- btree insertion with tests
Emir Pasic
9 years ago
parent
9563b15010
commit
28b826151a
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// Copyright (c) 2015, Emir Pasic. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Package btree implements a B tree.
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//
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// Structure is not thread safe.
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//
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// References: https://en.wikipedia.org/wiki/B-tree
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package btree
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import (
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"fmt"
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"github.com/emirpasic/gods/trees"
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"github.com/emirpasic/gods/utils"
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)
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func assertTreeImplementation() {
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var _ trees.Tree = (*Tree)(nil)
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}
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// Tree holds elements of the B-tree
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type Tree struct {
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root *Node // Root node
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comparator utils.Comparator // Key comparator
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size int // Total number of keys in the tree
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m int // Knuth order (maximum number of children)
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}
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// Node is a single element within the tree
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type Node struct {
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parent *Node
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entries []*Entry // Contained keys in node
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children []*Node // Children nodes
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}
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type Entry struct {
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key interface{}
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value interface{}
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}
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// NewWith instantiates a B-tree with the Knuth order (maximum number of children) and a custom key comparator.
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func NewWith(order int, comparator utils.Comparator) *Tree {
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if order < 2 {
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panic("Invalid order, should be at least 2")
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}
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return &Tree{m: order, comparator: comparator}
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}
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// NewWithIntComparator instantiates a B-tree with the Knuth order (maximum number of children) and the IntComparator, i.e. keys are of type int.
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func NewWithIntComparator(order int) *Tree {
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return NewWith(order, utils.IntComparator)
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}
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// NewWithStringComparator instantiates a B-tree with the Knuth order (maximum number of children) and the StringComparator, i.e. keys are of type string.
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func NewWithStringComparator(order int) *Tree {
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return NewWith(order, utils.StringComparator)
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}
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// Put inserts key-value pair node into the tree.
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// If key already exists, then its value is updated with the new value.
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// Key should adhere to the comparator's type assertion, otherwise method panics.
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func (tree *Tree) Put(key interface{}, value interface{}) {
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entry := &Entry{key: key, value: value}
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if tree.root == nil {
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tree.root = &Node{entries: []*Entry{entry}, children: []*Node{}}
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tree.size++
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return
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}
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if tree.insert(tree.root, entry) {
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tree.size++
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}
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}
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// Get searches the node in the tree by key and returns its value or nil if key is not found in tree.
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// Second return parameter is true if key was found, otherwise false.
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// Key should adhere to the comparator's type assertion, otherwise method panics.
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func (tree *Tree) Get(key interface{}) (value interface{}, found bool) {
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return nil, false
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}
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// Remove remove the node from the tree by key.
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// Key should adhere to the comparator's type assertion, otherwise method panics.
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func (tree *Tree) Remove(key interface{}) {
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// TODO
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}
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// Empty returns true if tree does not contain any nodes
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func (tree *Tree) Empty() bool {
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return tree.size == 0
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}
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// Size returns number of nodes in the tree.
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func (tree *Tree) Size() int {
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return tree.size
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}
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// Keys returns all keys in-order
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func (tree *Tree) Keys() []interface{} {
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return nil // TODO
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}
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// Values returns all values in-order based on the key.
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func (tree *Tree) Values() []interface{} {
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return nil // TODO
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}
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// Clear removes all nodes from the tree.
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func (tree *Tree) Clear() {
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tree.root = nil
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tree.size = 0
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}
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// String returns a string representation of container
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func (tree *Tree) String() string {
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str := "BTree\n"
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if !tree.Empty() {
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str += tree.root.String()
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}
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return str
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}
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func (node *Node) String() string {
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return fmt.Sprintf("%v", node.entries)
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}
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func (entry *Entry) String() string {
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return fmt.Sprintf("%v", entry.key)
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}
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func (tree *Tree) isLeaf(node *Node) bool {
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return len(node.children) == 0
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}
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func (tree *Tree) isFull(node *Node) bool {
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return len(node.entries) == tree.maxEntries()
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}
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func (tree *Tree) shouldSplit(node *Node) bool {
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return len(node.entries) > tree.maxEntries()
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}
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func (tree *Tree) maxChildren() int {
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return tree.m
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}
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func (tree *Tree) maxEntries() int {
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return tree.m - 1
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}
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func (tree *Tree) middle() int {
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return (tree.m - 1) / 2 // "-1" to favor right nodes to have more keys when splitting
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}
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func (tree *Tree) search(node *Node, entry *Entry) (index int, found bool) {
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low, high := 0, len(node.entries) - 1
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var mid int
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for low <= high {
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mid = (high + low) / 2
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compare := tree.comparator(entry.key, node.entries[mid].key)
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switch {
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case compare > 0:
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low = mid + 1
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case compare < 0:
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high = mid - 1
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case compare == 0:
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return mid, true
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}
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}
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return low, false
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}
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func (tree *Tree) insert(node *Node, entry *Entry) (inserted bool) {
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if tree.isLeaf(node) {
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return tree.insertIntoLeaf(node, entry)
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}
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return tree.insertIntoInternal(node, entry)
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}
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func (tree *Tree) insertIntoLeaf(node *Node, entry *Entry) (inserted bool) {
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insertPosition, found := tree.search(node, entry)
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if found {
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node.entries[insertPosition] = nil // GC
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node.entries[insertPosition] = entry
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return false
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}
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node.entries = append(node.entries, nil)
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copy(node.entries[insertPosition + 1:], node.entries[insertPosition:])
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node.entries[insertPosition] = entry
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tree.split(node)
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return true
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}
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func (tree *Tree) insertIntoInternal(node *Node, entry *Entry) (inserted bool) {
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insertPosition, found := tree.search(node, entry)
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if found {
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node.entries[insertPosition] = nil // GC
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node.entries[insertPosition] = entry
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return false
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}
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return tree.insert(node.children[insertPosition], entry)
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}
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func (tree *Tree) split(node *Node) {
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if !tree.shouldSplit(node) {
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return
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}
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if node == tree.root {
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tree.splitRoot()
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return
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}
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tree.splitNonRoot(node)
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}
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func (tree *Tree) splitNonRoot(node *Node) {
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middle := tree.middle()
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parent := node.parent
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left := &Node{entries: node.entries[:middle], parent: parent}
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right := &Node{entries: node.entries[middle + 1:], parent: parent}
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if !tree.isLeaf(node) {
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left.children = node.children[:middle + 1]
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right.children = node.children[middle + 1:]
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}
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insertPosition, _ := tree.search(parent, node.entries[middle])
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parent.entries = append(parent.entries, nil)
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copy(parent.entries[insertPosition + 1:], parent.entries[insertPosition:])
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parent.entries[insertPosition] = node.entries[middle]
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parent.children[insertPosition] = left
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parent.children = append(parent.children, nil)
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copy(parent.children[insertPosition + 2:], parent.children[insertPosition + 1:])
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parent.children[insertPosition + 1] = right
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node = nil // GC
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tree.split(parent)
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}
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func (tree *Tree) splitRoot() {
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middle := tree.middle()
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left := &Node{entries: tree.root.entries[:middle]}
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right := &Node{entries: tree.root.entries[middle + 1:]}
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if !tree.isLeaf(tree.root) {
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left.children = tree.root.children[:middle + 1]
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right.children = tree.root.children[middle + 1:]
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}
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newRoot := &Node{
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entries: []*Entry{tree.root.entries[middle]},
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children: []*Node{left, right},
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}
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left.parent = newRoot
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right.parent = newRoot
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tree.root = newRoot
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}
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