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-rw-r--r--pkg/segment/set.go400
1 files changed, 395 insertions, 5 deletions
diff --git a/pkg/segment/set.go b/pkg/segment/set.go
index 03e4f258f..1a17ad9cb 100644
--- a/pkg/segment/set.go
+++ b/pkg/segment/set.go
@@ -36,6 +36,34 @@ type Range interface{}
// Value is a required type parameter.
type Value interface{}
+// trackGaps is an optional parameter.
+//
+// If trackGaps is 1, the Set will track maximum gap size recursively,
+// enabling the GapIterator.{Prev,Next}LargeEnoughGap functions. In this
+// case, Key must be an unsigned integer.
+//
+// trackGaps must be 0 or 1.
+const trackGaps = 0
+
+var _ = uint8(trackGaps << 7) // Will fail if not zero or one.
+
+// dynamicGap is a type that disappears if trackGaps is 0.
+type dynamicGap [trackGaps]Key
+
+// Get returns the value of the gap.
+//
+// Precondition: trackGaps must be non-zero.
+func (d *dynamicGap) Get() Key {
+ return d[:][0]
+}
+
+// Set sets the value of the gap.
+//
+// Precondition: trackGaps must be non-zero.
+func (d *dynamicGap) Set(v Key) {
+ d[:][0] = v
+}
+
// Functions is a required type parameter that must be a struct implementing
// the methods defined by Functions.
type Functions interface {
@@ -327,8 +355,12 @@ func (s *Set) Insert(gap GapIterator, r Range, val Value) Iterator {
}
if prev.Ok() && prev.End() == r.Start {
if mval, ok := (Functions{}).Merge(prev.Range(), prev.Value(), r, val); ok {
+ shrinkMaxGap := trackGaps != 0 && gap.Range().Length() == gap.node.maxGap.Get()
prev.SetEndUnchecked(r.End)
prev.SetValue(mval)
+ if shrinkMaxGap {
+ gap.node.updateMaxGapLeaf()
+ }
if next.Ok() && next.Start() == r.End {
val = mval
if mval, ok := (Functions{}).Merge(prev.Range(), val, next.Range(), next.Value()); ok {
@@ -342,11 +374,16 @@ func (s *Set) Insert(gap GapIterator, r Range, val Value) Iterator {
}
if next.Ok() && next.Start() == r.End {
if mval, ok := (Functions{}).Merge(r, val, next.Range(), next.Value()); ok {
+ shrinkMaxGap := trackGaps != 0 && gap.Range().Length() == gap.node.maxGap.Get()
next.SetStartUnchecked(r.Start)
next.SetValue(mval)
+ if shrinkMaxGap {
+ gap.node.updateMaxGapLeaf()
+ }
return next
}
}
+ // InsertWithoutMergingUnchecked will maintain maxGap if necessary.
return s.InsertWithoutMergingUnchecked(gap, r, val)
}
@@ -373,11 +410,15 @@ func (s *Set) InsertWithoutMerging(gap GapIterator, r Range, val Value) Iterator
// Preconditions: r.Start >= gap.Start(); r.End <= gap.End().
func (s *Set) InsertWithoutMergingUnchecked(gap GapIterator, r Range, val Value) Iterator {
gap = gap.node.rebalanceBeforeInsert(gap)
+ splitMaxGap := trackGaps != 0 && (gap.node.nrSegments == 0 || gap.Range().Length() == gap.node.maxGap.Get())
copy(gap.node.keys[gap.index+1:], gap.node.keys[gap.index:gap.node.nrSegments])
copy(gap.node.values[gap.index+1:], gap.node.values[gap.index:gap.node.nrSegments])
gap.node.keys[gap.index] = r
gap.node.values[gap.index] = val
gap.node.nrSegments++
+ if splitMaxGap {
+ gap.node.updateMaxGapLeaf()
+ }
return Iterator{gap.node, gap.index}
}
@@ -399,12 +440,23 @@ func (s *Set) Remove(seg Iterator) GapIterator {
// overlap.
seg.SetRangeUnchecked(victim.Range())
seg.SetValue(victim.Value())
+ // Need to update the nextAdjacentNode's maxGap because the gap in between
+ // must have been modified by updating seg.Range() to victim.Range().
+ // seg.NextSegment() must exist since the last segment can't be in a
+ // non-leaf node.
+ nextAdjacentNode := seg.NextSegment().node
+ if trackGaps != 0 {
+ nextAdjacentNode.updateMaxGapLeaf()
+ }
return s.Remove(victim).NextGap()
}
copy(seg.node.keys[seg.index:], seg.node.keys[seg.index+1:seg.node.nrSegments])
copy(seg.node.values[seg.index:], seg.node.values[seg.index+1:seg.node.nrSegments])
Functions{}.ClearValue(&seg.node.values[seg.node.nrSegments-1])
seg.node.nrSegments--
+ if trackGaps != 0 {
+ seg.node.updateMaxGapLeaf()
+ }
return seg.node.rebalanceAfterRemove(GapIterator{seg.node, seg.index})
}
@@ -455,6 +507,7 @@ func (s *Set) MergeUnchecked(first, second Iterator) Iterator {
// overlaps second.
first.SetEndUnchecked(second.End())
first.SetValue(mval)
+ // Remove will handle the maxGap update if necessary.
return s.Remove(second).PrevSegment()
}
}
@@ -631,6 +684,12 @@ type node struct {
// than "isLeaf" because false must be the correct value for an empty root.
hasChildren bool
+ // The longest gap within this node. If the node is a leaf, it's simply the
+ // maximum gap among all the (nrSegments+1) gaps formed by its nrSegments keys
+ // including the 0th and nrSegments-th gap possibly shared with its upper-level
+ // nodes; if it's a non-leaf node, it's the max of all children's maxGap.
+ maxGap dynamicGap
+
// Nodes store keys and values in separate arrays to maximize locality in
// the common case (scanning keys for lookup).
keys [maxDegree - 1]Range
@@ -676,12 +735,12 @@ func (n *node) nextSibling() *node {
// required for insertion, and returns an updated iterator to the position
// represented by gap.
func (n *node) rebalanceBeforeInsert(gap GapIterator) GapIterator {
- if n.parent != nil {
- gap = n.parent.rebalanceBeforeInsert(gap)
- }
if n.nrSegments < maxDegree-1 {
return gap
}
+ if n.parent != nil {
+ gap = n.parent.rebalanceBeforeInsert(gap)
+ }
if n.parent == nil {
// n is root. Move all segments before and after n's median segment
// into new child nodes adjacent to the median segment, which is now
@@ -719,6 +778,13 @@ func (n *node) rebalanceBeforeInsert(gap GapIterator) GapIterator {
n.hasChildren = true
n.children[0] = left
n.children[1] = right
+ // In this case, n's maxGap won't violated as it's still the root,
+ // but the left and right children should be updated locally as they
+ // are newly split from n.
+ if trackGaps != 0 {
+ left.updateMaxGapLocal()
+ right.updateMaxGapLocal()
+ }
if gap.node != n {
return gap
}
@@ -758,6 +824,12 @@ func (n *node) rebalanceBeforeInsert(gap GapIterator) GapIterator {
}
}
n.nrSegments = minDegree - 1
+ // MaxGap of n's parent is not violated because the segments within is not changed.
+ // n and its sibling's maxGap need to be updated locally as they are two new nodes split from old n.
+ if trackGaps != 0 {
+ n.updateMaxGapLocal()
+ sibling.updateMaxGapLocal()
+ }
// gap.node can't be n.parent because gaps are always in leaf nodes.
if gap.node != n {
return gap
@@ -821,6 +893,12 @@ func (n *node) rebalanceAfterRemove(gap GapIterator) GapIterator {
}
n.nrSegments++
sibling.nrSegments--
+ // n's parent's maxGap does not need to be updated as its content is unmodified.
+ // n and its sibling must be updated with (new) maxGap because of the shift of keys.
+ if trackGaps != 0 {
+ n.updateMaxGapLocal()
+ sibling.updateMaxGapLocal()
+ }
if gap.node == sibling && gap.index == sibling.nrSegments {
return GapIterator{n, 0}
}
@@ -849,6 +927,12 @@ func (n *node) rebalanceAfterRemove(gap GapIterator) GapIterator {
}
n.nrSegments++
sibling.nrSegments--
+ // n's parent's maxGap does not need to be updated as its content is unmodified.
+ // n and its sibling must be updated with (new) maxGap because of the shift of keys.
+ if trackGaps != 0 {
+ n.updateMaxGapLocal()
+ sibling.updateMaxGapLocal()
+ }
if gap.node == sibling {
if gap.index == 0 {
return GapIterator{n, n.nrSegments}
@@ -886,6 +970,7 @@ func (n *node) rebalanceAfterRemove(gap GapIterator) GapIterator {
p.children[0] = nil
p.children[1] = nil
}
+ // No need to update maxGap of p as its content is not changed.
if gap.node == left {
return GapIterator{p, gap.index}
}
@@ -932,11 +1017,152 @@ func (n *node) rebalanceAfterRemove(gap GapIterator) GapIterator {
}
p.children[p.nrSegments] = nil
p.nrSegments--
+ // Update maxGap of left locally, no need to change p and right because
+ // p's contents is not changed and right is already invalid.
+ if trackGaps != 0 {
+ left.updateMaxGapLocal()
+ }
// This process robs p of one segment, so recurse into rebalancing p.
n = p
}
}
+// updateMaxGapLeaf updates maxGap bottom-up from the calling leaf until no
+// necessary update.
+//
+// Preconditions: n must be a leaf node, trackGaps must be 1.
+func (n *node) updateMaxGapLeaf() {
+ if n.hasChildren {
+ panic(fmt.Sprintf("updateMaxGapLeaf should always be called on leaf node: %v", n))
+ }
+ max := n.calculateMaxGapLeaf()
+ if max == n.maxGap.Get() {
+ // If new max equals the old maxGap, no update is needed.
+ return
+ }
+ oldMax := n.maxGap.Get()
+ n.maxGap.Set(max)
+ if max > oldMax {
+ // Grow ancestor maxGaps.
+ for p := n.parent; p != nil; p = p.parent {
+ if p.maxGap.Get() >= max {
+ // p and its ancestors already contain an equal or larger gap.
+ break
+ }
+ // Only if new maxGap is larger than parent's
+ // old maxGap, propagate this update to parent.
+ p.maxGap.Set(max)
+ }
+ return
+ }
+ // Shrink ancestor maxGaps.
+ for p := n.parent; p != nil; p = p.parent {
+ if p.maxGap.Get() > oldMax {
+ // p and its ancestors still contain a larger gap.
+ break
+ }
+ // If new max is smaller than the old maxGap, and this gap used
+ // to be the maxGap of its parent, iterate parent's children
+ // and calculate parent's new maxGap.(It's probable that parent
+ // has two children with the old maxGap, but we need to check it anyway.)
+ parentNewMax := p.calculateMaxGapInternal()
+ if p.maxGap.Get() == parentNewMax {
+ // p and its ancestors still contain a gap of at least equal size.
+ break
+ }
+ // If p's new maxGap differs from the old one, propagate this update.
+ p.maxGap.Set(parentNewMax)
+ }
+}
+
+// updateMaxGapLocal updates maxGap of the calling node solely with no
+// propagation to ancestor nodes.
+//
+// Precondition: trackGaps must be 1.
+func (n *node) updateMaxGapLocal() {
+ if !n.hasChildren {
+ // Leaf node iterates its gaps.
+ n.maxGap.Set(n.calculateMaxGapLeaf())
+ } else {
+ // Non-leaf node iterates its children.
+ n.maxGap.Set(n.calculateMaxGapInternal())
+ }
+}
+
+// calculateMaxGapLeaf iterates the gaps within a leaf node and calculate the
+// max.
+//
+// Preconditions: n must be a leaf node.
+func (n *node) calculateMaxGapLeaf() Key {
+ max := GapIterator{n, 0}.Range().Length()
+ for i := 1; i <= n.nrSegments; i++ {
+ if current := (GapIterator{n, i}).Range().Length(); current > max {
+ max = current
+ }
+ }
+ return max
+}
+
+// calculateMaxGapInternal iterates children's maxGap within an internal node n
+// and calculate the max.
+//
+// Preconditions: n must be a non-leaf node.
+func (n *node) calculateMaxGapInternal() Key {
+ max := n.children[0].maxGap.Get()
+ for i := 1; i <= n.nrSegments; i++ {
+ if current := n.children[i].maxGap.Get(); current > max {
+ max = current
+ }
+ }
+ return max
+}
+
+// searchFirstLargeEnoughGap returns the first gap having at least minSize length
+// in the subtree rooted by n. If not found, return a terminal gap iterator.
+func (n *node) searchFirstLargeEnoughGap(minSize Key) GapIterator {
+ if n.maxGap.Get() < minSize {
+ return GapIterator{}
+ }
+ if n.hasChildren {
+ for i := 0; i <= n.nrSegments; i++ {
+ if largeEnoughGap := n.children[i].searchFirstLargeEnoughGap(minSize); largeEnoughGap.Ok() {
+ return largeEnoughGap
+ }
+ }
+ } else {
+ for i := 0; i <= n.nrSegments; i++ {
+ currentGap := GapIterator{n, i}
+ if currentGap.Range().Length() >= minSize {
+ return currentGap
+ }
+ }
+ }
+ panic(fmt.Sprintf("invalid maxGap in %v", n))
+}
+
+// searchLastLargeEnoughGap returns the last gap having at least minSize length
+// in the subtree rooted by n. If not found, return a terminal gap iterator.
+func (n *node) searchLastLargeEnoughGap(minSize Key) GapIterator {
+ if n.maxGap.Get() < minSize {
+ return GapIterator{}
+ }
+ if n.hasChildren {
+ for i := n.nrSegments; i >= 0; i-- {
+ if largeEnoughGap := n.children[i].searchLastLargeEnoughGap(minSize); largeEnoughGap.Ok() {
+ return largeEnoughGap
+ }
+ }
+ } else {
+ for i := n.nrSegments; i >= 0; i-- {
+ currentGap := GapIterator{n, i}
+ if currentGap.Range().Length() >= minSize {
+ return currentGap
+ }
+ }
+ }
+ panic(fmt.Sprintf("invalid maxGap in %v", n))
+}
+
// A Iterator is conceptually one of:
//
// - A pointer to a segment in a set; or
@@ -1243,6 +1469,122 @@ func (gap GapIterator) NextGap() GapIterator {
return seg.NextGap()
}
+// NextLargeEnoughGap returns the iterated gap's first next gap with larger
+// length than minSize. If not found, return a terminal gap iterator (does NOT
+// include this gap itself).
+//
+// Precondition: trackGaps must be 1.
+func (gap GapIterator) NextLargeEnoughGap(minSize Key) GapIterator {
+ if trackGaps != 1 {
+ panic("set is not tracking gaps")
+ }
+ if gap.node != nil && gap.node.hasChildren && gap.index == gap.node.nrSegments {
+ // If gap is the trailing gap of an non-leaf node,
+ // translate it to the equivalent gap on leaf level.
+ gap.node = gap.NextSegment().node
+ gap.index = 0
+ return gap.nextLargeEnoughGapHelper(minSize)
+ }
+ return gap.nextLargeEnoughGapHelper(minSize)
+}
+
+// nextLargeEnoughGapHelper is the helper function used by NextLargeEnoughGap
+// to do the real recursions.
+//
+// Preconditions: gap is NOT the trailing gap of a non-leaf node.
+func (gap GapIterator) nextLargeEnoughGapHelper(minSize Key) GapIterator {
+ // Crawl up the tree if no large enough gap in current node or the
+ // current gap is the trailing one on leaf level.
+ for gap.node != nil &&
+ (gap.node.maxGap.Get() < minSize || (!gap.node.hasChildren && gap.index == gap.node.nrSegments)) {
+ gap.node, gap.index = gap.node.parent, gap.node.parentIndex
+ }
+ // If no large enough gap throughout the whole set, return a terminal
+ // gap iterator.
+ if gap.node == nil {
+ return GapIterator{}
+ }
+ // Iterate subsequent gaps.
+ gap.index++
+ for gap.index <= gap.node.nrSegments {
+ if gap.node.hasChildren {
+ if largeEnoughGap := gap.node.children[gap.index].searchFirstLargeEnoughGap(minSize); largeEnoughGap.Ok() {
+ return largeEnoughGap
+ }
+ } else {
+ if gap.Range().Length() >= minSize {
+ return gap
+ }
+ }
+ gap.index++
+ }
+ gap.node, gap.index = gap.node.parent, gap.node.parentIndex
+ if gap.node != nil && gap.index == gap.node.nrSegments {
+ // If gap is the trailing gap of a non-leaf node, crawl up to
+ // parent again and do recursion.
+ gap.node, gap.index = gap.node.parent, gap.node.parentIndex
+ }
+ return gap.nextLargeEnoughGapHelper(minSize)
+}
+
+// PrevLargeEnoughGap returns the iterated gap's first prev gap with larger or
+// equal length than minSize. If not found, return a terminal gap iterator
+// (does NOT include this gap itself).
+//
+// Precondition: trackGaps must be 1.
+func (gap GapIterator) PrevLargeEnoughGap(minSize Key) GapIterator {
+ if trackGaps != 1 {
+ panic("set is not tracking gaps")
+ }
+ if gap.node != nil && gap.node.hasChildren && gap.index == 0 {
+ // If gap is the first gap of an non-leaf node,
+ // translate it to the equivalent gap on leaf level.
+ gap.node = gap.PrevSegment().node
+ gap.index = gap.node.nrSegments
+ return gap.prevLargeEnoughGapHelper(minSize)
+ }
+ return gap.prevLargeEnoughGapHelper(minSize)
+}
+
+// prevLargeEnoughGapHelper is the helper function used by PrevLargeEnoughGap
+// to do the real recursions.
+//
+// Preconditions: gap is NOT the first gap of a non-leaf node.
+func (gap GapIterator) prevLargeEnoughGapHelper(minSize Key) GapIterator {
+ // Crawl up the tree if no large enough gap in current node or the
+ // current gap is the first one on leaf level.
+ for gap.node != nil &&
+ (gap.node.maxGap.Get() < minSize || (!gap.node.hasChildren && gap.index == 0)) {
+ gap.node, gap.index = gap.node.parent, gap.node.parentIndex
+ }
+ // If no large enough gap throughout the whole set, return a terminal
+ // gap iterator.
+ if gap.node == nil {
+ return GapIterator{}
+ }
+ // Iterate previous gaps.
+ gap.index--
+ for gap.index >= 0 {
+ if gap.node.hasChildren {
+ if largeEnoughGap := gap.node.children[gap.index].searchLastLargeEnoughGap(minSize); largeEnoughGap.Ok() {
+ return largeEnoughGap
+ }
+ } else {
+ if gap.Range().Length() >= minSize {
+ return gap
+ }
+ }
+ gap.index--
+ }
+ gap.node, gap.index = gap.node.parent, gap.node.parentIndex
+ if gap.node != nil && gap.index == 0 {
+ // If gap is the first gap of a non-leaf node, crawl up to
+ // parent again and do recursion.
+ gap.node, gap.index = gap.node.parent, gap.node.parentIndex
+ }
+ return gap.prevLargeEnoughGapHelper(minSize)
+}
+
// segmentBeforePosition returns the predecessor segment of the position given
// by n.children[i], which may or may not contain a child. If no such segment
// exists, segmentBeforePosition returns a terminal iterator.
@@ -1271,7 +1613,7 @@ func segmentAfterPosition(n *node, i int) Iterator {
func zeroValueSlice(slice []Value) {
// TODO(jamieliu): check if Go is actually smart enough to optimize a
- // ClearValue that assigns nil to a memset here
+ // ClearValue that assigns nil to a memset here.
for i := range slice {
Functions{}.ClearValue(&slice[i])
}
@@ -1310,7 +1652,15 @@ func (n *node) writeDebugString(buf *bytes.Buffer, prefix string) {
child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, i))
}
buf.WriteString(prefix)
- buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i]))
+ if n.hasChildren {
+ if trackGaps != 0 {
+ buf.WriteString(fmt.Sprintf("- % 3d: %v => %v, maxGap: %d\n", i, n.keys[i], n.values[i], n.maxGap.Get()))
+ } else {
+ buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i]))
+ }
+ } else {
+ buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i]))
+ }
}
if child := n.children[n.nrSegments]; child != nil {
child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, n.nrSegments))
@@ -1362,3 +1712,43 @@ func (s *Set) ImportSortedSlices(sds *SegmentDataSlices) error {
}
return nil
}
+
+// segmentTestCheck returns an error if s is incorrectly sorted, does not
+// contain exactly expectedSegments segments, or contains a segment which
+// fails the passed check.
+//
+// This should be used only for testing, and has been added to this package for
+// templating convenience.
+func (s *Set) segmentTestCheck(expectedSegments int, segFunc func(int, Range, Value) error) error {
+ havePrev := false
+ prev := Key(0)
+ nrSegments := 0
+ for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() {
+ next := seg.Start()
+ if havePrev && prev >= next {
+ return fmt.Errorf("incorrect order: key %d (segment %d) >= key %d (segment %d)", prev, nrSegments-1, next, nrSegments)
+ }
+ if segFunc != nil {
+ if err := segFunc(nrSegments, seg.Range(), seg.Value()); err != nil {
+ return err
+ }
+ }
+ prev = next
+ havePrev = true
+ nrSegments++
+ }
+ if nrSegments != expectedSegments {
+ return fmt.Errorf("incorrect number of segments: got %d, wanted %d", nrSegments, expectedSegments)
+ }
+ return nil
+}
+
+// countSegments counts the number of segments in the set.
+//
+// Similar to Check, this should only be used for testing.
+func (s *Set) countSegments() (segments int) {
+ for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() {
+ segments++
+ }
+ return segments
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-05 16:32:34 +0000