trees/btree/btree.go
// Copyright (c) 2015, Emir Pasic. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Package btree implements a B tree.
//
// According to Knuth's definition, a B-tree of order m is a tree which satisfies the following properties:
// - Every node has at most m children.
// - Every non-leaf node (except root) has at least âm/2â children.
// - The root has at least two children if it is not a leaf node.
// - A non-leaf node with k children contains kâ1 keys.
// - All leaves appear in the same level
//
// Structure is not thread safe.
//
// References: https://en.wikipedia.org/wiki/B-tree
package btree
import (
"bytes"
"fmt"
"strconv"
"strings"
"github.com/emirpasic/gods/trees"
"github.com/emirpasic/gods/utils"
)
func assertTreeImplementation() {
var _ trees.Tree = (*Tree)(nil)
}
// Tree holds elements of the B-tree
type Tree struct {
Root *Node // Root node
Comparator utils.Comparator // Key comparator
size int // Total number of keys in the tree
m int // order (maximum number of children)
}
// Node is a single element within the tree
type Node struct {
Parent *Node
Entries []*Entry // Contained keys in node
Children []*Node // Children nodes
}
// Entry represents the key-value pair contained within nodes
type Entry struct {
Key interface{}
Value interface{}
}
// NewWith instantiates a B-tree with the order (maximum number of children) and a custom key comparator.
func NewWith(order int, comparator utils.Comparator) *Tree {
if order < 3 {
panic("Invalid order, should be at least 3")
}
return &Tree{m: order, Comparator: comparator}
}
// NewWithIntComparator instantiates a B-tree with the order (maximum number of children) and the IntComparator, i.e. keys are of type int.
func NewWithIntComparator(order int) *Tree {
return NewWith(order, utils.IntComparator)
}
// NewWithStringComparator instantiates a B-tree with the order (maximum number of children) and the StringComparator, i.e. keys are of type string.
func NewWithStringComparator(order int) *Tree {
return NewWith(order, utils.StringComparator)
}
// Put inserts key-value pair node into the tree.
// If key already exists, then its value is updated with the new value.
// Key should adhere to the comparator's type assertion, otherwise method panics.
func (tree *Tree) Put(key interface{}, value interface{}) {
entry := &Entry{Key: key, Value: value}
if tree.Root == nil {
tree.Root = &Node{Entries: []*Entry{entry}, Children: []*Node{}}
tree.size++
return
}
if tree.insert(tree.Root, entry) {
tree.size++
}
}
// Get searches the node in the tree by key and returns its value or nil if key is not found in tree.
// Second return parameter is true if key was found, otherwise false.
// Key should adhere to the comparator's type assertion, otherwise method panics.
func (tree *Tree) Get(key interface{}) (value interface{}, found bool) {
node, index, found := tree.searchRecursively(tree.Root, key)
if found {
return node.Entries[index].Value, true
}
return nil, false
}
// Remove remove the node from the tree by key.
// Key should adhere to the comparator's type assertion, otherwise method panics.
func (tree *Tree) Remove(key interface{}) {
node, index, found := tree.searchRecursively(tree.Root, key)
if found {
tree.delete(node, index)
tree.size--
}
}
// Empty returns true if tree does not contain any nodes
func (tree *Tree) Empty() bool {
return tree.size == 0
}
// Size returns number of nodes in the tree.
func (tree *Tree) Size() int {
return tree.size
}
// Keys returns all keys in-order
func (tree *Tree) Keys() []interface{} {
keys := make([]interface{}, tree.size)
it := tree.Iterator()
for i := 0; it.Next(); i++ {
keys[i] = it.Key()
}
return keys
}
// Values returns all values in-order based on the key.
func (tree *Tree) Values() []interface{} {
values := make([]interface{}, tree.size)
it := tree.Iterator()
for i := 0; it.Next(); i++ {
values[i] = it.Value()
}
return values
}
func min(x, y int) int {
if x < y {
return x
}
return y
}
// Visualize returns all values in the b-tree.
func (tree *Tree) Visualize() string {
it := tree.Iterator()
dotString := "digraph G{bgcolor=azure;"
nodeIndexCount := 0
subGraphNumber := 0
m := make(map[interface{}]int)
KeyNodeMap := make(map[interface{}]int)
for i := 0; it.Next(); i++ {
node := it.CurrentNode()
Entries := node.Entries
ok := false
for j := 0; j < len(node.Entries); j++ {
_, ok = m[node.Entries[j]]
if ok {
break
}
m[node.Entries[j]] = 1
}
if ok {
continue
}
dotString += "subgraph cluster_" + strconv.Itoa(subGraphNumber) + "{fontcolor=plum;style=filled;color=plum;node [style=filled,color=white, shape=\"Msquare\"];"
subGraphNumber++
stringValues := []string{}
nodeEntrySize := len(Entries)
for j := 0; j < nodeEntrySize; j++ {
stringValues = append(stringValues, fmt.Sprintf("%v", Entries[j].Key))
stringValues = append(stringValues, fmt.Sprintf("%v", Entries[j].Value))
dotString += strconv.Itoa(nodeIndexCount) + "[fontcolor=blueviolet;label=\"" + stringValues[len(stringValues)-2] + "->" + stringValues[len(stringValues)-1] + "\"];"
KeyNodeMap[Entries[j].Key] = nodeIndexCount
nodeIndexCount++
}
dotString += "};"
}
it = tree.Iterator()
m = make(map[interface{}]int)
for i := 0; it.Next(); i++ {
node := it.CurrentNode()
ok := false
for j := 0; j < len(node.Entries); j++ {
_, ok = m[node.Entries[j]]
if ok {
break
}
m[node.Entries[j]] = 1
}
if ok {
continue
}
if len(node.Children) > len(node.Entries) {
for j := 1; j < (len(node.Children)); j++ {
dotString += strconv.Itoa(KeyNodeMap[node.Entries[j-1].Key]) + "->" + strconv.Itoa(KeyNodeMap[node.Children[j].Entries[0].Key]) + ";"
}
dotString += strconv.Itoa(KeyNodeMap[node.Entries[0].Key]) + "->" + strconv.Itoa(KeyNodeMap[node.Children[0].Entries[0].Key]) + ";"
} else {
for j := 0; j < min(len(node.Children), len(node.Entries)); j++ {
dotString += strconv.Itoa(KeyNodeMap[node.Entries[j].Key]) + "->" + strconv.Itoa(KeyNodeMap[node.Children[j].Entries[0].Key]) + ";"
}
}
}
dotString += "}"
return dotString
}
// Clear removes all nodes from the tree.
func (tree *Tree) Clear() {
tree.Root = nil
tree.size = 0
}
// Height returns the height of the tree.
func (tree *Tree) Height() int {
return tree.Root.height()
}
// Left returns the left-most (min) node or nil if tree is empty.
func (tree *Tree) Left() *Node {
return tree.left(tree.Root)
}
// LeftKey returns the left-most (min) key or nil if tree is empty.
func (tree *Tree) LeftKey() interface{} {
if left := tree.Left(); left != nil {
return left.Entries[0].Key
}
return nil
}
// LeftValue returns the left-most value or nil if tree is empty.
func (tree *Tree) LeftValue() interface{} {
if left := tree.Left(); left != nil {
return left.Entries[0].Value
}
return nil
}
// Right returns the right-most (max) node or nil if tree is empty.
func (tree *Tree) Right() *Node {
return tree.right(tree.Root)
}
// RightKey returns the right-most (max) key or nil if tree is empty.
func (tree *Tree) RightKey() interface{} {
if right := tree.Right(); right != nil {
return right.Entries[len(right.Entries)-1].Key
}
return nil
}
// RightValue returns the right-most value or nil if tree is empty.
func (tree *Tree) RightValue() interface{} {
if right := tree.Right(); right != nil {
return right.Entries[len(right.Entries)-1].Value
}
return nil
}
// String returns a string representation of container (for debugging purposes)
func (tree *Tree) String() string {
var buffer bytes.Buffer
if _, err := buffer.WriteString("BTree\n"); err != nil {
}
if !tree.Empty() {
tree.output(&buffer, tree.Root, 0, true)
}
return buffer.String()
}
func (entry *Entry) String() string {
return fmt.Sprintf("%v", entry.Key)
}
func (tree *Tree) output(buffer *bytes.Buffer, node *Node, level int, isTail bool) {
for e := 0; e < len(node.Entries)+1; e++ {
if e < len(node.Children) {
tree.output(buffer, node.Children[e], level+1, true)
}
if e < len(node.Entries) {
if _, err := buffer.WriteString(strings.Repeat(" ", level)); err != nil {
}
if _, err := buffer.WriteString(fmt.Sprintf("%v", node.Entries[e].Key) + "\n"); err != nil {
}
}
}
}
func (node *Node) height() int {
height := 0
for ; node != nil; node = node.Children[0] {
height++
if len(node.Children) == 0 {
break
}
}
return height
}
func (tree *Tree) isLeaf(node *Node) bool {
return len(node.Children) == 0
}
func (tree *Tree) isFull(node *Node) bool {
return len(node.Entries) == tree.maxEntries()
}
func (tree *Tree) shouldSplit(node *Node) bool {
return len(node.Entries) > tree.maxEntries()
}
func (tree *Tree) maxChildren() int {
return tree.m
}
func (tree *Tree) minChildren() int {
return (tree.m + 1) / 2 // ceil(m/2)
}
func (tree *Tree) maxEntries() int {
return tree.maxChildren() - 1
}
func (tree *Tree) minEntries() int {
return tree.minChildren() - 1
}
func (tree *Tree) middle() int {
return (tree.m - 1) / 2 // "-1" to favor right nodes to have more keys when splitting
}
// search searches only within the single node among its entries
func (tree *Tree) search(node *Node, key interface{}) (index int, found bool) {
low, high := 0, len(node.Entries)-1
var mid int
for low <= high {
mid = (high + low) / 2
compare := tree.Comparator(key, node.Entries[mid].Key)
switch {
case compare > 0:
low = mid + 1
case compare < 0:
high = mid - 1
case compare == 0:
return mid, true
}
}
return low, false
}
// searchRecursively searches recursively down the tree starting at the startNode
func (tree *Tree) searchRecursively(startNode *Node, key interface{}) (node *Node, index int, found bool) {
if tree.Empty() {
return nil, -1, false
}
node = startNode
for {
index, found = tree.search(node, key)
if found {
return node, index, true
}
if tree.isLeaf(node) {
return nil, -1, false
}
node = node.Children[index]
}
}
func (tree *Tree) insert(node *Node, entry *Entry) (inserted bool) {
if tree.isLeaf(node) {
return tree.insertIntoLeaf(node, entry)
}
return tree.insertIntoInternal(node, entry)
}
func (tree *Tree) insertIntoLeaf(node *Node, entry *Entry) (inserted bool) {
insertPosition, found := tree.search(node, entry.Key)
if found {
node.Entries[insertPosition] = entry
return false
}
// Insert entry's key in the middle of the node
node.Entries = append(node.Entries, nil)
copy(node.Entries[insertPosition+1:], node.Entries[insertPosition:])
node.Entries[insertPosition] = entry
tree.split(node)
return true
}
func (tree *Tree) insertIntoInternal(node *Node, entry *Entry) (inserted bool) {
insertPosition, found := tree.search(node, entry.Key)
if found {
node.Entries[insertPosition] = entry
return false
}
return tree.insert(node.Children[insertPosition], entry)
}
func (tree *Tree) split(node *Node) {
if !tree.shouldSplit(node) {
return
}
if node == tree.Root {
tree.splitRoot()
return
}
tree.splitNonRoot(node)
}
func (tree *Tree) splitNonRoot(node *Node) {
middle := tree.middle()
parent := node.Parent
left := &Node{Entries: append([]*Entry(nil), node.Entries[:middle]...), Parent: parent}
right := &Node{Entries: append([]*Entry(nil), node.Entries[middle+1:]...), Parent: parent}
// Move children from the node to be split into left and right nodes
if !tree.isLeaf(node) {
left.Children = append([]*Node(nil), node.Children[:middle+1]...)
right.Children = append([]*Node(nil), node.Children[middle+1:]...)
setParent(left.Children, left)
setParent(right.Children, right)
}
insertPosition, _ := tree.search(parent, node.Entries[middle].Key)
// Insert middle key into parent
parent.Entries = append(parent.Entries, nil)
copy(parent.Entries[insertPosition+1:], parent.Entries[insertPosition:])
parent.Entries[insertPosition] = node.Entries[middle]
// Set child left of inserted key in parent to the created left node
parent.Children[insertPosition] = left
// Set child right of inserted key in parent to the created right node
parent.Children = append(parent.Children, nil)
copy(parent.Children[insertPosition+2:], parent.Children[insertPosition+1:])
parent.Children[insertPosition+1] = right
tree.split(parent)
}
func (tree *Tree) splitRoot() {
middle := tree.middle()
left := &Node{Entries: append([]*Entry(nil), tree.Root.Entries[:middle]...)}
right := &Node{Entries: append([]*Entry(nil), tree.Root.Entries[middle+1:]...)}
// Move children from the node to be split into left and right nodes
if !tree.isLeaf(tree.Root) {
left.Children = append([]*Node(nil), tree.Root.Children[:middle+1]...)
right.Children = append([]*Node(nil), tree.Root.Children[middle+1:]...)
setParent(left.Children, left)
setParent(right.Children, right)
}
// Root is a node with one entry and two children (left and right)
newRoot := &Node{
Entries: []*Entry{tree.Root.Entries[middle]},
Children: []*Node{left, right},
}
left.Parent = newRoot
right.Parent = newRoot
tree.Root = newRoot
}
func setParent(nodes []*Node, parent *Node) {
for _, node := range nodes {
node.Parent = parent
}
}
func (tree *Tree) left(node *Node) *Node {
if tree.Empty() {
return nil
}
current := node
for {
if tree.isLeaf(current) {
return current
}
current = current.Children[0]
}
}
func (tree *Tree) right(node *Node) *Node {
if tree.Empty() {
return nil
}
current := node
for {
if tree.isLeaf(current) {
return current
}
current = current.Children[len(current.Children)-1]
}
}
// leftSibling returns the node's left sibling and child index (in parent) if it exists, otherwise (nil,-1)
// key is any of keys in node (could even be deleted).
func (tree *Tree) leftSibling(node *Node, key interface{}) (*Node, int) {
if node.Parent != nil {
index, _ := tree.search(node.Parent, key)
index--
if index >= 0 && index < len(node.Parent.Children) {
return node.Parent.Children[index], index
}
}
return nil, -1
}
// rightSibling returns the node's right sibling and child index (in parent) if it exists, otherwise (nil,-1)
// key is any of keys in node (could even be deleted).
func (tree *Tree) rightSibling(node *Node, key interface{}) (*Node, int) {
if node.Parent != nil {
index, _ := tree.search(node.Parent, key)
index++
if index < len(node.Parent.Children) {
return node.Parent.Children[index], index
}
}
return nil, -1
}
// delete deletes an entry in node at entries' index
// ref.: https://en.wikipedia.org/wiki/B-tree#Deletion
func (tree *Tree) delete(node *Node, index int) {
// deleting from a leaf node
if tree.isLeaf(node) {
deletedKey := node.Entries[index].Key
tree.deleteEntry(node, index)
tree.rebalance(node, deletedKey)
if len(tree.Root.Entries) == 0 {
tree.Root = nil
}
return
}
// deleting from an internal node
leftLargestNode := tree.right(node.Children[index]) // largest node in the left sub-tree (assumed to exist)
leftLargestEntryIndex := len(leftLargestNode.Entries) - 1
node.Entries[index] = leftLargestNode.Entries[leftLargestEntryIndex]
deletedKey := leftLargestNode.Entries[leftLargestEntryIndex].Key
tree.deleteEntry(leftLargestNode, leftLargestEntryIndex)
tree.rebalance(leftLargestNode, deletedKey)
}
// rebalance rebalances the tree after deletion if necessary and returns true, otherwise false.
// Note that we first delete the entry and then call rebalance, thus the passed deleted key as reference.
func (tree *Tree) rebalance(node *Node, deletedKey interface{}) {
// check if rebalancing is needed
if node == nil || len(node.Entries) >= tree.minEntries() {
return
}
// try to borrow from left sibling
leftSibling, leftSiblingIndex := tree.leftSibling(node, deletedKey)
if leftSibling != nil && len(leftSibling.Entries) > tree.minEntries() {
// rotate right
node.Entries = append([]*Entry{node.Parent.Entries[leftSiblingIndex]}, node.Entries...) // prepend parent's separator entry to node's entries
node.Parent.Entries[leftSiblingIndex] = leftSibling.Entries[len(leftSibling.Entries)-1]
tree.deleteEntry(leftSibling, len(leftSibling.Entries)-1)
if !tree.isLeaf(leftSibling) {
leftSiblingRightMostChild := leftSibling.Children[len(leftSibling.Children)-1]
leftSiblingRightMostChild.Parent = node
node.Children = append([]*Node{leftSiblingRightMostChild}, node.Children...)
tree.deleteChild(leftSibling, len(leftSibling.Children)-1)
}
return
}
// try to borrow from right sibling
rightSibling, rightSiblingIndex := tree.rightSibling(node, deletedKey)
if rightSibling != nil && len(rightSibling.Entries) > tree.minEntries() {
// rotate left
node.Entries = append(node.Entries, node.Parent.Entries[rightSiblingIndex-1]) // append parent's separator entry to node's entries
node.Parent.Entries[rightSiblingIndex-1] = rightSibling.Entries[0]
tree.deleteEntry(rightSibling, 0)
if !tree.isLeaf(rightSibling) {
rightSiblingLeftMostChild := rightSibling.Children[0]
rightSiblingLeftMostChild.Parent = node
node.Children = append(node.Children, rightSiblingLeftMostChild)
tree.deleteChild(rightSibling, 0)
}
return
}
// merge with siblings
if rightSibling != nil {
// merge with right sibling
node.Entries = append(node.Entries, node.Parent.Entries[rightSiblingIndex-1])
node.Entries = append(node.Entries, rightSibling.Entries...)
deletedKey = node.Parent.Entries[rightSiblingIndex-1].Key
tree.deleteEntry(node.Parent, rightSiblingIndex-1)
tree.appendChildren(node.Parent.Children[rightSiblingIndex], node)
tree.deleteChild(node.Parent, rightSiblingIndex)
} else if leftSibling != nil {
// merge with left sibling
entries := append([]*Entry(nil), leftSibling.Entries...)
entries = append(entries, node.Parent.Entries[leftSiblingIndex])
node.Entries = append(entries, node.Entries...)
deletedKey = node.Parent.Entries[leftSiblingIndex].Key
tree.deleteEntry(node.Parent, leftSiblingIndex)
tree.prependChildren(node.Parent.Children[leftSiblingIndex], node)
tree.deleteChild(node.Parent, leftSiblingIndex)
}
// make the merged node the root if its parent was the root and the root is empty
if node.Parent == tree.Root && len(tree.Root.Entries) == 0 {
tree.Root = node
node.Parent = nil
return
}
// parent might underflow, so try to rebalance if necessary
tree.rebalance(node.Parent, deletedKey)
}
func (tree *Tree) prependChildren(fromNode *Node, toNode *Node) {
children := append([]*Node(nil), fromNode.Children...)
toNode.Children = append(children, toNode.Children...)
setParent(fromNode.Children, toNode)
}
func (tree *Tree) appendChildren(fromNode *Node, toNode *Node) {
toNode.Children = append(toNode.Children, fromNode.Children...)
setParent(fromNode.Children, toNode)
}
func (tree *Tree) deleteEntry(node *Node, index int) {
copy(node.Entries[index:], node.Entries[index+1:])
node.Entries[len(node.Entries)-1] = nil
node.Entries = node.Entries[:len(node.Entries)-1]
}
func (tree *Tree) deleteChild(node *Node, index int) {
if index >= len(node.Children) {
return
}
copy(node.Children[index:], node.Children[index+1:])
node.Children[len(node.Children)-1] = nil
node.Children = node.Children[:len(node.Children)-1]
}