From ccd992355df7192993c666236047820244914598 Mon Sep 17 00:00:00 2001 From: Daniel Baumann Date: Tue, 16 Apr 2024 21:19:13 +0200 Subject: Adding upstream version 1.21.8. Signed-off-by: Daniel Baumann --- src/cmd/compile/internal/abt/avlint32.go | 832 ++++++++++++++++++++++++++ src/cmd/compile/internal/abt/avlint32_test.go | 700 ++++++++++++++++++++++ 2 files changed, 1532 insertions(+) create mode 100644 src/cmd/compile/internal/abt/avlint32.go create mode 100644 src/cmd/compile/internal/abt/avlint32_test.go (limited to 'src/cmd/compile/internal/abt') diff --git a/src/cmd/compile/internal/abt/avlint32.go b/src/cmd/compile/internal/abt/avlint32.go new file mode 100644 index 0000000..28c1642 --- /dev/null +++ b/src/cmd/compile/internal/abt/avlint32.go @@ -0,0 +1,832 @@ +// Copyright 2022 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package abt + +import ( + "fmt" + "strconv" + "strings" +) + +const ( + LEAF_HEIGHT = 1 + ZERO_HEIGHT = 0 + NOT_KEY32 = int32(-0x80000000) +) + +// T is the exported applicative balanced tree data type. +// A T can be used as a value; updates to one copy of the value +// do not change other copies. +type T struct { + root *node32 + size int +} + +// node32 is the internal tree node data type +type node32 struct { + // Standard conventions hold for left = smaller, right = larger + left, right *node32 + data interface{} + key int32 + height_ int8 +} + +func makeNode(key int32) *node32 { + return &node32{key: key, height_: LEAF_HEIGHT} +} + +// IsEmpty returns true iff t is empty. +func (t *T) IsEmpty() bool { + return t.root == nil +} + +// IsSingle returns true iff t is a singleton (leaf). +func (t *T) IsSingle() bool { + return t.root != nil && t.root.isLeaf() +} + +// VisitInOrder applies f to the key and data pairs in t, +// with keys ordered from smallest to largest. +func (t *T) VisitInOrder(f func(int32, interface{})) { + if t.root == nil { + return + } + t.root.visitInOrder(f) +} + +func (n *node32) nilOrData() interface{} { + if n == nil { + return nil + } + return n.data +} + +func (n *node32) nilOrKeyAndData() (k int32, d interface{}) { + if n == nil { + k = NOT_KEY32 + d = nil + } else { + k = n.key + d = n.data + } + return +} + +func (n *node32) height() int8 { + if n == nil { + return 0 + } + return n.height_ +} + +// Find returns the data associated with x in the tree, or +// nil if x is not in the tree. +func (t *T) Find(x int32) interface{} { + return t.root.find(x).nilOrData() +} + +// Insert either adds x to the tree if x was not previously +// a key in the tree, or updates the data for x in the tree if +// x was already a key in the tree. The previous data associated +// with x is returned, and is nil if x was not previously a +// key in the tree. +func (t *T) Insert(x int32, data interface{}) interface{} { + if x == NOT_KEY32 { + panic("Cannot use sentinel value -0x80000000 as key") + } + n := t.root + var newroot *node32 + var o *node32 + if n == nil { + n = makeNode(x) + newroot = n + } else { + newroot, n, o = n.aInsert(x) + } + var r interface{} + if o != nil { + r = o.data + } else { + t.size++ + } + n.data = data + t.root = newroot + return r +} + +func (t *T) Copy() *T { + u := *t + return &u +} + +func (t *T) Delete(x int32) interface{} { + n := t.root + if n == nil { + return nil + } + d, s := n.aDelete(x) + if d == nil { + return nil + } + t.root = s + t.size-- + return d.data +} + +func (t *T) DeleteMin() (int32, interface{}) { + n := t.root + if n == nil { + return NOT_KEY32, nil + } + d, s := n.aDeleteMin() + if d == nil { + return NOT_KEY32, nil + } + t.root = s + t.size-- + return d.key, d.data +} + +func (t *T) DeleteMax() (int32, interface{}) { + n := t.root + if n == nil { + return NOT_KEY32, nil + } + d, s := n.aDeleteMax() + if d == nil { + return NOT_KEY32, nil + } + t.root = s + t.size-- + return d.key, d.data +} + +func (t *T) Size() int { + return t.size +} + +// Intersection returns the intersection of t and u, where the result +// data for any common keys is given by f(t's data, u's data) -- f need +// not be symmetric. If f returns nil, then the key and data are not +// added to the result. If f itself is nil, then whatever value was +// already present in the smaller set is used. +func (t *T) Intersection(u *T, f func(x, y interface{}) interface{}) *T { + if t.Size() == 0 || u.Size() == 0 { + return &T{} + } + + // For faster execution and less allocation, prefer t smaller, iterate over t. + if t.Size() <= u.Size() { + v := t.Copy() + for it := t.Iterator(); !it.Done(); { + k, d := it.Next() + e := u.Find(k) + if e == nil { + v.Delete(k) + continue + } + if f == nil { + continue + } + if c := f(d, e); c != d { + if c == nil { + v.Delete(k) + } else { + v.Insert(k, c) + } + } + } + return v + } + v := u.Copy() + for it := u.Iterator(); !it.Done(); { + k, e := it.Next() + d := t.Find(k) + if d == nil { + v.Delete(k) + continue + } + if f == nil { + continue + } + if c := f(d, e); c != d { + if c == nil { + v.Delete(k) + } else { + v.Insert(k, c) + } + } + } + + return v +} + +// Union returns the union of t and u, where the result data for any common keys +// is given by f(t's data, u's data) -- f need not be symmetric. If f returns nil, +// then the key and data are not added to the result. If f itself is nil, then +// whatever value was already present in the larger set is used. +func (t *T) Union(u *T, f func(x, y interface{}) interface{}) *T { + if t.Size() == 0 { + return u + } + if u.Size() == 0 { + return t + } + + if t.Size() >= u.Size() { + v := t.Copy() + for it := u.Iterator(); !it.Done(); { + k, e := it.Next() + d := t.Find(k) + if d == nil { + v.Insert(k, e) + continue + } + if f == nil { + continue + } + if c := f(d, e); c != d { + if c == nil { + v.Delete(k) + } else { + v.Insert(k, c) + } + } + } + return v + } + + v := u.Copy() + for it := t.Iterator(); !it.Done(); { + k, d := it.Next() + e := u.Find(k) + if e == nil { + v.Insert(k, d) + continue + } + if f == nil { + continue + } + if c := f(d, e); c != d { + if c == nil { + v.Delete(k) + } else { + v.Insert(k, c) + } + } + } + return v +} + +// Difference returns the difference of t and u, subject to the result +// of f applied to data corresponding to equal keys. If f returns nil +// (or if f is nil) then the key+data are excluded, as usual. If f +// returns not-nil, then that key+data pair is inserted. instead. +func (t *T) Difference(u *T, f func(x, y interface{}) interface{}) *T { + if t.Size() == 0 { + return &T{} + } + if u.Size() == 0 { + return t + } + v := t.Copy() + for it := t.Iterator(); !it.Done(); { + k, d := it.Next() + e := u.Find(k) + if e != nil { + if f == nil { + v.Delete(k) + continue + } + c := f(d, e) + if c == nil { + v.Delete(k) + continue + } + if c != d { + v.Insert(k, c) + } + } + } + return v +} + +func (t *T) Iterator() Iterator { + return Iterator{it: t.root.iterator()} +} + +func (t *T) Equals(u *T) bool { + if t == u { + return true + } + if t.Size() != u.Size() { + return false + } + return t.root.equals(u.root) +} + +func (t *T) String() string { + var b strings.Builder + first := true + for it := t.Iterator(); !it.Done(); { + k, v := it.Next() + if first { + first = false + } else { + b.WriteString("; ") + } + b.WriteString(strconv.FormatInt(int64(k), 10)) + b.WriteString(":") + fmt.Fprint(&b, v) + } + return b.String() +} + +func (t *node32) equals(u *node32) bool { + if t == u { + return true + } + it, iu := t.iterator(), u.iterator() + for !it.done() && !iu.done() { + nt := it.next() + nu := iu.next() + if nt == nu { + continue + } + if nt.key != nu.key { + return false + } + if nt.data != nu.data { + return false + } + } + return it.done() == iu.done() +} + +func (t *T) Equiv(u *T, eqv func(x, y interface{}) bool) bool { + if t == u { + return true + } + if t.Size() != u.Size() { + return false + } + return t.root.equiv(u.root, eqv) +} + +func (t *node32) equiv(u *node32, eqv func(x, y interface{}) bool) bool { + if t == u { + return true + } + it, iu := t.iterator(), u.iterator() + for !it.done() && !iu.done() { + nt := it.next() + nu := iu.next() + if nt == nu { + continue + } + if nt.key != nu.key { + return false + } + if !eqv(nt.data, nu.data) { + return false + } + } + return it.done() == iu.done() +} + +type iterator struct { + parents []*node32 +} + +type Iterator struct { + it iterator +} + +func (it *Iterator) Next() (int32, interface{}) { + x := it.it.next() + if x == nil { + return NOT_KEY32, nil + } + return x.key, x.data +} + +func (it *Iterator) Done() bool { + return len(it.it.parents) == 0 +} + +func (t *node32) iterator() iterator { + if t == nil { + return iterator{} + } + it := iterator{parents: make([]*node32, 0, int(t.height()))} + it.leftmost(t) + return it +} + +func (it *iterator) leftmost(t *node32) { + for t != nil { + it.parents = append(it.parents, t) + t = t.left + } +} + +func (it *iterator) done() bool { + return len(it.parents) == 0 +} + +func (it *iterator) next() *node32 { + l := len(it.parents) + if l == 0 { + return nil + } + x := it.parents[l-1] // return value + if x.right != nil { + it.leftmost(x.right) + return x + } + // discard visited top of parents + l-- + it.parents = it.parents[:l] + y := x // y is known visited/returned + for l > 0 && y == it.parents[l-1].right { + y = it.parents[l-1] + l-- + it.parents = it.parents[:l] + } + + return x +} + +// Min returns the minimum element of t. +// If t is empty, then (NOT_KEY32, nil) is returned. +func (t *T) Min() (k int32, d interface{}) { + return t.root.min().nilOrKeyAndData() +} + +// Max returns the maximum element of t. +// If t is empty, then (NOT_KEY32, nil) is returned. +func (t *T) Max() (k int32, d interface{}) { + return t.root.max().nilOrKeyAndData() +} + +// Glb returns the greatest-lower-bound-exclusive of x and the associated +// data. If x has no glb in the tree, then (NOT_KEY32, nil) is returned. +func (t *T) Glb(x int32) (k int32, d interface{}) { + return t.root.glb(x, false).nilOrKeyAndData() +} + +// GlbEq returns the greatest-lower-bound-inclusive of x and the associated +// data. If x has no glbEQ in the tree, then (NOT_KEY32, nil) is returned. +func (t *T) GlbEq(x int32) (k int32, d interface{}) { + return t.root.glb(x, true).nilOrKeyAndData() +} + +// Lub returns the least-upper-bound-exclusive of x and the associated +// data. If x has no lub in the tree, then (NOT_KEY32, nil) is returned. +func (t *T) Lub(x int32) (k int32, d interface{}) { + return t.root.lub(x, false).nilOrKeyAndData() +} + +// LubEq returns the least-upper-bound-inclusive of x and the associated +// data. If x has no lubEq in the tree, then (NOT_KEY32, nil) is returned. +func (t *T) LubEq(x int32) (k int32, d interface{}) { + return t.root.lub(x, true).nilOrKeyAndData() +} + +func (t *node32) isLeaf() bool { + return t.left == nil && t.right == nil && t.height_ == LEAF_HEIGHT +} + +func (t *node32) visitInOrder(f func(int32, interface{})) { + if t.left != nil { + t.left.visitInOrder(f) + } + f(t.key, t.data) + if t.right != nil { + t.right.visitInOrder(f) + } +} + +func (t *node32) find(key int32) *node32 { + for t != nil { + if key < t.key { + t = t.left + } else if key > t.key { + t = t.right + } else { + return t + } + } + return nil +} + +func (t *node32) min() *node32 { + if t == nil { + return t + } + for t.left != nil { + t = t.left + } + return t +} + +func (t *node32) max() *node32 { + if t == nil { + return t + } + for t.right != nil { + t = t.right + } + return t +} + +func (t *node32) glb(key int32, allow_eq bool) *node32 { + var best *node32 = nil + for t != nil { + if key <= t.key { + if allow_eq && key == t.key { + return t + } + // t is too big, glb is to left. + t = t.left + } else { + // t is a lower bound, record it and seek a better one. + best = t + t = t.right + } + } + return best +} + +func (t *node32) lub(key int32, allow_eq bool) *node32 { + var best *node32 = nil + for t != nil { + if key >= t.key { + if allow_eq && key == t.key { + return t + } + // t is too small, lub is to right. + t = t.right + } else { + // t is an upper bound, record it and seek a better one. + best = t + t = t.left + } + } + return best +} + +func (t *node32) aInsert(x int32) (newroot, newnode, oldnode *node32) { + // oldnode default of nil is good, others should be assigned. + if x == t.key { + oldnode = t + newt := *t + newnode = &newt + newroot = newnode + return + } + if x < t.key { + if t.left == nil { + t = t.copy() + n := makeNode(x) + t.left = n + newnode = n + newroot = t + t.height_ = 2 // was balanced w/ 0, sibling is height 0 or 1 + return + } + var new_l *node32 + new_l, newnode, oldnode = t.left.aInsert(x) + t = t.copy() + t.left = new_l + if new_l.height() > 1+t.right.height() { + newroot = t.aLeftIsHigh(newnode) + } else { + t.height_ = 1 + max(t.left.height(), t.right.height()) + newroot = t + } + } else { // x > t.key + if t.right == nil { + t = t.copy() + n := makeNode(x) + t.right = n + newnode = n + newroot = t + t.height_ = 2 // was balanced w/ 0, sibling is height 0 or 1 + return + } + var new_r *node32 + new_r, newnode, oldnode = t.right.aInsert(x) + t = t.copy() + t.right = new_r + if new_r.height() > 1+t.left.height() { + newroot = t.aRightIsHigh(newnode) + } else { + t.height_ = 1 + max(t.left.height(), t.right.height()) + newroot = t + } + } + return +} + +func (t *node32) aDelete(key int32) (deleted, newSubTree *node32) { + if t == nil { + return nil, nil + } + + if key < t.key { + oh := t.left.height() + d, tleft := t.left.aDelete(key) + if tleft == t.left { + return d, t + } + return d, t.copy().aRebalanceAfterLeftDeletion(oh, tleft) + } else if key > t.key { + oh := t.right.height() + d, tright := t.right.aDelete(key) + if tright == t.right { + return d, t + } + return d, t.copy().aRebalanceAfterRightDeletion(oh, tright) + } + + if t.height() == LEAF_HEIGHT { + return t, nil + } + + // Interior delete by removing left.Max or right.Min, + // then swapping contents + if t.left.height() > t.right.height() { + oh := t.left.height() + d, tleft := t.left.aDeleteMax() + r := t + t = t.copy() + t.data, t.key = d.data, d.key + return r, t.aRebalanceAfterLeftDeletion(oh, tleft) + } + + oh := t.right.height() + d, tright := t.right.aDeleteMin() + r := t + t = t.copy() + t.data, t.key = d.data, d.key + return r, t.aRebalanceAfterRightDeletion(oh, tright) +} + +func (t *node32) aDeleteMin() (deleted, newSubTree *node32) { + if t == nil { + return nil, nil + } + if t.left == nil { // leaf or left-most + return t, t.right + } + oh := t.left.height() + d, tleft := t.left.aDeleteMin() + if tleft == t.left { + return d, t + } + return d, t.copy().aRebalanceAfterLeftDeletion(oh, tleft) +} + +func (t *node32) aDeleteMax() (deleted, newSubTree *node32) { + if t == nil { + return nil, nil + } + + if t.right == nil { // leaf or right-most + return t, t.left + } + + oh := t.right.height() + d, tright := t.right.aDeleteMax() + if tright == t.right { + return d, t + } + return d, t.copy().aRebalanceAfterRightDeletion(oh, tright) +} + +func (t *node32) aRebalanceAfterLeftDeletion(oldLeftHeight int8, tleft *node32) *node32 { + t.left = tleft + + if oldLeftHeight == tleft.height() || oldLeftHeight == t.right.height() { + // this node is still balanced and its height is unchanged + return t + } + + if oldLeftHeight > t.right.height() { + // left was larger + t.height_-- + return t + } + + // left height fell by 1 and it was already less than right height + t.right = t.right.copy() + return t.aRightIsHigh(nil) +} + +func (t *node32) aRebalanceAfterRightDeletion(oldRightHeight int8, tright *node32) *node32 { + t.right = tright + + if oldRightHeight == tright.height() || oldRightHeight == t.left.height() { + // this node is still balanced and its height is unchanged + return t + } + + if oldRightHeight > t.left.height() { + // left was larger + t.height_-- + return t + } + + // right height fell by 1 and it was already less than left height + t.left = t.left.copy() + return t.aLeftIsHigh(nil) +} + +// aRightIsHigh does rotations necessary to fix a high right child +// assume that t and t.right are already fresh copies. +func (t *node32) aRightIsHigh(newnode *node32) *node32 { + right := t.right + if right.right.height() < right.left.height() { + // double rotation + if newnode != right.left { + right.left = right.left.copy() + } + t.right = right.leftToRoot() + } + t = t.rightToRoot() + return t +} + +// aLeftIsHigh does rotations necessary to fix a high left child +// assume that t and t.left are already fresh copies. +func (t *node32) aLeftIsHigh(newnode *node32) *node32 { + left := t.left + if left.left.height() < left.right.height() { + // double rotation + if newnode != left.right { + left.right = left.right.copy() + } + t.left = left.rightToRoot() + } + t = t.leftToRoot() + return t +} + +// rightToRoot does that rotation, modifying t and t.right in the process. +func (t *node32) rightToRoot() *node32 { + // this + // left right + // rl rr + // + // becomes + // + // right + // this rr + // left rl + // + right := t.right + rl := right.left + right.left = t + // parent's child ptr fixed in caller + t.right = rl + t.height_ = 1 + max(rl.height(), t.left.height()) + right.height_ = 1 + max(t.height(), right.right.height()) + return right +} + +// leftToRoot does that rotation, modifying t and t.left in the process. +func (t *node32) leftToRoot() *node32 { + // this + // left right + // ll lr + // + // becomes + // + // left + // ll this + // lr right + // + left := t.left + lr := left.right + left.right = t + // parent's child ptr fixed in caller + t.left = lr + t.height_ = 1 + max(lr.height(), t.right.height()) + left.height_ = 1 + max(t.height(), left.left.height()) + return left +} + +func max(a, b int8) int8 { + if a > b { + return a + } + return b +} + +func (t *node32) copy() *node32 { + u := *t + return &u +} diff --git a/src/cmd/compile/internal/abt/avlint32_test.go b/src/cmd/compile/internal/abt/avlint32_test.go new file mode 100644 index 0000000..7fa9ed4 --- /dev/null +++ b/src/cmd/compile/internal/abt/avlint32_test.go @@ -0,0 +1,700 @@ +// Copyright 2022 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package abt + +import ( + "fmt" + "strconv" + "testing" +) + +func makeTree(te *testing.T, x []int32, check bool) (t *T, k int, min, max int32) { + t = &T{} + k = 0 + min = int32(0x7fffffff) + max = int32(-0x80000000) + history := []*T{} + + for _, d := range x { + d = d + d // double everything for Glb/Lub testing. + + if check { + history = append(history, t.Copy()) + } + + t.Insert(d, stringer(fmt.Sprintf("%v", d))) + + k++ + if d < min { + min = d + } + if d > max { + max = d + } + + if !check { + continue + } + + for j, old := range history { + s, i := old.wellFormed() + if s != "" { + te.Errorf("Old tree consistency problem %v at k=%d, j=%d, old=\n%v, t=\n%v", s, k, j, old.DebugString(), t.DebugString()) + return + } + if i != j { + te.Errorf("Wrong tree size %v, expected %v for old %v", i, j, old.DebugString()) + } + } + s, i := t.wellFormed() + if s != "" { + te.Errorf("Tree consistency problem at %v", s) + return + } + if i != k { + te.Errorf("Wrong tree size %v, expected %v for %v", i, k, t.DebugString()) + return + } + if t.Size() != k { + te.Errorf("Wrong t.Size() %v, expected %v for %v", t.Size(), k, t.DebugString()) + return + } + } + return +} + +func applicInsert(te *testing.T, x []int32) { + makeTree(te, x, true) +} + +func applicFind(te *testing.T, x []int32) { + t, _, _, _ := makeTree(te, x, false) + + for _, d := range x { + d = d + d // double everything for Glb/Lub testing. + s := fmt.Sprintf("%v", d) + f := t.Find(d) + + // data + if s != fmt.Sprint(f) { + te.Errorf("s(%v) != f(%v)", s, f) + } + } +} + +func applicBounds(te *testing.T, x []int32) { + t, _, min, max := makeTree(te, x, false) + for _, d := range x { + d = d + d // double everything for Glb/Lub testing. + s := fmt.Sprintf("%v", d) + + kg, g := t.Glb(d + 1) + kge, ge := t.GlbEq(d) + kl, l := t.Lub(d - 1) + kle, le := t.LubEq(d) + + // keys + if d != kg { + te.Errorf("d(%v) != kg(%v)", d, kg) + } + if d != kl { + te.Errorf("d(%v) != kl(%v)", d, kl) + } + if d != kge { + te.Errorf("d(%v) != kge(%v)", d, kge) + } + if d != kle { + te.Errorf("d(%v) != kle(%v)", d, kle) + } + // data + if s != fmt.Sprint(g) { + te.Errorf("s(%v) != g(%v)", s, g) + } + if s != fmt.Sprint(l) { + te.Errorf("s(%v) != l(%v)", s, l) + } + if s != fmt.Sprint(ge) { + te.Errorf("s(%v) != ge(%v)", s, ge) + } + if s != fmt.Sprint(le) { + te.Errorf("s(%v) != le(%v)", s, le) + } + } + + for _, d := range x { + d = d + d // double everything for Glb/Lub testing. + s := fmt.Sprintf("%v", d) + kge, ge := t.GlbEq(d + 1) + kle, le := t.LubEq(d - 1) + if d != kge { + te.Errorf("d(%v) != kge(%v)", d, kge) + } + if d != kle { + te.Errorf("d(%v) != kle(%v)", d, kle) + } + if s != fmt.Sprint(ge) { + te.Errorf("s(%v) != ge(%v)", s, ge) + } + if s != fmt.Sprint(le) { + te.Errorf("s(%v) != le(%v)", s, le) + } + } + + kg, g := t.Glb(min) + kge, ge := t.GlbEq(min - 1) + kl, l := t.Lub(max) + kle, le := t.LubEq(max + 1) + fmin := t.Find(min - 1) + fmax := t.Find(max + 1) + + if kg != NOT_KEY32 || kge != NOT_KEY32 || kl != NOT_KEY32 || kle != NOT_KEY32 { + te.Errorf("Got non-error-key for missing query") + } + + if g != nil || ge != nil || l != nil || le != nil || fmin != nil || fmax != nil { + te.Errorf("Got non-error-data for missing query") + } +} + +func applicDeleteMin(te *testing.T, x []int32) { + t, _, _, _ := makeTree(te, x, false) + _, size := t.wellFormed() + history := []*T{} + for !t.IsEmpty() { + k, _ := t.Min() + history = append(history, t.Copy()) + kd, _ := t.DeleteMin() + if kd != k { + te.Errorf("Deleted minimum key %v not equal to minimum %v", kd, k) + } + for j, old := range history { + s, i := old.wellFormed() + if s != "" { + te.Errorf("Tree consistency problem %s at old after DeleteMin, old=\n%stree=\n%v", s, old.DebugString(), t.DebugString()) + return + } + if i != len(x)-j { + te.Errorf("Wrong old tree size %v, expected %v after DeleteMin, old=\n%vtree\n%v", i, len(x)-j, old.DebugString(), t.DebugString()) + return + } + } + size-- + s, i := t.wellFormed() + if s != "" { + te.Errorf("Tree consistency problem at %v after DeleteMin, tree=\n%v", s, t.DebugString()) + return + } + if i != size { + te.Errorf("Wrong tree size %v, expected %v after DeleteMin", i, size) + return + } + if t.Size() != size { + te.Errorf("Wrong t.Size() %v, expected %v for %v", t.Size(), i, t.DebugString()) + return + } + } +} + +func applicDeleteMax(te *testing.T, x []int32) { + t, _, _, _ := makeTree(te, x, false) + _, size := t.wellFormed() + history := []*T{} + + for !t.IsEmpty() { + k, _ := t.Max() + history = append(history, t.Copy()) + kd, _ := t.DeleteMax() + if kd != k { + te.Errorf("Deleted maximum key %v not equal to maximum %v", kd, k) + } + + for j, old := range history { + s, i := old.wellFormed() + if s != "" { + te.Errorf("Tree consistency problem %s at old after DeleteMin, old=\n%stree=\n%v", s, old.DebugString(), t.DebugString()) + return + } + if i != len(x)-j { + te.Errorf("Wrong old tree size %v, expected %v after DeleteMin, old=\n%vtree\n%v", i, len(x)-j, old.DebugString(), t.DebugString()) + return + } + } + + size-- + s, i := t.wellFormed() + if s != "" { + te.Errorf("Tree consistency problem at %v after DeleteMax, tree=\n%v", s, t.DebugString()) + return + } + if i != size { + te.Errorf("Wrong tree size %v, expected %v after DeleteMax", i, size) + return + } + if t.Size() != size { + te.Errorf("Wrong t.Size() %v, expected %v for %v", t.Size(), i, t.DebugString()) + return + } + } +} + +func applicDelete(te *testing.T, x []int32) { + t, _, _, _ := makeTree(te, x, false) + _, size := t.wellFormed() + history := []*T{} + + missing := t.Delete(11) + if missing != nil { + te.Errorf("Returned a value when there should have been none, %v", missing) + return + } + + s, i := t.wellFormed() + if s != "" { + te.Errorf("Tree consistency problem at %v after delete of missing value, tree=\n%v", s, t.DebugString()) + return + } + if size != i { + te.Errorf("Delete of missing data should not change tree size, expected %d, got %d", size, i) + return + } + + for _, d := range x { + d += d // double + vWant := fmt.Sprintf("%v", d) + history = append(history, t.Copy()) + v := t.Delete(d) + + for j, old := range history { + s, i := old.wellFormed() + if s != "" { + te.Errorf("Tree consistency problem %s at old after DeleteMin, old=\n%stree=\n%v", s, old.DebugString(), t.DebugString()) + return + } + if i != len(x)-j { + te.Errorf("Wrong old tree size %v, expected %v after DeleteMin, old=\n%vtree\n%v", i, len(x)-j, old.DebugString(), t.DebugString()) + return + } + } + + if v.(*sstring).s != vWant { + te.Errorf("Deleted %v expected %v but got %v", d, vWant, v) + return + } + size-- + s, i := t.wellFormed() + if s != "" { + te.Errorf("Tree consistency problem at %v after Delete %d, tree=\n%v", s, d, t.DebugString()) + return + } + if i != size { + te.Errorf("Wrong tree size %v, expected %v after Delete", i, size) + return + } + if t.Size() != size { + te.Errorf("Wrong t.Size() %v, expected %v for %v", t.Size(), i, t.DebugString()) + return + } + } + +} + +func applicIterator(te *testing.T, x []int32) { + t, _, _, _ := makeTree(te, x, false) + it := t.Iterator() + for !it.Done() { + k0, d0 := it.Next() + k1, d1 := t.DeleteMin() + if k0 != k1 || d0 != d1 { + te.Errorf("Iterator and deleteMin mismatch, k0, k1, d0, d1 = %v, %v, %v, %v", k0, k1, d0, d1) + return + } + } + if t.Size() != 0 { + te.Errorf("Iterator ended early, remaining tree = \n%s", t.DebugString()) + return + } +} + +func equiv(a, b interface{}) bool { + sa, sb := a.(*sstring), b.(*sstring) + return *sa == *sb +} + +func applicEquals(te *testing.T, x, y []int32) { + t, _, _, _ := makeTree(te, x, false) + u, _, _, _ := makeTree(te, y, false) + if !t.Equiv(t, equiv) { + te.Errorf("Equiv failure, t == t, =\n%v", t.DebugString()) + return + } + if !t.Equiv(t.Copy(), equiv) { + te.Errorf("Equiv failure, t == t.Copy(), =\n%v", t.DebugString()) + return + } + if !t.Equiv(u, equiv) { + te.Errorf("Equiv failure, t == u, =\n%v", t.DebugString()) + return + } + v := t.Copy() + + v.DeleteMax() + if t.Equiv(v, equiv) { + te.Errorf("!Equiv failure, t != v, =\n%v\nand%v\n", t.DebugString(), v.DebugString()) + return + } + + if v.Equiv(u, equiv) { + te.Errorf("!Equiv failure, v != u, =\n%v\nand%v\n", v.DebugString(), u.DebugString()) + return + } + +} + +func tree(x []int32) *T { + t := &T{} + for _, d := range x { + t.Insert(d, stringer(fmt.Sprintf("%v", d))) + } + return t +} + +func treePlus1(x []int32) *T { + t := &T{} + for _, d := range x { + t.Insert(d, stringer(fmt.Sprintf("%v", d+1))) + } + return t +} +func TestApplicInsert(t *testing.T) { + applicInsert(t, []int32{24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}) + applicInsert(t, []int32{1, 2, 3, 4}) + applicInsert(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9}) + applicInsert(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}) + applicInsert(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicInsert(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicInsert(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}) + applicInsert(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2}) +} + +func TestApplicFind(t *testing.T) { + applicFind(t, []int32{24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}) + applicFind(t, []int32{1, 2, 3, 4}) + applicFind(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9}) + applicFind(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}) + applicFind(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicFind(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicFind(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}) + applicFind(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2}) +} + +func TestBounds(t *testing.T) { + applicBounds(t, []int32{24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}) + applicBounds(t, []int32{1, 2, 3, 4}) + applicBounds(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9}) + applicBounds(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}) + applicBounds(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicBounds(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicBounds(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}) + applicBounds(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2}) +} +func TestDeleteMin(t *testing.T) { + applicDeleteMin(t, []int32{1, 2, 3, 4}) + applicDeleteMin(t, []int32{24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}) + applicDeleteMin(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9}) + applicDeleteMin(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}) + applicDeleteMin(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicDeleteMin(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicDeleteMin(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}) + applicDeleteMin(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2}) +} +func TestDeleteMax(t *testing.T) { + applicDeleteMax(t, []int32{24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}) + applicDeleteMax(t, []int32{1, 2, 3, 4}) + applicDeleteMax(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9}) + applicDeleteMax(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}) + applicDeleteMax(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicDeleteMax(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicDeleteMax(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}) + applicDeleteMax(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2}) +} +func TestDelete(t *testing.T) { + applicDelete(t, []int32{24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}) + applicDelete(t, []int32{1, 2, 3, 4}) + applicDelete(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9}) + applicDelete(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}) + applicDelete(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicDelete(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicDelete(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}) + applicDelete(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2}) +} +func TestIterator(t *testing.T) { + applicIterator(t, []int32{1, 2, 3, 4}) + applicIterator(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9}) + applicIterator(t, []int32{24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}) + applicIterator(t, []int32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}) + applicIterator(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicIterator(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicIterator(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}) + applicIterator(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2}) +} +func TestEquals(t *testing.T) { + applicEquals(t, []int32{1, 2, 3, 4}, []int32{4, 3, 2, 1}) + + applicEquals(t, []int32{24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}, + []int32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}) + applicEquals(t, []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, + []int32{25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}) + applicEquals(t, []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}, + []int32{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2}) +} + +func first(x, y interface{}) interface{} { + return x +} +func second(x, y interface{}) interface{} { + return y +} +func alwaysNil(x, y interface{}) interface{} { + return nil +} +func smaller(x, y interface{}) interface{} { + xi, _ := strconv.Atoi(fmt.Sprint(x)) + yi, _ := strconv.Atoi(fmt.Sprint(y)) + if xi < yi { + return x + } + return y +} +func assert(t *testing.T, expected, got *T, what string) { + s, _ := got.wellFormed() + if s != "" { + t.Errorf("Tree consistency problem %v for 'got' in assert for %s, tree=\n%v", s, what, got.DebugString()) + return + } + + if !expected.Equiv(got, equiv) { + t.Errorf("%s fail, expected\n%vgot\n%v\n", what, expected.DebugString(), got.DebugString()) + } +} + +func TestSetOps(t *testing.T) { + A := tree([]int32{1, 2, 3, 4}) + B := tree([]int32{3, 4, 5, 6, 7}) + + AIB := tree([]int32{3, 4}) + ADB := tree([]int32{1, 2}) + BDA := tree([]int32{5, 6, 7}) + AUB := tree([]int32{1, 2, 3, 4, 5, 6, 7}) + AXB := tree([]int32{1, 2, 5, 6, 7}) + + aib1 := A.Intersection(B, first) + assert(t, AIB, aib1, "aib1") + if A.Find(3) != aib1.Find(3) { + t.Errorf("Failed aliasing/reuse check, A/aib1") + } + aib2 := A.Intersection(B, second) + assert(t, AIB, aib2, "aib2") + if B.Find(3) != aib2.Find(3) { + t.Errorf("Failed aliasing/reuse check, B/aib2") + } + aib3 := B.Intersection(A, first) + assert(t, AIB, aib3, "aib3") + if A.Find(3) != aib3.Find(3) { + // A is smaller, intersection favors reuse from smaller when function is "first" + t.Errorf("Failed aliasing/reuse check, A/aib3") + } + aib4 := B.Intersection(A, second) + assert(t, AIB, aib4, "aib4") + if A.Find(3) != aib4.Find(3) { + t.Errorf("Failed aliasing/reuse check, A/aib4") + } + + aub1 := A.Union(B, first) + assert(t, AUB, aub1, "aub1") + if B.Find(3) != aub1.Find(3) { + // B is larger, union favors reuse from larger when function is "first" + t.Errorf("Failed aliasing/reuse check, A/aub1") + } + aub2 := A.Union(B, second) + assert(t, AUB, aub2, "aub2") + if B.Find(3) != aub2.Find(3) { + t.Errorf("Failed aliasing/reuse check, B/aub2") + } + aub3 := B.Union(A, first) + assert(t, AUB, aub3, "aub3") + if B.Find(3) != aub3.Find(3) { + t.Errorf("Failed aliasing/reuse check, B/aub3") + } + aub4 := B.Union(A, second) + assert(t, AUB, aub4, "aub4") + if A.Find(3) != aub4.Find(3) { + t.Errorf("Failed aliasing/reuse check, A/aub4") + } + + axb1 := A.Union(B, alwaysNil) + assert(t, AXB, axb1, "axb1") + axb2 := B.Union(A, alwaysNil) + assert(t, AXB, axb2, "axb2") + + adb := A.Difference(B, alwaysNil) + assert(t, ADB, adb, "adb") + bda := B.Difference(A, nil) + assert(t, BDA, bda, "bda") + + Ap1 := treePlus1([]int32{1, 2, 3, 4}) + + ada1_1 := A.Difference(Ap1, smaller) + assert(t, A, ada1_1, "ada1_1") + ada1_2 := Ap1.Difference(A, smaller) + assert(t, A, ada1_2, "ada1_2") + +} + +type sstring struct { + s string +} + +func (s *sstring) String() string { + return s.s +} + +func stringer(s string) interface{} { + return &sstring{s} +} + +// wellFormed ensures that a red-black tree meets +// all of its invariants and returns a string identifying +// the first problem encountered. If there is no problem +// then the returned string is empty. The size is also +// returned to allow comparison of calculated tree size +// with expected. +func (t *T) wellFormed() (s string, i int) { + if t.root == nil { + s = "" + i = 0 + return + } + return t.root.wellFormedSubtree(nil, -0x80000000, 0x7fffffff) +} + +// wellFormedSubtree ensures that a red-black subtree meets +// all of its invariants and returns a string identifying +// the first problem encountered. If there is no problem +// then the returned string is empty. The size is also +// returned to allow comparison of calculated tree size +// with expected. +func (t *node32) wellFormedSubtree(parent *node32, keyMin, keyMax int32) (s string, i int) { + i = -1 // initialize to a failing value + s = "" // s is the reason for failure; empty means okay. + + if keyMin >= t.key { + s = " min >= t.key" + return + } + + if keyMax <= t.key { + s = " max <= t.key" + return + } + + l := t.left + r := t.right + + lh := l.height() + rh := r.height() + mh := max(lh, rh) + th := t.height() + dh := lh - rh + if dh < 0 { + dh = -dh + } + if dh > 1 { + s = fmt.Sprintf(" dh > 1, t=%d", t.key) + return + } + + if l == nil && r == nil { + if th != LEAF_HEIGHT { + s = " leaf height wrong" + return + } + } + + if th != mh+1 { + s = " th != mh + 1" + return + } + + if l != nil { + if th <= lh { + s = " t.height <= l.height" + } else if th > 2+lh { + s = " t.height > 2+l.height" + } else if t.key <= l.key { + s = " t.key <= l.key" + } + if s != "" { + return + } + + } + + if r != nil { + if th <= rh { + s = " t.height <= r.height" + } else if th > 2+rh { + s = " t.height > 2+r.height" + } else if t.key >= r.key { + s = " t.key >= r.key" + } + if s != "" { + return + } + } + + ii := 1 + if l != nil { + res, il := l.wellFormedSubtree(t, keyMin, t.key) + if res != "" { + s = ".L" + res + return + } + ii += il + } + if r != nil { + res, ir := r.wellFormedSubtree(t, t.key, keyMax) + if res != "" { + s = ".R" + res + return + } + ii += ir + } + i = ii + return +} + +func (t *T) DebugString() string { + if t.root == nil { + return "" + } + return t.root.DebugString(0) +} + +// DebugString prints the tree with nested information +// to allow an eyeball check on the tree balance. +func (t *node32) DebugString(indent int) string { + s := "" + if t.left != nil { + s = s + t.left.DebugString(indent+1) + } + for i := 0; i < indent; i++ { + s = s + " " + } + s = s + fmt.Sprintf("%v=%v:%d\n", t.key, t.data, t.height_) + if t.right != nil { + s = s + t.right.DebugString(indent+1) + } + return s +} -- cgit v1.2.3