| // 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) |
| } |