// 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 ( "math/rand" "reflect" "testing" "time" ) // TestIntervalTreeInsert tests interval tree insertion. func TestIntervalTreeInsert(t *testing.T) { // "Introduction to Algorithms" (Cormen et al, 3rd ed.) chapter 14, Figure 14.4 ivt := NewIntervalTree() ivt.Insert(NewInt64Interval(16, 21), 30) ivt.Insert(NewInt64Interval(8, 9), 23) ivt.Insert(NewInt64Interval(0, 3), 3) ivt.Insert(NewInt64Interval(5, 8), 10) ivt.Insert(NewInt64Interval(6, 10), 10) ivt.Insert(NewInt64Interval(15, 23), 23) ivt.Insert(NewInt64Interval(17, 19), 20) ivt.Insert(NewInt64Interval(25, 30), 30) ivt.Insert(NewInt64Interval(26, 26), 26) ivt.Insert(NewInt64Interval(19, 20), 20) expected := []visitedInterval{ {root: NewInt64Interval(16, 21), color: black, left: NewInt64Interval(8, 9), right: NewInt64Interval(25, 30), depth: 0}, {root: NewInt64Interval(8, 9), color: red, left: NewInt64Interval(5, 8), right: NewInt64Interval(15, 23), depth: 1}, {root: NewInt64Interval(25, 30), color: red, left: NewInt64Interval(17, 19), right: NewInt64Interval(26, 26), depth: 1}, {root: NewInt64Interval(5, 8), color: black, left: NewInt64Interval(0, 3), right: NewInt64Interval(6, 10), depth: 2}, {root: NewInt64Interval(15, 23), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 2}, {root: NewInt64Interval(17, 19), color: black, left: newInt64EmptyInterval(), right: NewInt64Interval(19, 20), depth: 2}, {root: NewInt64Interval(26, 26), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 2}, {root: NewInt64Interval(0, 3), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(6, 10), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(19, 20), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, } tr := ivt.(*intervalTree) visits := tr.visitLevel() if !reflect.DeepEqual(expected, visits) { t.Fatalf("level order expected %v, got %v", expected, visits) } } // TestIntervalTreeSelfBalanced ensures range tree is self-balanced after inserting ranges to the tree. // Use https://www.cs.usfca.edu/~galles/visualization/RedBlack.html for test case creation. // // Regular Binary Search Tree // [0,1] // \ // [1,2] // \ // [3,4] // \ // [5,6] // \ // [7,8] // \ // [8,9] // // Self-Balancing Binary Search Tree // [1,2] // / \ // [0,1] [5,6] // / \ // [3,4] [7,8] // \ // [8,9] // func TestIntervalTreeSelfBalanced(t *testing.T) { ivt := NewIntervalTree() ivt.Insert(NewInt64Interval(0, 1), 0) ivt.Insert(NewInt64Interval(1, 2), 0) ivt.Insert(NewInt64Interval(3, 4), 0) ivt.Insert(NewInt64Interval(5, 6), 0) ivt.Insert(NewInt64Interval(7, 8), 0) ivt.Insert(NewInt64Interval(8, 9), 0) expected := []visitedInterval{ {root: NewInt64Interval(1, 2), color: black, left: NewInt64Interval(0, 1), right: NewInt64Interval(5, 6), depth: 0}, {root: NewInt64Interval(0, 1), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 1}, {root: NewInt64Interval(5, 6), color: red, left: NewInt64Interval(3, 4), right: NewInt64Interval(7, 8), depth: 1}, {root: NewInt64Interval(3, 4), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 2}, {root: NewInt64Interval(7, 8), color: black, left: newInt64EmptyInterval(), right: NewInt64Interval(8, 9), depth: 2}, {root: NewInt64Interval(8, 9), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, } tr := ivt.(*intervalTree) visits := tr.visitLevel() if !reflect.DeepEqual(expected, visits) { t.Fatalf("level order expected %v, got %v", expected, visits) } if visits[len(visits)-1].depth != 3 { t.Fatalf("expected self-balanced tree with last level 3, but last level got %d", visits[len(visits)-1].depth) } } // TestIntervalTreeDelete ensures delete operation maintains red-black tree properties. // Use https://www.cs.usfca.edu/~galles/visualization/RedBlack.html for test case creation. // See https://github.com/etcd-io/etcd/issues/10877 for more detail. // // // After insertion: // [510,511] // / \ // ---------- ----------------------- // / \ // [82,83] [830,831] // / \ / \ // / \ / \ // [11,12] [383,384](red) [647,648] [899,900](red) // / \ / \ / \ // / \ / \ / \ // [261,262] [410,411] [514,515](red) [815,816](red) [888,889] [972,973] // / \ / // / \ / // [238,239](red) [292,293](red) [953,954](red) // // // After deleting 514 (no rebalance): // [510,511] // / \ // ---------- ----------------------- // / \ // [82,83] [830,831] // / \ / \ // / \ / \ // [11,12] [383,384](red) [647,648] [899,900](red) // / \ \ / \ // / \ \ / \ // [261,262] [410,411] [815,816](red) [888,889] [972,973] // / \ / // / \ / // [238,239](red) [292,293](red) [953,954](red) // // // After deleting 11 (requires rebalancing): // [510,511] // / \ // ---------- -------------------------- // / \ // [383,384] [830,831] // / \ / \ // / \ / \ // [261,262](red) [410,411] [647,648] [899,900](red) // / \ \ / \ // / \ \ / \ // [82,83] [292,293] [815,816](red) [888,889] [972,973] // \ / // \ / // [238,239](red) [953,954](red) // // func TestIntervalTreeDelete(t *testing.T) { ivt := NewIntervalTree() ivt.Insert(NewInt64Interval(510, 511), 0) ivt.Insert(NewInt64Interval(82, 83), 0) ivt.Insert(NewInt64Interval(830, 831), 0) ivt.Insert(NewInt64Interval(11, 12), 0) ivt.Insert(NewInt64Interval(383, 384), 0) ivt.Insert(NewInt64Interval(647, 648), 0) ivt.Insert(NewInt64Interval(899, 900), 0) ivt.Insert(NewInt64Interval(261, 262), 0) ivt.Insert(NewInt64Interval(410, 411), 0) ivt.Insert(NewInt64Interval(514, 515), 0) ivt.Insert(NewInt64Interval(815, 816), 0) ivt.Insert(NewInt64Interval(888, 889), 0) ivt.Insert(NewInt64Interval(972, 973), 0) ivt.Insert(NewInt64Interval(238, 239), 0) ivt.Insert(NewInt64Interval(292, 293), 0) ivt.Insert(NewInt64Interval(953, 954), 0) tr := ivt.(*intervalTree) expectedBeforeDelete := []visitedInterval{ {root: NewInt64Interval(510, 511), color: black, left: NewInt64Interval(82, 83), right: NewInt64Interval(830, 831), depth: 0}, {root: NewInt64Interval(82, 83), color: black, left: NewInt64Interval(11, 12), right: NewInt64Interval(383, 384), depth: 1}, {root: NewInt64Interval(830, 831), color: black, left: NewInt64Interval(647, 648), right: NewInt64Interval(899, 900), depth: 1}, {root: NewInt64Interval(11, 12), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 2}, {root: NewInt64Interval(383, 384), color: red, left: NewInt64Interval(261, 262), right: NewInt64Interval(410, 411), depth: 2}, {root: NewInt64Interval(647, 648), color: black, left: NewInt64Interval(514, 515), right: NewInt64Interval(815, 816), depth: 2}, {root: NewInt64Interval(899, 900), color: red, left: NewInt64Interval(888, 889), right: NewInt64Interval(972, 973), depth: 2}, {root: NewInt64Interval(261, 262), color: black, left: NewInt64Interval(238, 239), right: NewInt64Interval(292, 293), depth: 3}, {root: NewInt64Interval(410, 411), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(514, 515), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(815, 816), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(888, 889), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(972, 973), color: black, left: NewInt64Interval(953, 954), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(238, 239), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 4}, {root: NewInt64Interval(292, 293), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 4}, {root: NewInt64Interval(953, 954), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 4}, } visitsBeforeDelete := tr.visitLevel() if !reflect.DeepEqual(expectedBeforeDelete, visitsBeforeDelete) { t.Fatalf("level order after insertion expected %v, got %v", expectedBeforeDelete, visitsBeforeDelete) } // delete the node "514" range514 := NewInt64Interval(514, 515) if deleted := tr.Delete(NewInt64Interval(514, 515)); !deleted { t.Fatalf("range %v not deleted", range514) } expectedAfterDelete514 := []visitedInterval{ {root: NewInt64Interval(510, 511), color: black, left: NewInt64Interval(82, 83), right: NewInt64Interval(830, 831), depth: 0}, {root: NewInt64Interval(82, 83), color: black, left: NewInt64Interval(11, 12), right: NewInt64Interval(383, 384), depth: 1}, {root: NewInt64Interval(830, 831), color: black, left: NewInt64Interval(647, 648), right: NewInt64Interval(899, 900), depth: 1}, {root: NewInt64Interval(11, 12), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 2}, {root: NewInt64Interval(383, 384), color: red, left: NewInt64Interval(261, 262), right: NewInt64Interval(410, 411), depth: 2}, {root: NewInt64Interval(647, 648), color: black, left: newInt64EmptyInterval(), right: NewInt64Interval(815, 816), depth: 2}, {root: NewInt64Interval(899, 900), color: red, left: NewInt64Interval(888, 889), right: NewInt64Interval(972, 973), depth: 2}, {root: NewInt64Interval(261, 262), color: black, left: NewInt64Interval(238, 239), right: NewInt64Interval(292, 293), depth: 3}, {root: NewInt64Interval(410, 411), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(815, 816), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(888, 889), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(972, 973), color: black, left: NewInt64Interval(953, 954), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(238, 239), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 4}, {root: NewInt64Interval(292, 293), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 4}, {root: NewInt64Interval(953, 954), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 4}, } visitsAfterDelete514 := tr.visitLevel() if !reflect.DeepEqual(expectedAfterDelete514, visitsAfterDelete514) { t.Fatalf("level order after deleting '514' expected %v, got %v", expectedAfterDelete514, visitsAfterDelete514) } // delete the node "11" range11 := NewInt64Interval(11, 12) if deleted := tr.Delete(NewInt64Interval(11, 12)); !deleted { t.Fatalf("range %v not deleted", range11) } expectedAfterDelete11 := []visitedInterval{ {root: NewInt64Interval(510, 511), color: black, left: NewInt64Interval(383, 384), right: NewInt64Interval(830, 831), depth: 0}, {root: NewInt64Interval(383, 384), color: black, left: NewInt64Interval(261, 262), right: NewInt64Interval(410, 411), depth: 1}, {root: NewInt64Interval(830, 831), color: black, left: NewInt64Interval(647, 648), right: NewInt64Interval(899, 900), depth: 1}, {root: NewInt64Interval(261, 262), color: red, left: NewInt64Interval(82, 83), right: NewInt64Interval(292, 293), depth: 2}, {root: NewInt64Interval(410, 411), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 2}, {root: NewInt64Interval(647, 648), color: black, left: newInt64EmptyInterval(), right: NewInt64Interval(815, 816), depth: 2}, {root: NewInt64Interval(899, 900), color: red, left: NewInt64Interval(888, 889), right: NewInt64Interval(972, 973), depth: 2}, {root: NewInt64Interval(82, 83), color: black, left: newInt64EmptyInterval(), right: NewInt64Interval(238, 239), depth: 3}, {root: NewInt64Interval(292, 293), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(815, 816), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(888, 889), color: black, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(972, 973), color: black, left: NewInt64Interval(953, 954), right: newInt64EmptyInterval(), depth: 3}, {root: NewInt64Interval(238, 239), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 4}, {root: NewInt64Interval(953, 954), color: red, left: newInt64EmptyInterval(), right: newInt64EmptyInterval(), depth: 4}, } visitsAfterDelete11 := tr.visitLevel() if !reflect.DeepEqual(expectedAfterDelete11, visitsAfterDelete11) { t.Fatalf("level order after deleting '11' expected %v, got %v", expectedAfterDelete11, visitsAfterDelete11) } } func TestIntervalTreeIntersects(t *testing.T) { ivt := NewIntervalTree() ivt.Insert(NewStringInterval("1", "3"), 123) if ivt.Intersects(NewStringPoint("0")) { t.Errorf("contains 0") } if !ivt.Intersects(NewStringPoint("1")) { t.Errorf("missing 1") } if !ivt.Intersects(NewStringPoint("11")) { t.Errorf("missing 11") } if !ivt.Intersects(NewStringPoint("2")) { t.Errorf("missing 2") } if ivt.Intersects(NewStringPoint("3")) { t.Errorf("contains 3") } } func TestIntervalTreeStringAffine(t *testing.T) { ivt := NewIntervalTree() ivt.Insert(NewStringAffineInterval("8", ""), 123) if !ivt.Intersects(NewStringAffinePoint("9")) { t.Errorf("missing 9") } if ivt.Intersects(NewStringAffinePoint("7")) { t.Errorf("contains 7") } } func TestIntervalTreeStab(t *testing.T) { ivt := NewIntervalTree() 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) tr := ivt.(*intervalTree) if tr.root.max.Compare(StringComparable("8")) != 0 { t.Fatalf("wrong root max got %v, expected 8", tr.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 := NewIntervalTree() 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.Intersects(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()) } } // TestIntervalTreeSortedVisit tests that intervals are visited in sorted order. func TestIntervalTreeSortedVisit(t *testing.T) { tests := []struct { ivls []Interval visitRange Interval }{ { ivls: []Interval{NewInt64Interval(1, 10), NewInt64Interval(2, 5), NewInt64Interval(3, 6)}, visitRange: NewInt64Interval(0, 100), }, { ivls: []Interval{NewInt64Interval(1, 10), NewInt64Interval(10, 12), NewInt64Interval(3, 6)}, visitRange: NewInt64Interval(0, 100), }, { ivls: []Interval{NewInt64Interval(2, 3), NewInt64Interval(3, 4), NewInt64Interval(6, 7), NewInt64Interval(5, 6)}, visitRange: NewInt64Interval(0, 100), }, { ivls: []Interval{ NewInt64Interval(2, 3), NewInt64Interval(2, 4), NewInt64Interval(3, 7), NewInt64Interval(2, 5), NewInt64Interval(3, 8), NewInt64Interval(3, 5), }, visitRange: NewInt64Interval(0, 100), }, } for i, tt := range tests { ivt := NewIntervalTree() for _, ivl := range tt.ivls { ivt.Insert(ivl, struct{}{}) } last := tt.ivls[0].Begin count := 0 chk := func(iv *IntervalValue) bool { if last.Compare(iv.Ivl.Begin) > 0 { t.Errorf("#%d: expected less than %d, got interval %+v", i, last, iv.Ivl) } last = iv.Ivl.Begin count++ return true } ivt.Visit(tt.visitRange, chk) if count != len(tt.ivls) { t.Errorf("#%d: did not cover all intervals. expected %d, got %d", i, len(tt.ivls), count) } } } // TestIntervalTreeVisitExit tests that visiting can be stopped. func TestIntervalTreeVisitExit(t *testing.T) { ivls := []Interval{NewInt64Interval(1, 10), NewInt64Interval(2, 5), NewInt64Interval(3, 6), NewInt64Interval(4, 8)} ivlRange := NewInt64Interval(0, 100) tests := []struct { f IntervalVisitor wcount int }{ { f: func(n *IntervalValue) bool { return false }, wcount: 1, }, { f: func(n *IntervalValue) bool { return n.Ivl.Begin.Compare(ivls[0].Begin) <= 0 }, wcount: 2, }, { f: func(n *IntervalValue) bool { return n.Ivl.Begin.Compare(ivls[2].Begin) < 0 }, wcount: 3, }, { f: func(n *IntervalValue) bool { return true }, wcount: 4, }, } for i, tt := range tests { ivt := NewIntervalTree() for _, ivl := range ivls { ivt.Insert(ivl, struct{}{}) } count := 0 ivt.Visit(ivlRange, func(n *IntervalValue) bool { count++ return tt.f(n) }) if count != tt.wcount { t.Errorf("#%d: expected count %d, got %d", i, tt.wcount, count) } } } // TestIntervalTreeContains tests that contains returns true iff the ivt maps the entire interval. func TestIntervalTreeContains(t *testing.T) { tests := []struct { ivls []Interval chkIvl Interval wContains bool }{ { ivls: []Interval{NewInt64Interval(1, 10)}, chkIvl: NewInt64Interval(0, 100), wContains: false, }, { ivls: []Interval{NewInt64Interval(1, 10)}, chkIvl: NewInt64Interval(1, 10), wContains: true, }, { ivls: []Interval{NewInt64Interval(1, 10)}, chkIvl: NewInt64Interval(2, 8), wContains: true, }, { ivls: []Interval{NewInt64Interval(1, 5), NewInt64Interval(6, 10)}, chkIvl: NewInt64Interval(1, 10), wContains: false, }, { ivls: []Interval{NewInt64Interval(1, 5), NewInt64Interval(3, 10)}, chkIvl: NewInt64Interval(1, 10), wContains: true, }, { ivls: []Interval{NewInt64Interval(1, 4), NewInt64Interval(4, 7), NewInt64Interval(3, 10)}, chkIvl: NewInt64Interval(1, 10), wContains: true, }, { ivls: []Interval{}, chkIvl: NewInt64Interval(1, 10), wContains: false, }, } for i, tt := range tests { ivt := NewIntervalTree() for _, ivl := range tt.ivls { ivt.Insert(ivl, struct{}{}) } if v := ivt.Contains(tt.chkIvl); v != tt.wContains { t.Errorf("#%d: ivt.Contains got %v, expected %v", i, v, tt.wContains) } } }