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// Copyright 2014 Google Inc.
//
// 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 btree implements in-memory B-Trees of arbitrary degree.
//
// btree implements an in-memory B-Tree for use as an ordered data structure.
// It is not meant for persistent storage solutions.
//
// It has a flatter structure than an equivalent red-black or other binary tree,
// which in some cases yields better memory usage and/or performance.
// See some discussion on the matter here:
// http://google-opensource.blogspot.com/2013/01/c-containers-that-save-memory-and-time.html
// Note, though, that this project is in no way related to the C++ B-Tree
// implementation written about there.
//
// Within this tree, each node contains a slice of items and a (possibly nil)
// slice of children. For basic numeric values or raw structs, this can cause
// efficiency differences when compared to equivalent C++ template code that
// stores values in arrays within the node:
// * Due to the overhead of storing values as interfaces (each
// value needs to be stored as the value itself, then 2 words for the
// interface pointing to that value and its type), resulting in higher
// memory use.
// * Since interfaces can point to values anywhere in memory, values are
// most likely not stored in contiguous blocks, resulting in a higher
// number of cache misses.
// These issues don't tend to matter, though, when working with strings or other
// heap-allocated structures, since C++-equivalent structures also must store
// pointers and also distribute their values across the heap.
//
// This implementation is designed to be a drop-in replacement to gollrb.LLRB
// trees, (http://github.com/petar/gollrb), an excellent and probably the most
// widely used ordered tree implementation in the Go ecosystem currently.
// Its functions, therefore, exactly mirror those of
// llrb.LLRB where possible. Unlike gollrb, though, we currently don't
// support storing multiple equivalent values.
package btree
import (
"fmt"
"io"
"sort"
"strings"
"sync"
)
// Item represents a single object in the tree.
type Item interface {
// Less tests whether the current item is less than the given argument.
//
// This must provide a strict weak ordering.
// If !a.Less(b) && !b.Less(a), we treat this to mean a == b (i.e. we can only
// hold one of either a or b in the tree).
Less(than Item) bool
}
const (
DefaultFreeListSize = 32
)
var (
nilItems = make(items, 16)
nilChildren = make(children, 16)
)
// FreeList represents a free list of btree nodes. By default each
// BTree has its own FreeList, but multiple BTrees can share the same
// FreeList.
// Two Btrees using the same freelist are safe for concurrent write access.
type FreeList struct {
mu sync.Mutex
freelist []*node
}
// NewFreeList creates a new free list.
// size is the maximum size of the returned free list.
func NewFreeList(size int) *FreeList {
return &FreeList{freelist: make([]*node, 0, size)}
}
func (f *FreeList) newNode() (n *node) {
f.mu.Lock()
index := len(f.freelist) - 1
if index < 0 {
f.mu.Unlock()
return new(node)
}
n = f.freelist[index]
f.freelist[index] = nil
f.freelist = f.freelist[:index]
f.mu.Unlock()
return
}
// freeNode adds the given node to the list, returning true if it was added
// and false if it was discarded.
func (f *FreeList) freeNode(n *node) (out bool) {
f.mu.Lock()
if len(f.freelist) < cap(f.freelist) {
f.freelist = append(f.freelist, n)
out = true
}
f.mu.Unlock()
return
}
// ItemIterator allows callers of Ascend* to iterate in-order over portions of
// the tree. When this function returns false, iteration will stop and the
// associated Ascend* function will immediately return.
type ItemIterator func(i Item) bool
// New creates a new B-Tree with the given degree.
//
// New(2), for example, will create a 2-3-4 tree (each node contains 1-3 items
// and 2-4 children).
func New(degree int) *BTree {
return NewWithFreeList(degree, NewFreeList(DefaultFreeListSize))
}
// NewWithFreeList creates a new B-Tree that uses the given node free list.
func NewWithFreeList(degree int, f *FreeList) *BTree {
if degree <= 1 {
panic("bad degree")
}
return &BTree{
degree: degree,
cow: &copyOnWriteContext{freelist: f},
}
}
// items stores items in a node.
type items []Item
// insertAt inserts a value into the given index, pushing all subsequent values
// forward.
func (s *items) insertAt(index int, item Item) {
*s = append(*s, nil)
if index < len(*s) {
copy((*s)[index+1:], (*s)[index:])
}
(*s)[index] = item
}
// removeAt removes a value at a given index, pulling all subsequent values
// back.
func (s *items) removeAt(index int) Item {
item := (*s)[index]
copy((*s)[index:], (*s)[index+1:])
(*s)[len(*s)-1] = nil
*s = (*s)[:len(*s)-1]
return item
}
// pop removes and returns the last element in the list.
func (s *items) pop() (out Item) {
index := len(*s) - 1
out = (*s)[index]
(*s)[index] = nil
*s = (*s)[:index]
return
}
// truncate truncates this instance at index so that it contains only the
// first index items. index must be less than or equal to length.
func (s *items) truncate(index int) {
var toClear items
*s, toClear = (*s)[:index], (*s)[index:]
for len(toClear) > 0 {
toClear = toClear[copy(toClear, nilItems):]
}
}
// find returns the index where the given item should be inserted into this
// list. 'found' is true if the item already exists in the list at the given
// index.
func (s items) find(item Item) (index int, found bool) {
i := sort.Search(len(s), func(i int) bool {
return item.Less(s[i])
})
if i > 0 && !s[i-1].Less(item) {
return i - 1, true
}
return i, false
}
// children stores child nodes in a node.
type children []*node
// insertAt inserts a value into the given index, pushing all subsequent values
// forward.
func (s *children) insertAt(index int, n *node) {
*s = append(*s, nil)
if index < len(*s) {
copy((*s)[index+1:], (*s)[index:])
}
(*s)[index] = n
}
// removeAt removes a value at a given index, pulling all subsequent values
// back.
func (s *children) removeAt(index int) *node {
n := (*s)[index]
copy((*s)[index:], (*s)[index+1:])
(*s)[len(*s)-1] = nil
*s = (*s)[:len(*s)-1]
return n
}
// pop removes and returns the last element in the list.
func (s *children) pop() (out *node) {
index := len(*s) - 1
out = (*s)[index]
(*s)[index] = nil
*s = (*s)[:index]
return
}
// truncate truncates this instance at index so that it contains only the
// first index children. index must be less than or equal to length.
func (s *children) truncate(index int) {
var toClear children
*s, toClear = (*s)[:index], (*s)[index:]
for len(toClear) > 0 {
toClear = toClear[copy(toClear, nilChildren):]
}
}
// node is an internal node in a tree.
//
// It must at all times maintain the invariant that either
// * len(children) == 0, len(items) unconstrained
// * len(children) == len(items) + 1
type node struct {
items items
children children
cow *copyOnWriteContext
}
func (n *node) mutableFor(cow *copyOnWriteContext) *node {
if n.cow == cow {
return n
}
out := cow.newNode()
if cap(out.items) >= len(n.items) {
out.items = out.items[:len(n.items)]
} else {
out.items = make(items, len(n.items), cap(n.items))
}
copy(out.items, n.items)
// Copy children
if cap(out.children) >= len(n.children) {
out.children = out.children[:len(n.children)]
} else {
out.children = make(children, len(n.children), cap(n.children))
}
copy(out.children, n.children)
return out
}
func (n *node) mutableChild(i int) *node {
c := n.children[i].mutableFor(n.cow)
n.children[i] = c
return c
}
// split splits the given node at the given index. The current node shrinks,
// and this function returns the item that existed at that index and a new node
// containing all items/children after it.
func (n *node) split(i int) (Item, *node) {
item := n.items[i]
next := n.cow.newNode()
next.items = append(next.items, n.items[i+1:]...)
n.items.truncate(i)
if len(n.children) > 0 {
next.children = append(next.children, n.children[i+1:]...)
n.children.truncate(i + 1)
}
return item, next
}
// maybeSplitChild checks if a child should be split, and if so splits it.
// Returns whether or not a split occurred.
func (n *node) maybeSplitChild(i, maxItems int) bool {
if len(n.children[i].items) < maxItems {
return false
}
first := n.mutableChild(i)
item, second := first.split(maxItems / 2)
n.items.insertAt(i, item)
n.children.insertAt(i+1, second)
return true
}
// insert inserts an item into the subtree rooted at this node, making sure
// no nodes in the subtree exceed maxItems items. Should an equivalent item be
// be found/replaced by insert, it will be returned.
func (n *node) insert(item Item, maxItems int) Item {
i, found := n.items.find(item)
if found {
out := n.items[i]
n.items[i] = item
return out
}
if len(n.children) == 0 {
n.items.insertAt(i, item)
return nil
}
if n.maybeSplitChild(i, maxItems) {
inTree := n.items[i]
switch {
case item.Less(inTree):
// no change, we want first split node
case inTree.Less(item):
i++ // we want second split node
default:
out := n.items[i]
n.items[i] = item
return out
}
}
return n.mutableChild(i).insert(item, maxItems)
}
// get finds the given key in the subtree and returns it.
func (n *node) get(key Item) Item {
i, found := n.items.find(key)
if found {
return n.items[i]
} else if len(n.children) > 0 {
return n.children[i].get(key)
}
return nil
}
// min returns the first item in the subtree.
func min(n *node) Item {
if n == nil {
return nil
}
for len(n.children) > 0 {
n = n.children[0]
}
if len(n.items) == 0 {
return nil
}
return n.items[0]
}
// max returns the last item in the subtree.
func max(n *node) Item {
if n == nil {
return nil
}
for len(n.children) > 0 {
n = n.children[len(n.children)-1]
}
if len(n.items) == 0 {
return nil
}
return n.items[len(n.items)-1]
}
// toRemove details what item to remove in a node.remove call.
type toRemove int
const (
removeItem toRemove = iota // removes the given item
removeMin // removes smallest item in the subtree
removeMax // removes largest item in the subtree
)
// remove removes an item from the subtree rooted at this node.
func (n *node) remove(item Item, minItems int, typ toRemove) Item {
var i int
var found bool
switch typ {
case removeMax:
if len(n.children) == 0 {
return n.items.pop()
}
i = len(n.items)
case removeMin:
if len(n.children) == 0 {
return n.items.removeAt(0)
}
i = 0
case removeItem:
i, found = n.items.find(item)
if len(n.children) == 0 {
if found {
return n.items.removeAt(i)
}
return nil
}
default:
panic("invalid type")
}
// If we get to here, we have children.
if len(n.children[i].items) <= minItems {
return n.growChildAndRemove(i, item, minItems, typ)
}
child := n.mutableChild(i)
// Either we had enough items to begin with, or we've done some
// merging/stealing, because we've got enough now and we're ready to return
// stuff.
if found {
// The item exists at index 'i', and the child we've selected can give us a
// predecessor, since if we've gotten here it's got > minItems items in it.
out := n.items[i]
// We use our special-case 'remove' call with typ=maxItem to pull the
// predecessor of item i (the rightmost leaf of our immediate left child)
// and set it into where we pulled the item from.
n.items[i] = child.remove(nil, minItems, removeMax)
return out
}
// Final recursive call. Once we're here, we know that the item isn't in this
// node and that the child is big enough to remove from.
return child.remove(item, minItems, typ)
}
// growChildAndRemove grows child 'i' to make sure it's possible to remove an
// item from it while keeping it at minItems, then calls remove to actually
// remove it.
//
// Most documentation says we have to do two sets of special casing:
// 1) item is in this node
// 2) item is in child
// In both cases, we need to handle the two subcases:
// A) node has enough values that it can spare one
// B) node doesn't have enough values
// For the latter, we have to check:
// a) left sibling has node to spare
// b) right sibling has node to spare
// c) we must merge
// To simplify our code here, we handle cases #1 and #2 the same:
// If a node doesn't have enough items, we make sure it does (using a,b,c).
// We then simply redo our remove call, and the second time (regardless of
// whether we're in case 1 or 2), we'll have enough items and can guarantee
// that we hit case A.
func (n *node) growChildAndRemove(i int, item Item, minItems int, typ toRemove) Item {
if i > 0 && len(n.children[i-1].items) > minItems {
// Steal from left child
child := n.mutableChild(i)
stealFrom := n.mutableChild(i - 1)
stolenItem := stealFrom.items.pop()
child.items.insertAt(0, n.items[i-1])
n.items[i-1] = stolenItem
if len(stealFrom.children) > 0 {
child.children.insertAt(0, stealFrom.children.pop())
}
} else if i < len(n.items) && len(n.children[i+1].items) > minItems {
// steal from right child
child := n.mutableChild(i)
stealFrom := n.mutableChild(i + 1)
stolenItem := stealFrom.items.removeAt(0)
child.items = append(child.items, n.items[i])
n.items[i] = stolenItem
if len(stealFrom.children) > 0 {
child.children = append(child.children, stealFrom.children.removeAt(0))
}
} else {
if i >= len(n.items) {
i--
}
child := n.mutableChild(i)
// merge with right child
mergeItem := n.items.removeAt(i)
mergeChild := n.children.removeAt(i + 1)
child.items = append(child.items, mergeItem)
child.items = append(child.items, mergeChild.items...)
child.children = append(child.children, mergeChild.children...)
n.cow.freeNode(mergeChild)
}
return n.remove(item, minItems, typ)
}
type direction int
const (
descend = direction(-1)
ascend = direction(+1)
)
// iterate provides a simple method for iterating over elements in the tree.
//
// When ascending, the 'start' should be less than 'stop' and when descending,
// the 'start' should be greater than 'stop'. Setting 'includeStart' to true
// will force the iterator to include the first item when it equals 'start',
// thus creating a "greaterOrEqual" or "lessThanEqual" rather than just a
// "greaterThan" or "lessThan" queries.
func (n *node) iterate(dir direction, start, stop Item, includeStart bool, hit bool, iter ItemIterator) (bool, bool) {
var ok bool
switch dir {
case ascend:
for i := 0; i < len(n.items); i++ {
if start != nil && n.items[i].Less(start) {
continue
}
if len(n.children) > 0 {
if hit, ok = n.children[i].iterate(dir, start, stop, includeStart, hit, iter); !ok {
return hit, false
}
}
if !includeStart && !hit && start != nil && !start.Less(n.items[i]) {
hit = true
continue
}
hit = true
if stop != nil && !n.items[i].Less(stop) {
return hit, false
}
if !iter(n.items[i]) {
return hit, false
}
}
if len(n.children) > 0 {
if hit, ok = n.children[len(n.children)-1].iterate(dir, start, stop, includeStart, hit, iter); !ok {
return hit, false
}
}
case descend:
for i := len(n.items) - 1; i >= 0; i-- {
if start != nil && !n.items[i].Less(start) {
if !includeStart || hit || start.Less(n.items[i]) {
continue
}
}
if len(n.children) > 0 {
if hit, ok = n.children[i+1].iterate(dir, start, stop, includeStart, hit, iter); !ok {
return hit, false
}
}
if stop != nil && !stop.Less(n.items[i]) {
return hit, false // continue
}
hit = true
if !iter(n.items[i]) {
return hit, false
}
}
if len(n.children) > 0 {
if hit, ok = n.children[0].iterate(dir, start, stop, includeStart, hit, iter); !ok {
return hit, false
}
}
}
return hit, true
}
// Used for testing/debugging purposes.
func (n *node) print(w io.Writer, level int) {
fmt.Fprintf(w, "%sNODE:%v\n", strings.Repeat(" ", level), n.items)
for _, c := range n.children {
c.print(w, level+1)
}
}
// BTree is an implementation of a B-Tree.
//
// BTree stores Item instances in an ordered structure, allowing easy insertion,
// removal, and iteration.
//
// Write operations are not safe for concurrent mutation by multiple
// goroutines, but Read operations are.
type BTree struct {
degree int
length int
root *node
cow *copyOnWriteContext
}
// copyOnWriteContext pointers determine node ownership... a tree with a write
// context equivalent to a node's write context is allowed to modify that node.
// A tree whose write context does not match a node's is not allowed to modify
// it, and must create a new, writable copy (IE: it's a Clone).
//
// When doing any write operation, we maintain the invariant that the current
// node's context is equal to the context of the tree that requested the write.
// We do this by, before we descend into any node, creating a copy with the
// correct context if the contexts don't match.
//
// Since the node we're currently visiting on any write has the requesting
// tree's context, that node is modifiable in place. Children of that node may
// not share context, but before we descend into them, we'll make a mutable
// copy.
type copyOnWriteContext struct {
freelist *FreeList
}
// Clone clones the btree, lazily. Clone should not be called concurrently,
// but the original tree (t) and the new tree (t2) can be used concurrently
// once the Clone call completes.
//
// The internal tree structure of b is marked read-only and shared between t and
// t2. Writes to both t and t2 use copy-on-write logic, creating new nodes
// whenever one of b's original nodes would have been modified. Read operations
// should have no performance degredation. Write operations for both t and t2
// will initially experience minor slow-downs caused by additional allocs and
// copies due to the aforementioned copy-on-write logic, but should converge to
// the original performance characteristics of the original tree.
func (t *BTree) Clone() (t2 *BTree) {
// Create two entirely new copy-on-write contexts.
// This operation effectively creates three trees:
// the original, shared nodes (old b.cow)
// the new b.cow nodes
// the new out.cow nodes
cow1, cow2 := *t.cow, *t.cow
out := *t
t.cow = &cow1
out.cow = &cow2
return &out
}
// maxItems returns the max number of items to allow per node.
func (t *BTree) maxItems() int {
return t.degree*2 - 1
}
// minItems returns the min number of items to allow per node (ignored for the
// root node).
func (t *BTree) minItems() int {
return t.degree - 1
}
func (c *copyOnWriteContext) newNode() (n *node) {
n = c.freelist.newNode()
n.cow = c
return
}
type freeType int
const (
ftFreelistFull freeType = iota // node was freed (available for GC, not stored in freelist)
ftStored // node was stored in the freelist for later use
ftNotOwned // node was ignored by COW, since it's owned by another one
)
// freeNode frees a node within a given COW context, if it's owned by that
// context. It returns what happened to the node (see freeType const
// documentation).
func (c *copyOnWriteContext) freeNode(n *node) freeType {
if n.cow == c {
// clear to allow GC
n.items.truncate(0)
n.children.truncate(0)
n.cow = nil
if c.freelist.freeNode(n) {
return ftStored
} else {
return ftFreelistFull
}
} else {
return ftNotOwned
}
}
// ReplaceOrInsert adds the given item to the tree. If an item in the tree
// already equals the given one, it is removed from the tree and returned.
// Otherwise, nil is returned.
//
// nil cannot be added to the tree (will panic).
func (t *BTree) ReplaceOrInsert(item Item) Item {
if item == nil {
panic("nil item being added to BTree")
}
if t.root == nil {
t.root = t.cow.newNode()
t.root.items = append(t.root.items, item)
t.length++
return nil
} else {
t.root = t.root.mutableFor(t.cow)
if len(t.root.items) >= t.maxItems() {
item2, second := t.root.split(t.maxItems() / 2)
oldroot := t.root
t.root = t.cow.newNode()
t.root.items = append(t.root.items, item2)
t.root.children = append(t.root.children, oldroot, second)
}
}
out := t.root.insert(item, t.maxItems())
if out == nil {
t.length++
}
return out
}
// Delete removes an item equal to the passed in item from the tree, returning
// it. If no such item exists, returns nil.
func (t *BTree) Delete(item Item) Item {
return t.deleteItem(item, removeItem)
}
// DeleteMin removes the smallest item in the tree and returns it.
// If no such item exists, returns nil.
func (t *BTree) DeleteMin() Item {
return t.deleteItem(nil, removeMin)
}
// DeleteMax removes the largest item in the tree and returns it.
// If no such item exists, returns nil.
func (t *BTree) DeleteMax() Item {
return t.deleteItem(nil, removeMax)
}
func (t *BTree) deleteItem(item Item, typ toRemove) Item {
if t.root == nil || len(t.root.items) == 0 {
return nil
}
t.root = t.root.mutableFor(t.cow)
out := t.root.remove(item, t.minItems(), typ)
if len(t.root.items) == 0 && len(t.root.children) > 0 {
oldroot := t.root
t.root = t.root.children[0]
t.cow.freeNode(oldroot)
}
if out != nil {
t.length--
}
return out
}
// AscendRange calls the iterator for every value in the tree within the range
// [greaterOrEqual, lessThan), until iterator returns false.
func (t *BTree) AscendRange(greaterOrEqual, lessThan Item, iterator ItemIterator) {
if t.root == nil {
return
}
t.root.iterate(ascend, greaterOrEqual, lessThan, true, false, iterator)
}
// AscendLessThan calls the iterator for every value in the tree within the range
// [first, pivot), until iterator returns false.
func (t *BTree) AscendLessThan(pivot Item, iterator ItemIterator) {
if t.root == nil {
return
}
t.root.iterate(ascend, nil, pivot, false, false, iterator)
}
// AscendGreaterOrEqual calls the iterator for every value in the tree within
// the range [pivot, last], until iterator returns false.
func (t *BTree) AscendGreaterOrEqual(pivot Item, iterator ItemIterator) {
if t.root == nil {
return
}
t.root.iterate(ascend, pivot, nil, true, false, iterator)
}
// Ascend calls the iterator for every value in the tree within the range
// [first, last], until iterator returns false.
func (t *BTree) Ascend(iterator ItemIterator) {
if t.root == nil {
return
}
t.root.iterate(ascend, nil, nil, false, false, iterator)
}
// DescendRange calls the iterator for every value in the tree within the range
// [lessOrEqual, greaterThan), until iterator returns false.
func (t *BTree) DescendRange(lessOrEqual, greaterThan Item, iterator ItemIterator) {
if t.root == nil {
return
}
t.root.iterate(descend, lessOrEqual, greaterThan, true, false, iterator)
}
// DescendLessOrEqual calls the iterator for every value in the tree within the range
// [pivot, first], until iterator returns false.
func (t *BTree) DescendLessOrEqual(pivot Item, iterator ItemIterator) {
if t.root == nil {
return
}
t.root.iterate(descend, pivot, nil, true, false, iterator)
}
// DescendGreaterThan calls the iterator for every value in the tree within
// the range (pivot, last], until iterator returns false.
func (t *BTree) DescendGreaterThan(pivot Item, iterator ItemIterator) {
if t.root == nil {
return
}
t.root.iterate(descend, nil, pivot, false, false, iterator)
}
// Descend calls the iterator for every value in the tree within the range
// [last, first], until iterator returns false.
func (t *BTree) Descend(iterator ItemIterator) {
if t.root == nil {
return
}
t.root.iterate(descend, nil, nil, false, false, iterator)
}
// Get looks for the key item in the tree, returning it. It returns nil if
// unable to find that item.
func (t *BTree) Get(key Item) Item {
if t.root == nil {
return nil
}
return t.root.get(key)
}
// Min returns the smallest item in the tree, or nil if the tree is empty.
func (t *BTree) Min() Item {
return min(t.root)
}
// Max returns the largest item in the tree, or nil if the tree is empty.
func (t *BTree) Max() Item {
return max(t.root)
}
// Has returns true if the given key is in the tree.
func (t *BTree) Has(key Item) bool {
return t.Get(key) != nil
}
// Len returns the number of items currently in the tree.
func (t *BTree) Len() int {
return t.length
}
// Clear removes all items from the btree. If addNodesToFreelist is true,
// t's nodes are added to its freelist as part of this call, until the freelist
// is full. Otherwise, the root node is simply dereferenced and the subtree
// left to Go's normal GC processes.
//
// This can be much faster
// than calling Delete on all elements, because that requires finding/removing
// each element in the tree and updating the tree accordingly. It also is
// somewhat faster than creating a new tree to replace the old one, because
// nodes from the old tree are reclaimed into the freelist for use by the new
// one, instead of being lost to the garbage collector.
//
// This call takes:
// O(1): when addNodesToFreelist is false, this is a single operation.
// O(1): when the freelist is already full, it breaks out immediately
// O(freelist size): when the freelist is empty and the nodes are all owned
// by this tree, nodes are added to the freelist until full.
// O(tree size): when all nodes are owned by another tree, all nodes are
// iterated over looking for nodes to add to the freelist, and due to
// ownership, none are.
func (t *BTree) Clear(addNodesToFreelist bool) {
if t.root != nil && addNodesToFreelist {
t.root.reset(t.cow)
}
t.root, t.length = nil, 0
}
// reset returns a subtree to the freelist. It breaks out immediately if the
// freelist is full, since the only benefit of iterating is to fill that
// freelist up. Returns true if parent reset call should continue.
func (n *node) reset(c *copyOnWriteContext) bool {
for _, child := range n.children {
if !child.reset(c) {
return false
}
}
return c.freeNode(n) != ftFreelistFull
}
// Int implements the Item interface for integers.
type Int int
// Less returns true if int(a) < int(b).
func (a Int) Less(b Item) bool {
return a < b.(Int)
}