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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)
-}