" |
| "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 int |
| |
| const ( |
| black rbcolor = iota |
| red |
| ) |
| |
| // 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) bool { |
| if x == nil { |
| return true |
| } |
| v := iv.Compare(&x.iv.Ivl) |
| switch { |
| case v < 0: |
| if !x.left.visit(iv, nv) { |
| return false |
| } |
| case v > 0: |
| maxiv := Interval{x.iv.Ivl.Begin, x.max} |
| if maxiv.Compare(iv) == 0 { |
| if !x.left.visit(iv, nv) || !x.right.visit(iv, nv) { |
| return false |
| } |
| } |
| default: |
| if !x.left.visit(iv, nv) || !nv(x) || !x.right.visit(iv, nv) { |
| return false |
| } |
| } |
| return true |
| } |
| |
| 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) |
| } |
| |
| // 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, 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 |
| } |
| |
| // 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 != 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 |
| } |
| |
| // 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 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 |
| } |
| |
| // 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) |
| } |