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992 lines
30 KiB
Go
992 lines
30 KiB
Go
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// Copyright 2014 Google Inc. All Rights Reserved.
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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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// Package btree implements in-memory B-Trees of arbitrary degree.
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//
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// This implementation is based on google/btree (http://github.com/google/btree), and
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// much of the code is taken from there. But the API has been changed significantly,
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// particularly around iteration, and support for indexing by position has been
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// added.
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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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package btree
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import (
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"fmt"
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"sort"
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"sync"
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)
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// Key represents a key into the tree.
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type Key interface{}
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type Value interface{}
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// item is a key-value pair.
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type item struct {
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key Key
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value Value
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}
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type lessFunc func(interface{}, interface{}) bool
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// New creates a new B-Tree with the given degree and comparison function.
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//
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// New(2, less), 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 less function tests whether the current item is less than the given argument.
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// It must provide a strict weak ordering.
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// If !less(a, b) && !less(b, a), we treat this to mean a == b (i.e. the tree
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// can hold only one of a or b).
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func New(degree int, less func(interface{}, interface{}) bool) *BTree {
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if degree <= 1 {
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panic("bad degree")
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}
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return &BTree{
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degree: degree,
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less: less,
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cow: ©OnWriteContext{},
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}
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}
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// items stores items in a node.
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type items []item
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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) insertAt(index int, m item) {
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*s = append(*s, item{})
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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] = m
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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) removeAt(index int) item {
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m := (*s)[index]
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copy((*s)[index:], (*s)[index+1:])
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(*s)[len(*s)-1] = item{}
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*s = (*s)[:len(*s)-1]
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return m
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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) pop() item {
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index := len(*s) - 1
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out := (*s)[index]
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(*s)[index] = item{}
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*s = (*s)[:index]
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return out
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}
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var nilItems = make(items, 16)
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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) truncate(index int) {
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var toClear items
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*s, toClear = (*s)[:index], (*s)[index:]
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for len(toClear) > 0 {
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toClear = toClear[copy(toClear, nilItems):]
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}
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}
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// find returns the index where an item with key 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) find(k Key, less lessFunc) (index int, found bool) {
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i := sort.Search(len(s), func(i int) bool { return less(k, s[i].key) })
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// i is the smallest index of s for which k.Less(s[i].Key), or len(s).
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if i > 0 && !less(s[i-1].key, k) {
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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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// children stores child nodes in a node.
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type children []*node
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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 *children) insertAt(index int, n *node) {
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*s = append(*s, nil)
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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] = n
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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 *children) removeAt(index int) *node {
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n := (*s)[index]
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copy((*s)[index:], (*s)[index+1:])
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(*s)[len(*s)-1] = nil
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*s = (*s)[:len(*s)-1]
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return n
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}
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// pop removes and returns the last element in the list.
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func (s *children) pop() (out *node) {
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index := len(*s) - 1
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out = (*s)[index]
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(*s)[index] = nil
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*s = (*s)[:index]
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return
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}
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var nilChildren = make(children, 16)
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// truncate truncates this instance at index so that it contains only the
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// first index children. index must be less than or equal to length.
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func (s *children) truncate(index int) {
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var toClear children
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*s, toClear = (*s)[:index], (*s)[index:]
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for len(toClear) > 0 {
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toClear = toClear[copy(toClear, nilChildren):]
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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 struct {
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items items
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children children
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size int // number of items in the subtree: len(items) + sum over i of children[i].size
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cow *copyOnWriteContext
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}
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func (n *node) computeSize() int {
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sz := len(n.items)
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for _, c := range n.children {
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sz += c.size
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}
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return sz
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}
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func (n *node) checkSize() {
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sz := n.computeSize()
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if n.size != sz {
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panic(fmt.Sprintf("n.size = %d, computed size = %d", n.size, sz))
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}
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}
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func (n *node) mutableFor(cow *copyOnWriteContext) *node {
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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, 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(children, len(n.children), cap(n.children))
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}
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copy(out.children, n.children)
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out.size = n.size
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return out
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}
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func (n *node) mutableChild(i int) *node {
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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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// 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) split(i int) (item, *node) {
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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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n.size = n.computeSize()
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next.size = next.computeSize()
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return item, next
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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) 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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// The size of n doesn't change.
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return true
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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, its value will be returned.
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func (n *node) insert(m item, maxItems int, less lessFunc) (old Value, present bool) {
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i, found := n.items.find(m.key, less)
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if found {
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out := n.items[i]
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n.items[i] = m
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return out.value, true
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}
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if len(n.children) == 0 {
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n.items.insertAt(i, m)
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n.size++
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return old, false
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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 less(m.key, inTree.key):
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// no change, we want first split node
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case less(inTree.key, m.key):
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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] = m
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return out.value, true
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}
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}
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old, present = n.mutableChild(i).insert(m, maxItems, less)
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if !present {
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n.size++
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}
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return old, present
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}
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// get finds the given key in the subtree and returns the corresponding item, along with a boolean reporting
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// whether it was found.
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// If withIndex is true, it also returns the index of the key relative to the node's subtree.
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func (n *node) get(k Key, withIndex bool, less lessFunc) (item, bool, int) {
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i, found := n.items.find(k, less)
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if found {
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idx := i
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if withIndex && len(n.children) > 0 {
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idx = n.partialSize(i+1) - 1
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}
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return n.items[i], true, idx
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}
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if len(n.children) > 0 {
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m, found, idx := n.children[i].get(k, withIndex, less)
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if withIndex && found {
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idx += n.partialSize(i)
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}
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return m, found, idx
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}
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return item{}, false, -1
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}
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// Returns the size of the non-leaf node up to but not including child i.
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func (n *node) partialSize(i int) int {
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var sz int
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for j, c := range n.children {
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if j == i {
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break
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}
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sz += c.size + 1
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}
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return sz
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}
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// cursorStackForKey returns a stack of cursors for the key, along with whether the key was found and the index.
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func (n *node) cursorStackForKey(k Key, cs cursorStack, less lessFunc) (cursorStack, bool, int) {
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i, found := n.items.find(k, less)
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cs.push(cursor{n, i})
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idx := i
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if found {
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if len(n.children) > 0 {
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idx = n.partialSize(i+1) - 1
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}
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return cs, true, idx
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}
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if len(n.children) > 0 {
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cs, found, idx := n.children[i].cursorStackForKey(k, cs, less)
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return cs, found, idx + n.partialSize(i)
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}
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return cs, false, idx
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}
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// at returns the item at the i'th position in the subtree rooted at n.
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// It assumes i is in range.
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func (n *node) at(i int) item {
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if len(n.children) == 0 {
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return n.items[i]
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}
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for j, c := range n.children {
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if i < c.size {
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return c.at(i)
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}
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i -= c.size
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if i == 0 {
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return n.items[j]
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}
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i--
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}
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panic("impossible")
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}
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// cursorStackForIndex returns a stack of cursors for the index.
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// It assumes i is in range.
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func (n *node) cursorStackForIndex(i int, cs cursorStack) cursorStack {
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if len(n.children) == 0 {
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return cs.push(cursor{n, i})
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}
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for j, c := range n.children {
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if i < c.size {
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return c.cursorStackForIndex(i, cs.push(cursor{n, j}))
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}
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i -= c.size
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if i == 0 {
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return cs.push(cursor{n, j})
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}
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i--
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}
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panic("impossible")
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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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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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// remove removes an item from the subtree rooted at this node.
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func (n *node) remove(key Key, minItems int, typ toRemove, less lessFunc) (item, 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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n.size--
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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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n.size--
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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(key, less)
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if len(n.children) == 0 {
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if found {
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n.size--
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return n.items.removeAt(i), true
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}
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return item{}, false
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}
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default:
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||
|
panic("invalid type")
|
||
|
}
|
||
|
// If we get to here, we have children.
|
||
|
if len(n.children[i].items) <= minItems {
|
||
|
return n.growChildAndRemove(i, key, minItems, typ, less)
|
||
|
}
|
||
|
child := n.mutableChild(i)
|
||
|
// Either we had enough items to begin with, or we've done some
|
||
|
// merging/stealing, because we've got enough now and we're ready to return
|
||
|
// stuff.
|
||
|
if found {
|
||
|
// The item exists at index 'i', and the child we've selected can give us a
|
||
|
// predecessor, since if we've gotten here it's got > minItems items in it.
|
||
|
out := n.items[i]
|
||
|
// We use our special-case 'remove' call with typ=maxItem to pull the
|
||
|
// predecessor of item i (the rightmost leaf of our immediate left child)
|
||
|
// and set it into where we pulled the item from.
|
||
|
n.items[i], _ = child.remove(nil, minItems, removeMax, less)
|
||
|
n.size--
|
||
|
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.
|
||
|
m, removed := child.remove(key, minItems, typ, less)
|
||
|
if removed {
|
||
|
n.size--
|
||
|
}
|
||
|
return m, removed
|
||
|
}
|
||
|
|
||
|
// growChildAndRemove grows child 'i' to make sure it's possible to remove an
|
||
|
// item from it while keeping it at minItems, then calls remove to actually
|
||
|
// remove it.
|
||
|
//
|
||
|
// Most documentation says we have to do two sets of special casing:
|
||
|
// 1) item is in this node
|
||
|
// 2) item is in child
|
||
|
// In both cases, we need to handle the two subcases:
|
||
|
// A) node has enough values that it can spare one
|
||
|
// B) node doesn't have enough values
|
||
|
// For the latter, we have to check:
|
||
|
// a) left sibling has node to spare
|
||
|
// b) right sibling has node to spare
|
||
|
// c) we must merge
|
||
|
// To simplify our code here, we handle cases #1 and #2 the same:
|
||
|
// If a node doesn't have enough items, we make sure it does (using a,b,c).
|
||
|
// We then simply redo our remove call, and the second time (regardless of
|
||
|
// whether we're in case 1 or 2), we'll have enough items and can guarantee
|
||
|
// that we hit case A.
|
||
|
func (n *node) growChildAndRemove(i int, key Key, minItems int, typ toRemove, less lessFunc) (item, 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()
|
||
|
stealFrom.size--
|
||
|
child.items.insertAt(0, n.items[i-1])
|
||
|
child.size++
|
||
|
n.items[i-1] = stolenItem
|
||
|
if len(stealFrom.children) > 0 {
|
||
|
c := stealFrom.children.pop()
|
||
|
stealFrom.size -= c.size
|
||
|
child.children.insertAt(0, c)
|
||
|
child.size += c.size
|
||
|
}
|
||
|
} 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)
|
||
|
stealFrom.size--
|
||
|
child.items = append(child.items, n.items[i])
|
||
|
child.size++
|
||
|
n.items[i] = stolenItem
|
||
|
if len(stealFrom.children) > 0 {
|
||
|
c := stealFrom.children.removeAt(0)
|
||
|
stealFrom.size -= c.size
|
||
|
child.children = append(child.children, c)
|
||
|
child.size += c.size
|
||
|
}
|
||
|
} 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...)
|
||
|
child.size = child.computeSize()
|
||
|
n.cow.freeNode(mergeChild)
|
||
|
}
|
||
|
return n.remove(key, minItems, typ, less)
|
||
|
}
|
||
|
|
||
|
// BTree is an implementation of a B-Tree.
|
||
|
//
|
||
|
// BTree stores item instances in an ordered structure, allowing easy insertion,
|
||
|
// removal, and iteration.
|
||
|
//
|
||
|
// Write operations are not safe for concurrent mutation by multiple
|
||
|
// goroutines, but Read operations are.
|
||
|
type BTree struct {
|
||
|
degree int
|
||
|
less lessFunc
|
||
|
root *node
|
||
|
cow *copyOnWriteContext
|
||
|
}
|
||
|
|
||
|
// copyOnWriteContext pointers determine node ownership. A tree with a cow
|
||
|
// context equivalent to a node's cow context is allowed to modify that node.
|
||
|
// A tree whose write context does not match a node's is not allowed to modify
|
||
|
// it, and must create a new, writable copy (IE: it's a Clone).
|
||
|
//
|
||
|
// When doing any write operation, we maintain the invariant that the current
|
||
|
// node's context is equal to the context of the tree that requested the write.
|
||
|
// We do this by, before we descend into any node, creating a copy with the
|
||
|
// correct context if the contexts don't match.
|
||
|
//
|
||
|
// Since the node we're currently visiting on any write has the requesting
|
||
|
// tree's context, that node is modifiable in place. Children of that node may
|
||
|
// not share context, but before we descend into them, we'll make a mutable
|
||
|
// copy.
|
||
|
type copyOnWriteContext struct{ byte } // non-empty, because empty structs may have same addr
|
||
|
|
||
|
// 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() *BTree {
|
||
|
// Create two entirely new copy-on-write contexts.
|
||
|
// This operation effectively creates three trees:
|
||
|
// the original, shared nodes (old b.cow)
|
||
|
// the new b.cow nodes
|
||
|
// the new out.cow nodes
|
||
|
cow1, cow2 := *t.cow, *t.cow
|
||
|
out := *t
|
||
|
t.cow = &cow1
|
||
|
out.cow = &cow2
|
||
|
return &out
|
||
|
}
|
||
|
|
||
|
// maxItems returns the max number of items to allow per node.
|
||
|
func (t *BTree) maxItems() int {
|
||
|
return t.degree*2 - 1
|
||
|
}
|
||
|
|
||
|
// minItems returns the min number of items to allow per node (ignored for the
|
||
|
// root node).
|
||
|
func (t *BTree) minItems() int {
|
||
|
return t.degree - 1
|
||
|
}
|
||
|
|
||
|
var nodePool = sync.Pool{New: func() interface{} { return new(node) }}
|
||
|
|
||
|
func (c *copyOnWriteContext) newNode() *node {
|
||
|
n := nodePool.Get().(*node)
|
||
|
n.cow = c
|
||
|
return n
|
||
|
}
|
||
|
|
||
|
func (c *copyOnWriteContext) freeNode(n *node) {
|
||
|
if n.cow == c {
|
||
|
// clear to allow GC
|
||
|
n.items.truncate(0)
|
||
|
n.children.truncate(0)
|
||
|
n.cow = nil
|
||
|
nodePool.Put(n)
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// Set sets the given key to the given value in the tree. If the key is present in
|
||
|
// the tree, its value is changed and the old value is returned along with a second
|
||
|
// return value of true. If the key is not in the tree, it is added, and the second
|
||
|
// return value is false.
|
||
|
func (t *BTree) Set(k Key, v Value) (old Value, present bool) {
|
||
|
if t.root == nil {
|
||
|
t.root = t.cow.newNode()
|
||
|
t.root.items = append(t.root.items, item{k, v})
|
||
|
t.root.size = 1
|
||
|
return old, false
|
||
|
}
|
||
|
t.root = t.root.mutableFor(t.cow)
|
||
|
if len(t.root.items) >= t.maxItems() {
|
||
|
sz := t.root.size
|
||
|
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)
|
||
|
t.root.size = sz
|
||
|
}
|
||
|
|
||
|
return t.root.insert(item{k, v}, t.maxItems(), t.less)
|
||
|
}
|
||
|
|
||
|
// Delete removes the item with the given key, returning its value. The second return value
|
||
|
// reports whether the key was found.
|
||
|
func (t *BTree) Delete(k Key) (Value, bool) {
|
||
|
m, removed := t.deleteItem(k, removeItem)
|
||
|
return m.value, removed
|
||
|
}
|
||
|
|
||
|
// DeleteMin removes the smallest item in the tree and returns its key and value.
|
||
|
// If the tree is empty, it returns zero values.
|
||
|
func (t *BTree) DeleteMin() (Key, Value) {
|
||
|
item, _ := t.deleteItem(nil, removeMin)
|
||
|
return item.key, item.value
|
||
|
}
|
||
|
|
||
|
// DeleteMax removes the largest item in the tree and returns its key and value.
|
||
|
// If the tree is empty, it returns zero values.
|
||
|
func (t *BTree) DeleteMax() (Key, Value) {
|
||
|
item, _ := t.deleteItem(nil, removeMax)
|
||
|
return item.key, item.value
|
||
|
}
|
||
|
|
||
|
func (t *BTree) deleteItem(key Key, typ toRemove) (item, bool) {
|
||
|
if t.root == nil || len(t.root.items) == 0 {
|
||
|
return item{}, false
|
||
|
}
|
||
|
t.root = t.root.mutableFor(t.cow)
|
||
|
out, removed := t.root.remove(key, t.minItems(), typ, t.less)
|
||
|
if len(t.root.items) == 0 && len(t.root.children) > 0 {
|
||
|
oldroot := t.root
|
||
|
t.root = t.root.children[0]
|
||
|
t.cow.freeNode(oldroot)
|
||
|
}
|
||
|
return out, removed
|
||
|
}
|
||
|
|
||
|
// Get returns the value for the given key in the tree, or the zero value if the
|
||
|
// key is not in the tree.
|
||
|
//
|
||
|
// To distinguish a zero value from a key that is not present, use GetWithIndex.
|
||
|
func (t *BTree) Get(k Key) Value {
|
||
|
var z Value
|
||
|
if t.root == nil {
|
||
|
return z
|
||
|
}
|
||
|
item, ok, _ := t.root.get(k, false, t.less)
|
||
|
if !ok {
|
||
|
return z
|
||
|
}
|
||
|
return item.value
|
||
|
}
|
||
|
|
||
|
// GetWithIndex returns the value and index for the given key in the tree, or the
|
||
|
// zero value and -1 if the key is not in the tree.
|
||
|
func (t *BTree) GetWithIndex(k Key) (Value, int) {
|
||
|
var z Value
|
||
|
if t.root == nil {
|
||
|
return z, -1
|
||
|
}
|
||
|
item, _, index := t.root.get(k, true, t.less)
|
||
|
return item.value, index
|
||
|
}
|
||
|
|
||
|
// At returns the key and value at index i. The minimum item has index 0.
|
||
|
// If i is outside the range [0, t.Len()), At panics.
|
||
|
func (t *BTree) At(i int) (Key, Value) {
|
||
|
if i < 0 || i >= t.Len() {
|
||
|
panic("btree: index out of range")
|
||
|
}
|
||
|
item := t.root.at(i)
|
||
|
return item.key, item.value
|
||
|
}
|
||
|
|
||
|
// Has reports whether the given key is in the tree.
|
||
|
func (t *BTree) Has(k Key) bool {
|
||
|
if t.root == nil {
|
||
|
return false
|
||
|
}
|
||
|
_, ok, _ := t.root.get(k, false, t.less)
|
||
|
return ok
|
||
|
}
|
||
|
|
||
|
// Min returns the smallest key in the tree and its value. If the tree is empty, it
|
||
|
// returns zero values.
|
||
|
func (t *BTree) Min() (Key, Value) {
|
||
|
var k Key
|
||
|
var v Value
|
||
|
if t.root == nil {
|
||
|
return k, v
|
||
|
}
|
||
|
n := t.root
|
||
|
for len(n.children) > 0 {
|
||
|
n = n.children[0]
|
||
|
}
|
||
|
if len(n.items) == 0 {
|
||
|
return k, v
|
||
|
}
|
||
|
return n.items[0].key, n.items[0].value
|
||
|
}
|
||
|
|
||
|
// Max returns the largest key in the tree and its value. If the tree is empty, both
|
||
|
// return values are zero values.
|
||
|
func (t *BTree) Max() (Key, Value) {
|
||
|
var k Key
|
||
|
var v Value
|
||
|
if t.root == nil {
|
||
|
return k, v
|
||
|
}
|
||
|
n := t.root
|
||
|
for len(n.children) > 0 {
|
||
|
n = n.children[len(n.children)-1]
|
||
|
}
|
||
|
if len(n.items) == 0 {
|
||
|
return k, v
|
||
|
}
|
||
|
m := n.items[len(n.items)-1]
|
||
|
return m.key, m.value
|
||
|
}
|
||
|
|
||
|
// Len returns the number of items currently in the tree.
|
||
|
func (t *BTree) Len() int {
|
||
|
if t.root == nil {
|
||
|
return 0
|
||
|
}
|
||
|
return t.root.size
|
||
|
}
|
||
|
|
||
|
// Before returns an iterator positioned just before k. After the first call to Next,
|
||
|
// the Iterator will be at k, or at the key just greater than k if k is not in the tree.
|
||
|
// Subsequent calls to Next will traverse the tree's items in ascending order.
|
||
|
func (t *BTree) Before(k Key) *Iterator {
|
||
|
if t.root == nil {
|
||
|
return &Iterator{}
|
||
|
}
|
||
|
var cs cursorStack
|
||
|
cs, found, idx := t.root.cursorStackForKey(k, cs, t.less)
|
||
|
// If we found the key, the cursor stack is pointing to it. Since that is
|
||
|
// the first element we want, don't advance the iterator on the initial call to Next.
|
||
|
// If we haven't found the key, then the top of the cursor stack is either pointing at the
|
||
|
// item just after k, in which case we do not want to move the iterator; or the index
|
||
|
// is past the end of the items slice, in which case we do.
|
||
|
var stay bool
|
||
|
top := cs[len(cs)-1]
|
||
|
if found {
|
||
|
stay = true
|
||
|
} else if top.index < len(top.node.items) {
|
||
|
stay = true
|
||
|
} else {
|
||
|
idx--
|
||
|
}
|
||
|
return &Iterator{
|
||
|
cursors: cs,
|
||
|
stay: stay,
|
||
|
descending: false,
|
||
|
Index: idx,
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// After returns an iterator positioned just after k. After the first call to Next,
|
||
|
// the Iterator will be at k, or at the key just less than k if k is not in the tree.
|
||
|
// Subsequent calls to Next will traverse the tree's items in descending order.
|
||
|
func (t *BTree) After(k Key) *Iterator {
|
||
|
if t.root == nil {
|
||
|
return &Iterator{}
|
||
|
}
|
||
|
var cs cursorStack
|
||
|
cs, found, idx := t.root.cursorStackForKey(k, cs, t.less)
|
||
|
// If we found the key, the cursor stack is pointing to it. Since that is
|
||
|
// the first element we want, don't advance the iterator on the initial call to Next.
|
||
|
// If we haven't found the key, the the cursor stack is pointing just after the first item,
|
||
|
// so we do want to advance.
|
||
|
return &Iterator{
|
||
|
cursors: cs,
|
||
|
stay: found,
|
||
|
descending: true,
|
||
|
Index: idx,
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// BeforeIndex returns an iterator positioned just before the item with the given index.
|
||
|
// The iterator will traverse the tree's items in ascending order.
|
||
|
// If i is not in the range [0, tr.Len()], BeforeIndex panics.
|
||
|
// Note that it is not an error to provide an index of tr.Len().
|
||
|
func (t *BTree) BeforeIndex(i int) *Iterator {
|
||
|
return t.indexIterator(i, false)
|
||
|
}
|
||
|
|
||
|
// AfterIndex returns an iterator positioned just after the item with the given index.
|
||
|
// The iterator will traverse the tree's items in descending order.
|
||
|
// If i is not in the range [0, tr.Len()], AfterIndex panics.
|
||
|
// Note that it is not an error to provide an index of tr.Len().
|
||
|
func (t *BTree) AfterIndex(i int) *Iterator {
|
||
|
return t.indexIterator(i, true)
|
||
|
}
|
||
|
|
||
|
func (t *BTree) indexIterator(i int, descending bool) *Iterator {
|
||
|
if i < 0 || i > t.Len() {
|
||
|
panic("btree: index out of range")
|
||
|
}
|
||
|
if i == t.Len() {
|
||
|
return &Iterator{}
|
||
|
}
|
||
|
var cs cursorStack
|
||
|
return &Iterator{
|
||
|
cursors: t.root.cursorStackForIndex(i, cs),
|
||
|
stay: true,
|
||
|
descending: descending,
|
||
|
Index: i,
|
||
|
}
|
||
|
}
|
||
|
|
||
|
// An Iterator supports traversing the items in the tree.
|
||
|
type Iterator struct {
|
||
|
Key Key
|
||
|
Value Value
|
||
|
// Index is the position of the item in the tree viewed as a sequence.
|
||
|
// The minimum item has index zero.
|
||
|
Index int
|
||
|
|
||
|
cursors cursorStack // stack of nodes with indices; last element is the top
|
||
|
stay bool // don't do anything on the first call to Next.
|
||
|
descending bool // traverse the items in descending order
|
||
|
}
|
||
|
|
||
|
// Next advances the Iterator to the next item in the tree. If Next returns true,
|
||
|
// the Iterator's Key, Value and Index fields refer to the next item. If Next returns
|
||
|
// false, there are no more items and the values of Key, Value and Index are undefined.
|
||
|
//
|
||
|
// If the tree is modified during iteration, the behavior is undefined.
|
||
|
func (it *Iterator) Next() bool {
|
||
|
var more bool
|
||
|
switch {
|
||
|
case len(it.cursors) == 0:
|
||
|
more = false
|
||
|
case it.stay:
|
||
|
it.stay = false
|
||
|
more = true
|
||
|
case it.descending:
|
||
|
more = it.dec()
|
||
|
default:
|
||
|
more = it.inc()
|
||
|
}
|
||
|
if !more {
|
||
|
return false
|
||
|
}
|
||
|
top := it.cursors[len(it.cursors)-1]
|
||
|
item := top.node.items[top.index]
|
||
|
it.Key = item.key
|
||
|
it.Value = item.value
|
||
|
return true
|
||
|
}
|
||
|
|
||
|
// When inc returns true, the top cursor on the stack refers to the new current item.
|
||
|
func (it *Iterator) inc() bool {
|
||
|
// Useful invariants for understanding this function:
|
||
|
// - Leaf nodes have zero children, and zero or more items.
|
||
|
// - Nonleaf nodes have one more child than item, and children[i] < items[i] < children[i+1].
|
||
|
// - The current item in the iterator is top.node.items[top.index].
|
||
|
|
||
|
it.Index++
|
||
|
// If we are at a non-leaf node, the current item is items[i], so
|
||
|
// now we want to continue with children[i+1], which must exist
|
||
|
// by the node invariant. We want the minimum item in that child's subtree.
|
||
|
top := it.cursors.incTop(1)
|
||
|
for len(top.node.children) > 0 {
|
||
|
top = cursor{top.node.children[top.index], 0}
|
||
|
it.cursors.push(top)
|
||
|
}
|
||
|
// Here, we are at a leaf node. top.index points to
|
||
|
// the new current item, if it's within the items slice.
|
||
|
for top.index >= len(top.node.items) {
|
||
|
// We've gone through everything in this node. Pop it off the stack.
|
||
|
it.cursors.pop()
|
||
|
// If the stack is now empty,we're past the last item in the tree.
|
||
|
if it.cursors.empty() {
|
||
|
return false
|
||
|
}
|
||
|
top = it.cursors.top()
|
||
|
// The new top's index points to a child, which we've just finished
|
||
|
// exploring. The next item is the one at the same index in the items slice.
|
||
|
}
|
||
|
// Here, the top cursor on the stack points to the new current item.
|
||
|
return true
|
||
|
}
|
||
|
|
||
|
func (it *Iterator) dec() bool {
|
||
|
// See the invariants for inc, above.
|
||
|
it.Index--
|
||
|
top := it.cursors.top()
|
||
|
// If we are at a non-leaf node, the current item is items[i], so
|
||
|
// now we want to continue with children[i]. We want the maximum item in that child's subtree.
|
||
|
for len(top.node.children) > 0 {
|
||
|
c := top.node.children[top.index]
|
||
|
top = cursor{c, len(c.items)}
|
||
|
it.cursors.push(top)
|
||
|
}
|
||
|
top = it.cursors.incTop(-1)
|
||
|
// Here, we are at a leaf node. top.index points to
|
||
|
// the new current item, if it's within the items slice.
|
||
|
for top.index < 0 {
|
||
|
// We've gone through everything in this node. Pop it off the stack.
|
||
|
it.cursors.pop()
|
||
|
// If the stack is now empty,we're past the last item in the tree.
|
||
|
if it.cursors.empty() {
|
||
|
return false
|
||
|
}
|
||
|
// The new top's index points to a child, which we've just finished
|
||
|
// exploring. That child is to the right of the item we want to advance to,
|
||
|
// so decrement the index.
|
||
|
top = it.cursors.incTop(-1)
|
||
|
}
|
||
|
return true
|
||
|
}
|
||
|
|
||
|
// A cursor is effectively a pointer into a node. A stack of cursors identifies an item in the tree,
|
||
|
// and makes it possible to move to the next or previous item efficiently.
|
||
|
//
|
||
|
// If the cursor is on the top of the stack, its index points into the node's items slice, selecting
|
||
|
// the current item. Otherwise, the index points into the children slice and identifies the child
|
||
|
// that is next in the stack.
|
||
|
type cursor struct {
|
||
|
node *node
|
||
|
index int
|
||
|
}
|
||
|
|
||
|
// A cursorStack is a stack of cursors, representing a path of nodes from the root of the tree.
|
||
|
type cursorStack []cursor
|
||
|
|
||
|
func (s *cursorStack) push(c cursor) cursorStack {
|
||
|
*s = append(*s, c)
|
||
|
return *s
|
||
|
}
|
||
|
|
||
|
func (s *cursorStack) pop() cursor {
|
||
|
last := len(*s) - 1
|
||
|
t := (*s)[last]
|
||
|
*s = (*s)[:last]
|
||
|
return t
|
||
|
}
|
||
|
|
||
|
func (s *cursorStack) top() cursor {
|
||
|
return (*s)[len(*s)-1]
|
||
|
}
|
||
|
|
||
|
func (s *cursorStack) empty() bool {
|
||
|
return len(*s) == 0
|
||
|
}
|
||
|
|
||
|
// incTop increments top's index by n and returns it.
|
||
|
func (s *cursorStack) incTop(n int) cursor {
|
||
|
(*s)[len(*s)-1].index += n // Don't call top: modify the original, not a copy.
|
||
|
return s.top()
|
||
|
}
|