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@@ -0,0 +1,1083 @@
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+// Copyright 2014-2022 Google Inc.
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+//
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+// Licensed under the Apache License, Version 2.0 (the "License");
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+// you may not use this file except in compliance with the License.
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+// You may obtain a copy of the License at
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+//
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+// http://www.apache.org/licenses/LICENSE-2.0
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+//
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+// Unless required by applicable law or agreed to in writing, software
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+// distributed under the License is distributed on an "AS IS" BASIS,
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+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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+// See the License for the specific language governing permissions and
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+// limitations under the License.
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+
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+//go:build go1.18
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+// +build go1.18
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+
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+// In Go 1.18 and beyond, a BTreeG generic is created, and BTree is a specific
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+// instantiation of that generic for the Item interface, with a backwards-
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+// compatible API. Before go1.18, generics are not supported,
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+// and BTree is just an implementation based around the Item interface.
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+
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+// Package btree implements in-memory B-Trees of arbitrary degree.
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+//
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+// btree implements an in-memory B-Tree for use as an ordered data structure.
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+// It is not meant for persistent storage solutions.
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+//
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+// It has a flatter structure than an equivalent red-black or other binary tree,
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+// which in some cases yields better memory usage and/or performance.
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+// See some discussion on the matter here:
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+// http://google-opensource.blogspot.com/2013/01/c-containers-that-save-memory-and-time.html
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+// Note, though, that this project is in no way related to the C++ B-Tree
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+// implementation written about there.
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+//
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+// Within this tree, each node contains a slice of items and a (possibly nil)
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+// slice of children. For basic numeric values or raw structs, this can cause
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+// efficiency differences when compared to equivalent C++ template code that
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+// stores values in arrays within the node:
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+// * Due to the overhead of storing values as interfaces (each
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+// value needs to be stored as the value itself, then 2 words for the
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+// interface pointing to that value and its type), resulting in higher
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+// memory use.
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+// * Since interfaces can point to values anywhere in memory, values are
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+// most likely not stored in contiguous blocks, resulting in a higher
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+// number of cache misses.
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+// These issues don't tend to matter, though, when working with strings or other
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+// heap-allocated structures, since C++-equivalent structures also must store
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+// pointers and also distribute their values across the heap.
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+//
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+// This implementation is designed to be a drop-in replacement to gollrb.LLRB
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+// trees, (http://github.com/petar/gollrb), an excellent and probably the most
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+// widely used ordered tree implementation in the Go ecosystem currently.
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+// Its functions, therefore, exactly mirror those of
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+// llrb.LLRB where possible. Unlike gollrb, though, we currently don't
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+// support storing multiple equivalent values.
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+//
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+// There are two implementations; those suffixed with 'G' are generics, usable
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+// for any type, and require a passed-in "less" function to define their ordering.
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+// Those without this prefix are specific to the 'Item' interface, and use
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+// its 'Less' function for ordering.
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+package btree
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+
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+import (
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+ "fmt"
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+ "io"
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+ "sort"
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+ "strings"
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+ "sync"
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+)
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+
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+// Item represents a single object in the tree.
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+type Item interface {
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+ // Less tests whether the current item is less than the given argument.
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+ //
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+ // This must provide a strict weak ordering.
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+ // If !a.Less(b) && !b.Less(a), we treat this to mean a == b (i.e. we can only
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+ // hold one of either a or b in the tree).
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+ Less(than Item) bool
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+}
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+
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+const (
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+ DefaultFreeListSize = 32
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+)
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+
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+// FreeListG represents a free list of btree nodes. By default each
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+// BTree has its own FreeList, but multiple BTrees can share the same
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+// FreeList, in particular when they're created with Clone.
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+// Two Btrees using the same freelist are safe for concurrent write access.
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+type FreeListG[T any] struct {
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+ mu sync.Mutex
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+ freelist []*node[T]
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+}
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+
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+// NewFreeListG creates a new free list.
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+// size is the maximum size of the returned free list.
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+func NewFreeListG[T any](size int) *FreeListG[T] {
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+ return &FreeListG[T]{freelist: make([]*node[T], 0, size)}
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+}
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+
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+func (f *FreeListG[T]) newNode() (n *node[T]) {
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+ f.mu.Lock()
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+ index := len(f.freelist) - 1
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+ if index < 0 {
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+ f.mu.Unlock()
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+ return new(node[T])
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+ }
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+ n = f.freelist[index]
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+ f.freelist[index] = nil
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+ f.freelist = f.freelist[:index]
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+ f.mu.Unlock()
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+ return
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+}
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+
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+func (f *FreeListG[T]) freeNode(n *node[T]) (out bool) {
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+ f.mu.Lock()
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+ if len(f.freelist) < cap(f.freelist) {
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+ f.freelist = append(f.freelist, n)
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+ out = true
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+ }
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+ f.mu.Unlock()
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+ return
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+}
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+
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+// ItemIteratorG allows callers of {A/De}scend* to iterate in-order over portions of
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+// the tree. When this function returns false, iteration will stop and the
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+// associated Ascend* function will immediately return.
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+type ItemIteratorG[T any] func(item T) bool
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+
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+// Ordered represents the set of types for which the '<' operator work.
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+type Ordered interface {
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+ ~int | ~int8 | ~int16 | ~int32 | ~int64 | ~uint | ~uint8 | ~uint16 | ~uint32 | ~uint64 | ~float32 | ~float64 | ~string
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+}
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+
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+// Less[T] returns a default LessFunc that uses the '<' operator for types that support it.
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+func Less[T Ordered]() LessFunc[T] {
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+ return func(a, b T) bool { return a < b }
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+}
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+
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+// NewOrderedG creates a new B-Tree for ordered types.
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+func NewOrderedG[T Ordered](degree int) *BTreeG[T] {
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+ return NewG[T](degree, Less[T]())
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+}
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+
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+// NewG creates a new B-Tree with the given degree.
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+//
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+// NewG(2), for example, will create a 2-3-4 tree (each node contains 1-3 items
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+// and 2-4 children).
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+//
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+// The passed-in LessFunc determines how objects of type T are ordered.
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+func NewG[T any](degree int, less LessFunc[T]) *BTreeG[T] {
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+ return NewWithFreeListG(degree, less, NewFreeListG[T](DefaultFreeListSize))
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+}
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+
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+// NewWithFreeListG creates a new B-Tree that uses the given node free list.
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+func NewWithFreeListG[T any](degree int, less LessFunc[T], f *FreeListG[T]) *BTreeG[T] {
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+ if degree <= 1 {
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+ panic("bad degree")
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+ }
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+ return &BTreeG[T]{
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+ degree: degree,
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+ cow: ©OnWriteContext[T]{freelist: f, less: less},
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+ }
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+}
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+
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+// items stores items in a node.
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+type items[T any] []T
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+
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+// insertAt inserts a value into the given index, pushing all subsequent values
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+// forward.
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+func (s *items[T]) insertAt(index int, item T) {
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+ var zero T
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+ *s = append(*s, zero)
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+ if index < len(*s) {
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+ copy((*s)[index+1:], (*s)[index:])
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+ }
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+ (*s)[index] = item
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+}
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+
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+// removeAt removes a value at a given index, pulling all subsequent values
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+// back.
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+func (s *items[T]) removeAt(index int) T {
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+ item := (*s)[index]
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+ copy((*s)[index:], (*s)[index+1:])
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+ var zero T
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+ (*s)[len(*s)-1] = zero
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+ *s = (*s)[:len(*s)-1]
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+ return item
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+}
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+
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+// pop removes and returns the last element in the list.
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+func (s *items[T]) pop() (out T) {
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+ index := len(*s) - 1
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+ out = (*s)[index]
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+ var zero T
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+ (*s)[index] = zero
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+ *s = (*s)[:index]
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+ return
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+}
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+
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+// truncate truncates this instance at index so that it contains only the
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+// first index items. index must be less than or equal to length.
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+func (s *items[T]) truncate(index int) {
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+ var toClear items[T]
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+ *s, toClear = (*s)[:index], (*s)[index:]
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+ var zero T
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+ for i := 0; i < len(toClear); i++ {
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+ toClear[i] = zero
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+ }
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+}
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+
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+// find returns the index where the given item should be inserted into this
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+// list. 'found' is true if the item already exists in the list at the given
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+// index.
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+func (s items[T]) find(item T, less func(T, T) bool) (index int, found bool) {
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+ i := sort.Search(len(s), func(i int) bool {
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+ return less(item, s[i])
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+ })
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+ if i > 0 && !less(s[i-1], item) {
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+ return i - 1, true
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+ }
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+ return i, false
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+}
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+
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+// node is an internal node in a tree.
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+//
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+// It must at all times maintain the invariant that either
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+// * len(children) == 0, len(items) unconstrained
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+// * len(children) == len(items) + 1
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+type node[T any] struct {
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+ items items[T]
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+ children items[*node[T]]
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+ cow *copyOnWriteContext[T]
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+}
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+
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+func (n *node[T]) mutableFor(cow *copyOnWriteContext[T]) *node[T] {
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+ if n.cow == cow {
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+ return n
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+ }
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+ out := cow.newNode()
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+ if cap(out.items) >= len(n.items) {
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+ out.items = out.items[:len(n.items)]
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+ } else {
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+ out.items = make(items[T], len(n.items), cap(n.items))
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+ }
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+ copy(out.items, n.items)
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+ // Copy children
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+ if cap(out.children) >= len(n.children) {
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+ out.children = out.children[:len(n.children)]
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+ } else {
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+ out.children = make(items[*node[T]], len(n.children), cap(n.children))
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+ }
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+ copy(out.children, n.children)
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+ return out
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+}
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+
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+func (n *node[T]) mutableChild(i int) *node[T] {
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+ c := n.children[i].mutableFor(n.cow)
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+ n.children[i] = c
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+ return c
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+}
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+
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+// split splits the given node at the given index. The current node shrinks,
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+// and this function returns the item that existed at that index and a new node
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+// containing all items/children after it.
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+func (n *node[T]) split(i int) (T, *node[T]) {
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+ item := n.items[i]
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+ next := n.cow.newNode()
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+ next.items = append(next.items, n.items[i+1:]...)
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+ n.items.truncate(i)
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+ if len(n.children) > 0 {
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+ next.children = append(next.children, n.children[i+1:]...)
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+ n.children.truncate(i + 1)
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+ }
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+ return item, next
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+}
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+
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+// maybeSplitChild checks if a child should be split, and if so splits it.
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+// Returns whether or not a split occurred.
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+func (n *node[T]) maybeSplitChild(i, maxItems int) bool {
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+ if len(n.children[i].items) < maxItems {
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+ return false
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+ }
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+ first := n.mutableChild(i)
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+ item, second := first.split(maxItems / 2)
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+ n.items.insertAt(i, item)
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+ n.children.insertAt(i+1, second)
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+ return true
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+}
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+
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+// insert inserts an item into the subtree rooted at this node, making sure
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+// no nodes in the subtree exceed maxItems items. Should an equivalent item be
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+// be found/replaced by insert, it will be returned.
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+func (n *node[T]) insert(item T, maxItems int) (_ T, _ bool) {
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+ i, found := n.items.find(item, n.cow.less)
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+ if found {
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+ out := n.items[i]
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+ n.items[i] = item
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+ return out, true
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+ }
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+ if len(n.children) == 0 {
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+ n.items.insertAt(i, item)
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+ return
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+ }
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+ if n.maybeSplitChild(i, maxItems) {
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+ inTree := n.items[i]
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+ switch {
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+ case n.cow.less(item, inTree):
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+ // no change, we want first split node
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+ case n.cow.less(inTree, item):
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+ i++ // we want second split node
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+ default:
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+ out := n.items[i]
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+ n.items[i] = item
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+ return out, true
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+ }
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+ }
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+ return n.mutableChild(i).insert(item, maxItems)
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+}
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+
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+// get finds the given key in the subtree and returns it.
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+func (n *node[T]) get(key T) (_ T, _ bool) {
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+ i, found := n.items.find(key, n.cow.less)
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+ if found {
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+ return n.items[i], true
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+ } else if len(n.children) > 0 {
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+ return n.children[i].get(key)
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+ }
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+ return
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+}
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+
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+// min returns the first item in the subtree.
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+func min[T any](n *node[T]) (_ T, found bool) {
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+ if n == nil {
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+ return
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+ }
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+ for len(n.children) > 0 {
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+ n = n.children[0]
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+ }
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+ if len(n.items) == 0 {
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+ return
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+ }
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+ return n.items[0], true
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+}
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+
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+// max returns the last item in the subtree.
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+func max[T any](n *node[T]) (_ T, found bool) {
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+ if n == nil {
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+ return
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+ }
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+ for len(n.children) > 0 {
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+ n = n.children[len(n.children)-1]
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+ }
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+ if len(n.items) == 0 {
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+ return
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+ }
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+ return n.items[len(n.items)-1], true
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+}
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+
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+// toRemove details what item to remove in a node.remove call.
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+type toRemove int
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+
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+const (
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+ removeItem toRemove = iota // removes the given item
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+ removeMin // removes smallest item in the subtree
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+ removeMax // removes largest item in the subtree
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+)
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+
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+// remove removes an item from the subtree rooted at this node.
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+func (n *node[T]) remove(item T, minItems int, typ toRemove) (_ T, _ bool) {
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+ var i int
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+ var found bool
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+ switch typ {
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+ case removeMax:
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+ if len(n.children) == 0 {
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+ return n.items.pop(), true
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+ }
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+ i = len(n.items)
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+ case removeMin:
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+ if len(n.children) == 0 {
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+ return n.items.removeAt(0), true
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+ }
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+ i = 0
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+ case removeItem:
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+ i, found = n.items.find(item, n.cow.less)
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+ if len(n.children) == 0 {
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+ if found {
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+ return n.items.removeAt(i), true
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+ }
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+ return
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+ }
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+ default:
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+ panic("invalid type")
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+ }
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+ // If we get to here, we have children.
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+ if len(n.children[i].items) <= minItems {
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+ return n.growChildAndRemove(i, item, minItems, typ)
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+ }
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+ child := n.mutableChild(i)
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|
|
+ // 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)
|
|
|
+}
|
Akihiro Suda