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BTreeBuilder.swift
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BTreeBuilder.swift
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//
// BTreeBuilder.swift
// BTree
//
// Created by Károly Lőrentey on 2016-02-28.
// Copyright © 2016–2017 Károly Lőrentey.
//
extension BTree {
//MARK: Bulk loading initializers
/// Create a new B-tree from elements of an unsorted sequence, using a stable sort algorithm.
///
/// - Parameter elements: An unsorted sequence of arbitrary length.
/// - Parameter order: The desired B-tree order. If not specified (recommended), the default order is used.
/// - Complexity: O(count * log(`count`))
/// - SeeAlso: `init(sortedElements:order:fillFactor:)` for a (faster) variant that can be used if the sequence is already sorted.
public init<S: Sequence>(_ elements: S, dropDuplicates: Bool = false, order: Int? = nil)
where S.Element == Element {
let order = order ?? Node.defaultOrder
self.init(Node(order: order))
withCursorAtEnd { cursor in
for element in elements {
cursor.move(to: element.0, choosing: .last)
let match = !cursor.isAtEnd && cursor.key == element.0
if match {
if dropDuplicates {
cursor.element = element
}
else {
cursor.insertAfter(element)
}
}
else {
cursor.insert(element)
}
}
}
}
/// Create a new B-tree from elements of a sequence sorted by key.
///
/// - Parameter sortedElements: A sequence of arbitrary length, sorted by key.
/// - Parameter order: The desired B-tree order. If not specified (recommended), the default order is used.
/// - Parameter fillFactor: The desired fill factor in each node of the new tree. Must be between 0.5 and 1.0.
/// If not specified, a value of 1.0 is used, i.e., nodes will be loaded with as many elements as possible.
/// - Complexity: O(count)
/// - SeeAlso: `init(elements:order:fillFactor:)` for a (slower) unsorted variant.
public init<S: Sequence>(sortedElements elements: S, dropDuplicates: Bool = false, order: Int? = nil, fillFactor: Double = 1) where S.Element == Element {
var iterator = elements.makeIterator()
self.init(order: order ?? Node.defaultOrder, fillFactor: fillFactor, dropDuplicates: dropDuplicates, next: { iterator.next() })
}
internal init(order: Int, fillFactor: Double = 1, dropDuplicates: Bool = false, next: () -> Element?) {
precondition(order > 1)
precondition(fillFactor >= 0.5 && fillFactor <= 1)
let keysPerNode = Int(fillFactor * Double(order - 1) + 0.5)
assert(keysPerNode >= (order - 1) / 2 && keysPerNode <= order - 1)
var builder = BTreeBuilder<Key, Value>(order: order, keysPerNode: keysPerNode)
if dropDuplicates {
guard var buffer = next() else {
self.init(Node(order: order))
return
}
while let element = next() {
precondition(buffer.0 <= element.0)
if buffer.0 < element.0 {
builder.append(buffer)
}
buffer = element
}
builder.append(buffer)
}
else {
var lastKey: Key? = nil
while let element = next() {
precondition(lastKey == nil || lastKey! <= element.0)
lastKey = element.0
builder.append(element)
}
}
self.init(builder.finish())
}
}
private enum BuilderState {
/// The builder needs a separator element.
case separator
/// The builder is filling up a seedling node.
case element
}
/// A construct for efficiently building a fully loaded B-tree from a series of elements.
///
/// The bulk loading algorithm works growing a line of perfectly loaded saplings, in order of decreasing depth,
/// with a separator element between each of them.
///
/// Added elements are collected into a separator and a new leaf node (called the "seedling").
/// When the seedling becomes full it is appended to or recursively merged into the list of saplings.
///
/// When `finish` is called, the final list of saplings plus the last partial seedling is joined
/// into a single tree, which becomes the root.
internal struct BTreeBuilder<Key: Comparable, Value> {
typealias Node = BTreeNode<Key, Value>
typealias Element = Node.Element
typealias Splinter = Node.Splinter
private let order: Int
private let keysPerNode: Int
private var saplings: [Node]
private var separators: [Element]
private var seedling: Node
private var state: BuilderState
init(order: Int) {
self.init(order: order, keysPerNode: order - 1)
}
init(order: Int, keysPerNode: Int) {
precondition(order > 1)
precondition(keysPerNode >= (order - 1) / 2 && keysPerNode <= order - 1)
self.order = order
self.keysPerNode = keysPerNode
self.saplings = []
self.separators = []
self.seedling = Node(order: order)
self.state = .element
}
var lastKey: Key? {
switch state {
case .separator:
return saplings.last?.last?.0
case .element:
return seedling.last?.0 ?? separators.last?.0
}
}
func isValidNextKey(_ key: Key) -> Bool {
guard let last = lastKey else { return true }
return last <= key
}
mutating func append(_ element: Element) {
assert(isValidNextKey(element.0))
switch state {
case .separator:
separators.append(element)
state = .element
case .element:
seedling.append(element)
if seedling.count == keysPerNode {
closeSeedling()
state = .separator
}
}
}
private mutating func closeSeedling() {
append(sapling: seedling)
seedling = Node(order: order)
}
mutating func append(_ node: Node) {
appendWithoutCloning(node.clone())
}
mutating func appendWithoutCloning(_ node: Node) {
assert(node.order == order)
if node.isEmpty { return }
assert(isValidNextKey(node.first!.0))
if node.depth == 0 {
if state == .separator {
assert(seedling.isEmpty)
separators.append(node.elements.removeFirst())
node.count -= 1
state = .element
if node.isEmpty { return }
seedling = node
}
else if seedling.count > 0 {
let sep = seedling.elements.removeLast()
seedling.count -= 1
if let splinter = seedling.shiftSlots(separator: sep, node: node, target: keysPerNode) {
closeSeedling()
separators.append(splinter.separator)
seedling = splinter.node
}
}
else {
seedling = node
}
if seedling.count >= keysPerNode {
closeSeedling()
state = .separator
}
return
}
if state == .element && seedling.count > 0 {
let sep = seedling.elements.removeLast()
seedling.count -= 1
closeSeedling()
separators.append(sep)
}
if state == .separator {
let cursor = BTreeCursor(BTreeCursorPath(endOf: saplings.removeLast()))
cursor.moveBackward()
let separator = cursor.remove()
saplings.append(cursor.finish())
separators.append(separator)
}
assert(seedling.isEmpty)
append(sapling: node)
state = .separator
}
private mutating func append(sapling: Node) {
var sapling = sapling
while !saplings.isEmpty {
assert(saplings.count == separators.count)
var previous = saplings.removeLast()
let separator = separators.removeLast()
// Join previous saplings together until they grow at least as deep as the new one.
while previous.depth < sapling.depth {
if saplings.isEmpty {
// If the single remaining sapling is too shallow, just join it to the new sapling and call it a day.
saplings.append(Node.join(left: previous, separator: separator, right: sapling))
return
}
previous = Node.join(left: saplings.removeLast(), separator: separators.removeLast(), right: previous)
}
let fullPrevious = previous.elements.count >= keysPerNode
let fullSapling = sapling.elements.count >= keysPerNode
if previous.depth == sapling.depth + 1 && !fullPrevious && fullSapling {
// Graft node under the last sapling, as a new child branch.
previous.elements.append(separator)
previous.children.append(sapling)
previous.count += sapling.count + 1
sapling = previous
}
else if previous.depth == sapling.depth && fullPrevious && fullSapling {
// We have two full nodes; add them as two branches of a new, deeper node.
sapling = Node(left: previous, separator: separator, right: sapling)
}
else if previous.depth > sapling.depth || fullPrevious {
// The new sapling can be appended to the line and we're done.
saplings.append(previous)
separators.append(separator)
break
}
else if let splinter = previous.shiftSlots(separator: separator, node: sapling, target: keysPerNode) {
// We have made the previous sapling full; add it as a new one before trying again with the remainder.
assert(previous.elements.count == keysPerNode)
append(sapling: previous)
separators.append(splinter.separator)
sapling = splinter.node
}
else {
// We've combined the two saplings; try again with the result.
sapling = previous
}
}
saplings.append(sapling)
}
mutating func finish() -> Node {
// Merge all saplings and the seedling into a single tree.
var root: Node
if separators.count == saplings.count - 1 {
assert(seedling.count == 0)
root = saplings.removeLast()
}
else {
root = seedling
}
assert(separators.count == saplings.count)
while !saplings.isEmpty {
root = Node.join(left: saplings.removeLast(), separator: separators.removeLast(), right: root)
}
state = .element
return root
}
}