Remove BPA from Makefile

[icn.git] / cmd / bpa-operator / vendor / github.com / google / btree / btree.go

// 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, found bool
        var index int
        switch dir {
        case ascend:
                if start != nil {
                        index, _ = n.items.find(start)
                }
                for i := index; i < len(n.items); i++ {
                        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:
                if start != nil {
                        index, found = n.items.find(start)
                        if !found {
                                index = index - 1
                        }
                } else {
                        index = len(n.items) - 1
                }
                for i := index; 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)
}