mirror of
https://github.com/ceph/ceph-csi.git
synced 2025-03-09 17:09:29 +00:00
f87d06ed85
Several packages are only used while running the e2e suite. These packages are less important to update, as the they can not influence the final executable that is part of the Ceph-CSI container-image. By moving these dependencies out of the main Ceph-CSI go.mod, it is easier to identify if a reported CVE affects Ceph-CSI, or only the testing (like most of the Kubernetes CVEs). Signed-off-by: Niels de Vos <ndevos@ibm.com>
1084 lines
35 KiB
Go
1084 lines
35 KiB
Go
// Copyright 2014-2022 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.
|
|
|
|
//go:build go1.18
|
|
// +build go1.18
|
|
|
|
// In Go 1.18 and beyond, a BTreeG generic is created, and BTree is a specific
|
|
// instantiation of that generic for the Item interface, with a backwards-
|
|
// compatible API. Before go1.18, generics are not supported,
|
|
// and BTree is just an implementation based around the Item interface.
|
|
|
|
// 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.
|
|
//
|
|
// There are two implementations; those suffixed with 'G' are generics, usable
|
|
// for any type, and require a passed-in "less" function to define their ordering.
|
|
// Those without this prefix are specific to the 'Item' interface, and use
|
|
// its 'Less' function for ordering.
|
|
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
|
|
)
|
|
|
|
// FreeListG represents a free list of btree nodes. By default each
|
|
// BTree has its own FreeList, but multiple BTrees can share the same
|
|
// FreeList, in particular when they're created with Clone.
|
|
// Two Btrees using the same freelist are safe for concurrent write access.
|
|
type FreeListG[T any] struct {
|
|
mu sync.Mutex
|
|
freelist []*node[T]
|
|
}
|
|
|
|
// NewFreeListG creates a new free list.
|
|
// size is the maximum size of the returned free list.
|
|
func NewFreeListG[T any](size int) *FreeListG[T] {
|
|
return &FreeListG[T]{freelist: make([]*node[T], 0, size)}
|
|
}
|
|
|
|
func (f *FreeListG[T]) newNode() (n *node[T]) {
|
|
f.mu.Lock()
|
|
index := len(f.freelist) - 1
|
|
if index < 0 {
|
|
f.mu.Unlock()
|
|
return new(node[T])
|
|
}
|
|
n = f.freelist[index]
|
|
f.freelist[index] = nil
|
|
f.freelist = f.freelist[:index]
|
|
f.mu.Unlock()
|
|
return
|
|
}
|
|
|
|
func (f *FreeListG[T]) freeNode(n *node[T]) (out bool) {
|
|
f.mu.Lock()
|
|
if len(f.freelist) < cap(f.freelist) {
|
|
f.freelist = append(f.freelist, n)
|
|
out = true
|
|
}
|
|
f.mu.Unlock()
|
|
return
|
|
}
|
|
|
|
// ItemIteratorG allows callers of {A/De}scend* 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 ItemIteratorG[T any] func(item T) bool
|
|
|
|
// Ordered represents the set of types for which the '<' operator work.
|
|
type Ordered interface {
|
|
~int | ~int8 | ~int16 | ~int32 | ~int64 | ~uint | ~uint8 | ~uint16 | ~uint32 | ~uint64 | ~float32 | ~float64 | ~string
|
|
}
|
|
|
|
// Less[T] returns a default LessFunc that uses the '<' operator for types that support it.
|
|
func Less[T Ordered]() LessFunc[T] {
|
|
return func(a, b T) bool { return a < b }
|
|
}
|
|
|
|
// NewOrderedG creates a new B-Tree for ordered types.
|
|
func NewOrderedG[T Ordered](degree int) *BTreeG[T] {
|
|
return NewG[T](degree, Less[T]())
|
|
}
|
|
|
|
// NewG creates a new B-Tree with the given degree.
|
|
//
|
|
// NewG(2), for example, will create a 2-3-4 tree (each node contains 1-3 items
|
|
// and 2-4 children).
|
|
//
|
|
// The passed-in LessFunc determines how objects of type T are ordered.
|
|
func NewG[T any](degree int, less LessFunc[T]) *BTreeG[T] {
|
|
return NewWithFreeListG(degree, less, NewFreeListG[T](DefaultFreeListSize))
|
|
}
|
|
|
|
// NewWithFreeListG creates a new B-Tree that uses the given node free list.
|
|
func NewWithFreeListG[T any](degree int, less LessFunc[T], f *FreeListG[T]) *BTreeG[T] {
|
|
if degree <= 1 {
|
|
panic("bad degree")
|
|
}
|
|
return &BTreeG[T]{
|
|
degree: degree,
|
|
cow: ©OnWriteContext[T]{freelist: f, less: less},
|
|
}
|
|
}
|
|
|
|
// items stores items in a node.
|
|
type items[T any] []T
|
|
|
|
// insertAt inserts a value into the given index, pushing all subsequent values
|
|
// forward.
|
|
func (s *items[T]) insertAt(index int, item T) {
|
|
var zero T
|
|
*s = append(*s, zero)
|
|
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[T]) removeAt(index int) T {
|
|
item := (*s)[index]
|
|
copy((*s)[index:], (*s)[index+1:])
|
|
var zero T
|
|
(*s)[len(*s)-1] = zero
|
|
*s = (*s)[:len(*s)-1]
|
|
return item
|
|
}
|
|
|
|
// pop removes and returns the last element in the list.
|
|
func (s *items[T]) pop() (out T) {
|
|
index := len(*s) - 1
|
|
out = (*s)[index]
|
|
var zero T
|
|
(*s)[index] = zero
|
|
*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[T]) truncate(index int) {
|
|
var toClear items[T]
|
|
*s, toClear = (*s)[:index], (*s)[index:]
|
|
var zero T
|
|
for i := 0; i < len(toClear); i++ {
|
|
toClear[i] = zero
|
|
}
|
|
}
|
|
|
|
// 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[T]) find(item T, less func(T, T) bool) (index int, found bool) {
|
|
i := sort.Search(len(s), func(i int) bool {
|
|
return less(item, s[i])
|
|
})
|
|
if i > 0 && !less(s[i-1], item) {
|
|
return i - 1, true
|
|
}
|
|
return i, false
|
|
}
|
|
|
|
// 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[T any] struct {
|
|
items items[T]
|
|
children items[*node[T]]
|
|
cow *copyOnWriteContext[T]
|
|
}
|
|
|
|
func (n *node[T]) mutableFor(cow *copyOnWriteContext[T]) *node[T] {
|
|
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[T], 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(items[*node[T]], len(n.children), cap(n.children))
|
|
}
|
|
copy(out.children, n.children)
|
|
return out
|
|
}
|
|
|
|
func (n *node[T]) mutableChild(i int) *node[T] {
|
|
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[T]) split(i int) (T, *node[T]) {
|
|
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[T]) 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[T]) insert(item T, maxItems int) (_ T, _ bool) {
|
|
i, found := n.items.find(item, n.cow.less)
|
|
if found {
|
|
out := n.items[i]
|
|
n.items[i] = item
|
|
return out, true
|
|
}
|
|
if len(n.children) == 0 {
|
|
n.items.insertAt(i, item)
|
|
return
|
|
}
|
|
if n.maybeSplitChild(i, maxItems) {
|
|
inTree := n.items[i]
|
|
switch {
|
|
case n.cow.less(item, inTree):
|
|
// no change, we want first split node
|
|
case n.cow.less(inTree, item):
|
|
i++ // we want second split node
|
|
default:
|
|
out := n.items[i]
|
|
n.items[i] = item
|
|
return out, true
|
|
}
|
|
}
|
|
return n.mutableChild(i).insert(item, maxItems)
|
|
}
|
|
|
|
// get finds the given key in the subtree and returns it.
|
|
func (n *node[T]) get(key T) (_ T, _ bool) {
|
|
i, found := n.items.find(key, n.cow.less)
|
|
if found {
|
|
return n.items[i], true
|
|
} else if len(n.children) > 0 {
|
|
return n.children[i].get(key)
|
|
}
|
|
return
|
|
}
|
|
|
|
// min returns the first item in the subtree.
|
|
func min[T any](n *node[T]) (_ T, found bool) {
|
|
if n == nil {
|
|
return
|
|
}
|
|
for len(n.children) > 0 {
|
|
n = n.children[0]
|
|
}
|
|
if len(n.items) == 0 {
|
|
return
|
|
}
|
|
return n.items[0], true
|
|
}
|
|
|
|
// max returns the last item in the subtree.
|
|
func max[T any](n *node[T]) (_ T, found bool) {
|
|
if n == nil {
|
|
return
|
|
}
|
|
for len(n.children) > 0 {
|
|
n = n.children[len(n.children)-1]
|
|
}
|
|
if len(n.items) == 0 {
|
|
return
|
|
}
|
|
return n.items[len(n.items)-1], true
|
|
}
|
|
|
|
// 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[T]) remove(item T, minItems int, typ toRemove) (_ T, _ bool) {
|
|
var i int
|
|
var found bool
|
|
switch typ {
|
|
case removeMax:
|
|
if len(n.children) == 0 {
|
|
return n.items.pop(), true
|
|
}
|
|
i = len(n.items)
|
|
case removeMin:
|
|
if len(n.children) == 0 {
|
|
return n.items.removeAt(0), true
|
|
}
|
|
i = 0
|
|
case removeItem:
|
|
i, found = n.items.find(item, n.cow.less)
|
|
if len(n.children) == 0 {
|
|
if found {
|
|
return n.items.removeAt(i), true
|
|
}
|
|
return
|
|
}
|
|
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.
|
|
var zero T
|
|
n.items[i], _ = child.remove(zero, minItems, removeMax)
|
|
return out, true
|
|
}
|
|
// 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[T]) growChildAndRemove(i int, item T, minItems int, typ toRemove) (T, bool) {
|
|
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)
|
|
)
|
|
|
|
type optionalItem[T any] struct {
|
|
item T
|
|
valid bool
|
|
}
|
|
|
|
func optional[T any](item T) optionalItem[T] {
|
|
return optionalItem[T]{item: item, valid: true}
|
|
}
|
|
func empty[T any]() optionalItem[T] {
|
|
return optionalItem[T]{}
|
|
}
|
|
|
|
// 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[T]) iterate(dir direction, start, stop optionalItem[T], includeStart bool, hit bool, iter ItemIteratorG[T]) (bool, bool) {
|
|
var ok, found bool
|
|
var index int
|
|
switch dir {
|
|
case ascend:
|
|
if start.valid {
|
|
index, _ = n.items.find(start.item, n.cow.less)
|
|
}
|
|
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.valid && !n.cow.less(start.item, n.items[i]) {
|
|
hit = true
|
|
continue
|
|
}
|
|
hit = true
|
|
if stop.valid && !n.cow.less(n.items[i], stop.item) {
|
|
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.valid {
|
|
index, found = n.items.find(start.item, n.cow.less)
|
|
if !found {
|
|
index = index - 1
|
|
}
|
|
} else {
|
|
index = len(n.items) - 1
|
|
}
|
|
for i := index; i >= 0; i-- {
|
|
if start.valid && !n.cow.less(n.items[i], start.item) {
|
|
if !includeStart || hit || n.cow.less(start.item, 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.valid && !n.cow.less(stop.item, 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
|
|
}
|
|
|
|
// print is used for testing/debugging purposes.
|
|
func (n *node[T]) 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)
|
|
}
|
|
}
|
|
|
|
// BTreeG is a generic implementation of a B-Tree.
|
|
//
|
|
// BTreeG stores items of type T 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 BTreeG[T any] struct {
|
|
degree int
|
|
length int
|
|
root *node[T]
|
|
cow *copyOnWriteContext[T]
|
|
}
|
|
|
|
// LessFunc[T] determines how to order a type 'T'. It should implement a strict
|
|
// ordering, and should return true if within that ordering, 'a' < 'b'.
|
|
type LessFunc[T any] func(a, b T) bool
|
|
|
|
// 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[T any] struct {
|
|
freelist *FreeListG[T]
|
|
less LessFunc[T]
|
|
}
|
|
|
|
// 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 *BTreeG[T]) Clone() (t2 *BTreeG[T]) {
|
|
// 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 *BTreeG[T]) 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 *BTreeG[T]) minItems() int {
|
|
return t.degree - 1
|
|
}
|
|
|
|
func (c *copyOnWriteContext[T]) newNode() (n *node[T]) {
|
|
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[T]) freeNode(n *node[T]) 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,
|
|
// and the second return value is true. Otherwise, (zeroValue, false)
|
|
//
|
|
// nil cannot be added to the tree (will panic).
|
|
func (t *BTreeG[T]) ReplaceOrInsert(item T) (_ T, _ bool) {
|
|
if t.root == nil {
|
|
t.root = t.cow.newNode()
|
|
t.root.items = append(t.root.items, item)
|
|
t.length++
|
|
return
|
|
} 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, outb := t.root.insert(item, t.maxItems())
|
|
if !outb {
|
|
t.length++
|
|
}
|
|
return out, outb
|
|
}
|
|
|
|
// Delete removes an item equal to the passed in item from the tree, returning
|
|
// it. If no such item exists, returns (zeroValue, false).
|
|
func (t *BTreeG[T]) Delete(item T) (T, bool) {
|
|
return t.deleteItem(item, removeItem)
|
|
}
|
|
|
|
// DeleteMin removes the smallest item in the tree and returns it.
|
|
// If no such item exists, returns (zeroValue, false).
|
|
func (t *BTreeG[T]) DeleteMin() (T, bool) {
|
|
var zero T
|
|
return t.deleteItem(zero, removeMin)
|
|
}
|
|
|
|
// DeleteMax removes the largest item in the tree and returns it.
|
|
// If no such item exists, returns (zeroValue, false).
|
|
func (t *BTreeG[T]) DeleteMax() (T, bool) {
|
|
var zero T
|
|
return t.deleteItem(zero, removeMax)
|
|
}
|
|
|
|
func (t *BTreeG[T]) deleteItem(item T, typ toRemove) (_ T, _ bool) {
|
|
if t.root == nil || len(t.root.items) == 0 {
|
|
return
|
|
}
|
|
t.root = t.root.mutableFor(t.cow)
|
|
out, outb := 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 outb {
|
|
t.length--
|
|
}
|
|
return out, outb
|
|
}
|
|
|
|
// AscendRange calls the iterator for every value in the tree within the range
|
|
// [greaterOrEqual, lessThan), until iterator returns false.
|
|
func (t *BTreeG[T]) AscendRange(greaterOrEqual, lessThan T, iterator ItemIteratorG[T]) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
t.root.iterate(ascend, optional[T](greaterOrEqual), optional[T](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 *BTreeG[T]) AscendLessThan(pivot T, iterator ItemIteratorG[T]) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
t.root.iterate(ascend, empty[T](), optional(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 *BTreeG[T]) AscendGreaterOrEqual(pivot T, iterator ItemIteratorG[T]) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
t.root.iterate(ascend, optional[T](pivot), empty[T](), true, false, iterator)
|
|
}
|
|
|
|
// Ascend calls the iterator for every value in the tree within the range
|
|
// [first, last], until iterator returns false.
|
|
func (t *BTreeG[T]) Ascend(iterator ItemIteratorG[T]) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
t.root.iterate(ascend, empty[T](), empty[T](), false, false, iterator)
|
|
}
|
|
|
|
// DescendRange calls the iterator for every value in the tree within the range
|
|
// [lessOrEqual, greaterThan), until iterator returns false.
|
|
func (t *BTreeG[T]) DescendRange(lessOrEqual, greaterThan T, iterator ItemIteratorG[T]) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
t.root.iterate(descend, optional[T](lessOrEqual), optional[T](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 *BTreeG[T]) DescendLessOrEqual(pivot T, iterator ItemIteratorG[T]) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
t.root.iterate(descend, optional[T](pivot), empty[T](), true, false, iterator)
|
|
}
|
|
|
|
// DescendGreaterThan calls the iterator for every value in the tree within
|
|
// the range [last, pivot), until iterator returns false.
|
|
func (t *BTreeG[T]) DescendGreaterThan(pivot T, iterator ItemIteratorG[T]) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
t.root.iterate(descend, empty[T](), optional[T](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 *BTreeG[T]) Descend(iterator ItemIteratorG[T]) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
t.root.iterate(descend, empty[T](), empty[T](), false, false, iterator)
|
|
}
|
|
|
|
// Get looks for the key item in the tree, returning it. It returns
|
|
// (zeroValue, false) if unable to find that item.
|
|
func (t *BTreeG[T]) Get(key T) (_ T, _ bool) {
|
|
if t.root == nil {
|
|
return
|
|
}
|
|
return t.root.get(key)
|
|
}
|
|
|
|
// Min returns the smallest item in the tree, or (zeroValue, false) if the tree is empty.
|
|
func (t *BTreeG[T]) Min() (_ T, _ bool) {
|
|
return min(t.root)
|
|
}
|
|
|
|
// Max returns the largest item in the tree, or (zeroValue, false) if the tree is empty.
|
|
func (t *BTreeG[T]) Max() (_ T, _ bool) {
|
|
return max(t.root)
|
|
}
|
|
|
|
// Has returns true if the given key is in the tree.
|
|
func (t *BTreeG[T]) Has(key T) bool {
|
|
_, ok := t.Get(key)
|
|
return ok
|
|
}
|
|
|
|
// Len returns the number of items currently in the tree.
|
|
func (t *BTreeG[T]) 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 *BTreeG[T]) 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[T]) reset(c *copyOnWriteContext[T]) 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)
|
|
}
|
|
|
|
// 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 BTreeG[Item]
|
|
|
|
var itemLess LessFunc[Item] = func(a, b Item) bool {
|
|
return a.Less(b)
|
|
}
|
|
|
|
// 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 (*BTree)(NewG[Item](degree, itemLess))
|
|
}
|
|
|
|
// 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 FreeListG[Item]
|
|
|
|
// NewFreeList creates a new free list.
|
|
// size is the maximum size of the returned free list.
|
|
func NewFreeList(size int) *FreeList {
|
|
return (*FreeList)(NewFreeListG[Item](size))
|
|
}
|
|
|
|
// NewWithFreeList creates a new B-Tree that uses the given node free list.
|
|
func NewWithFreeList(degree int, f *FreeList) *BTree {
|
|
return (*BTree)(NewWithFreeListG[Item](degree, itemLess, (*FreeListG[Item])(f)))
|
|
}
|
|
|
|
// 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 ItemIteratorG[Item]
|
|
|
|
// 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) {
|
|
return (*BTree)((*BTreeG[Item])(t).Clone())
|
|
}
|
|
|
|
// 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 {
|
|
i, _ := (*BTreeG[Item])(t).Delete(item)
|
|
return i
|
|
}
|
|
|
|
// DeleteMax removes the largest item in the tree and returns it.
|
|
// If no such item exists, returns nil.
|
|
func (t *BTree) DeleteMax() Item {
|
|
i, _ := (*BTreeG[Item])(t).DeleteMax()
|
|
return i
|
|
}
|
|
|
|
// DeleteMin removes the smallest item in the tree and returns it.
|
|
// If no such item exists, returns nil.
|
|
func (t *BTree) DeleteMin() Item {
|
|
i, _ := (*BTreeG[Item])(t).DeleteMin()
|
|
return i
|
|
}
|
|
|
|
// 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 {
|
|
i, _ := (*BTreeG[Item])(t).Get(key)
|
|
return i
|
|
}
|
|
|
|
// Max returns the largest item in the tree, or nil if the tree is empty.
|
|
func (t *BTree) Max() Item {
|
|
i, _ := (*BTreeG[Item])(t).Max()
|
|
return i
|
|
}
|
|
|
|
// Min returns the smallest item in the tree, or nil if the tree is empty.
|
|
func (t *BTree) Min() Item {
|
|
i, _ := (*BTreeG[Item])(t).Min()
|
|
return i
|
|
}
|
|
|
|
// Has returns true if the given key is in the tree.
|
|
func (t *BTree) Has(key Item) bool {
|
|
return (*BTreeG[Item])(t).Has(key)
|
|
}
|
|
|
|
// 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 {
|
|
i, _ := (*BTreeG[Item])(t).ReplaceOrInsert(item)
|
|
return i
|
|
}
|
|
|
|
// 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) {
|
|
(*BTreeG[Item])(t).AscendRange(greaterOrEqual, lessThan, (ItemIteratorG[Item])(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) {
|
|
(*BTreeG[Item])(t).AscendLessThan(pivot, (ItemIteratorG[Item])(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) {
|
|
(*BTreeG[Item])(t).AscendGreaterOrEqual(pivot, (ItemIteratorG[Item])(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) {
|
|
(*BTreeG[Item])(t).Ascend((ItemIteratorG[Item])(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) {
|
|
(*BTreeG[Item])(t).DescendRange(lessOrEqual, greaterThan, (ItemIteratorG[Item])(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) {
|
|
(*BTreeG[Item])(t).DescendLessOrEqual(pivot, (ItemIteratorG[Item])(iterator))
|
|
}
|
|
|
|
// DescendGreaterThan calls the iterator for every value in the tree within
|
|
// the range [last, pivot), until iterator returns false.
|
|
func (t *BTree) DescendGreaterThan(pivot Item, iterator ItemIterator) {
|
|
(*BTreeG[Item])(t).DescendGreaterThan(pivot, (ItemIteratorG[Item])(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) {
|
|
(*BTreeG[Item])(t).Descend((ItemIteratorG[Item])(iterator))
|
|
}
|
|
|
|
// Len returns the number of items currently in the tree.
|
|
func (t *BTree) Len() int {
|
|
return (*BTreeG[Item])(t).Len()
|
|
}
|
|
|
|
// 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) {
|
|
(*BTreeG[Item])(t).Clear(addNodesToFreelist)
|
|
}
|