547 lines
12 KiB
JavaScript
547 lines
12 KiB
JavaScript
/**
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* Red-black-tree implementation.
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*
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* @module tree
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*/
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// @ts-nocheck TODO: remove or refactor this file
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const rotate = (tree, parent, newParent, n) => {
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if (parent === null) {
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tree.root = newParent
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newParent._parent = null
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} else if (parent.left === n) {
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parent.left = newParent
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} else if (parent.right === n) {
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parent.right = newParent
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} else {
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throw new Error('The elements are wrongly connected!')
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}
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}
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/**
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* @template V
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*/
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class N {
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/**
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* A created node is always red!
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*
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* @param {V} val
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*/
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constructor (val) {
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this.val = val
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this.color = true
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this._left = null
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this._right = null
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this._parent = null
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}
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isRed () { return this.color }
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isBlack () { return !this.color }
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redden () { this.color = true; return this }
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blacken () { this.color = false; return this }
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get grandparent () {
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return this.parent.parent
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}
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get parent () {
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return this._parent
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}
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get sibling () {
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return (this === this.parent.left)
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? this.parent.right
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: this.parent.left
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}
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get left () {
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return this._left
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}
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get right () {
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return this._right
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}
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set left (n) {
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if (n !== null) {
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n._parent = this
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}
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this._left = n
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}
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set right (n) {
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if (n !== null) {
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n._parent = this
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}
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this._right = n
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}
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rotateLeft (tree) {
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const parent = this.parent
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const newParent = this.right
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const newRight = this.right.left
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newParent.left = this
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this.right = newRight
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rotate(tree, parent, newParent, this)
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}
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next () {
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if (this.right !== null) {
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// search the most left node in the right tree
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let o = this.right
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while (o.left !== null) {
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o = o.left
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}
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return o
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} else {
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let p = this
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while (p.parent !== null && p !== p.parent.left) {
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p = p.parent
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}
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return p.parent
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}
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}
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prev () {
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if (this.left !== null) {
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// search the most right node in the left tree
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let o = this.left
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while (o.right !== null) {
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o = o.right
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}
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return o
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} else {
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let p = this
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while (p.parent !== null && p !== p.parent.right) {
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p = p.parent
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}
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return p.parent
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}
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}
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rotateRight (tree) {
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const parent = this.parent
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const newParent = this.left
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const newLeft = this.left.right
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newParent.right = this
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this.left = newLeft
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rotate(tree, parent, newParent, this)
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}
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getUncle () {
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// we can assume that grandparent exists when this is called!
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if (this.parent === this.parent.parent.left) {
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return this.parent.parent.right
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} else {
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return this.parent.parent.left
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}
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}
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}
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const isBlack = node =>
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node !== null ? node.isBlack() : true
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const isRed = (node) =>
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node !== null ? node.isRed() : false
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/**
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* This is a Red Black Tree implementation
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*
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* @template K,V
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*/
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export class Tree {
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constructor () {
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this.root = null
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this.length = 0
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}
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/**
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* @param {K} id
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*/
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findNext (id) {
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const nextID = id.clone()
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nextID.clock += 1
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return this.findWithLowerBound(nextID)
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}
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/**
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* @param {K} id
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*/
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findPrev (id) {
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const prevID = id.clone()
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prevID.clock -= 1
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return this.findWithUpperBound(prevID)
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}
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/**
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* @param {K} from
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*/
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findNodeWithLowerBound (from) {
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let o = this.root
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if (o === null) {
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return null
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} else {
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while (true) {
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if (from === null || (from.lessThan(o.val._id) && o.left !== null)) {
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// o is included in the bound
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// try to find an element that is closer to the bound
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o = o.left
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} else if (from !== null && o.val._id.lessThan(from)) {
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// o is not within the bound, maybe one of the right elements is..
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if (o.right !== null) {
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o = o.right
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} else {
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// there is no right element. Search for the next bigger element,
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// this should be within the bounds
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return o.next()
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}
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} else {
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return o
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}
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}
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}
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}
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/**
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* @param {K} to
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*/
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findNodeWithUpperBound (to) {
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if (to === undefined) {
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throw new Error('You must define from!')
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}
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let o = this.root
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if (o === null) {
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return null
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} else {
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while (true) {
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if ((to === null || o.val._id.lessThan(to)) && o.right !== null) {
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// o is included in the bound
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// try to find an element that is closer to the bound
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o = o.right
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} else if (to !== null && to.lessThan(o.val._id)) {
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// o is not within the bound, maybe one of the left elements is..
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if (o.left !== null) {
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o = o.left
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} else {
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// there is no left element. Search for the prev smaller element,
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// this should be within the bounds
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return o.prev()
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}
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} else {
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return o
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}
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}
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}
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}
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/**
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* @return {V}
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*/
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findSmallestNode () {
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let o = this.root
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while (o != null && o.left != null) {
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o = o.left
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}
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return o
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}
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/**
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* @param {K} from
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* @return {V}
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*/
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findWithLowerBound (from) {
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const n = this.findNodeWithLowerBound(from)
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return n == null ? null : n.val
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}
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/**
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* @param {K} to
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* @return {V}
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*/
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findWithUpperBound (to) {
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const n = this.findNodeWithUpperBound(to)
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return n == null ? null : n.val
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}
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/**
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* @param {K} from
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* @param {V} from
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* @param {function(V):void} f
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*/
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iterate (from, to, f) {
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let o
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if (from === null) {
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o = this.findSmallestNode()
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} else {
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o = this.findNodeWithLowerBound(from)
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}
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while (
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o !== null &&
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(
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to === null || // eslint-disable-line no-unmodified-loop-condition
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o.val._id.lessThan(to) ||
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o.val._id.equals(to)
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)
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) {
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f(o.val)
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o = o.next()
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}
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}
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/**
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* @param {K} id
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* @return {V|null}
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*/
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find (id) {
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const n = this.findNode(id)
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if (n !== null) {
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return n.val
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} else {
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return null
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}
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}
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/**
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* @param {K} id
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* @return {N<V>|null}
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*/
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findNode (id) {
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let o = this.root
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if (o === null) {
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return null
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} else {
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while (true) {
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if (o === null) {
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return null
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}
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if (id.lessThan(o.val._id)) {
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o = o.left
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} else if (o.val._id.lessThan(id)) {
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o = o.right
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} else {
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return o
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}
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}
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}
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}
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/**
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* @param {K} id
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*/
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delete (id) {
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let d = this.findNode(id)
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if (d == null) {
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// throw new Error('Element does not exist!')
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return
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}
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this.length--
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if (d.left !== null && d.right !== null) {
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// switch d with the greates element in the left subtree.
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// o should have at most one child.
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let o = d.left
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// find
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while (o.right !== null) {
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o = o.right
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}
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// switch
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d.val = o.val
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d = o
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}
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// d has at most one child
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// let n be the node that replaces d
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let isFakeChild
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let child = d.left || d.right
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if (child === null) {
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isFakeChild = true
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child = new N(null)
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child.blacken()
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d.right = child
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} else {
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isFakeChild = false
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}
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if (d.parent === null) {
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if (!isFakeChild) {
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this.root = child
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child.blacken()
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child._parent = null
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} else {
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this.root = null
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}
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return
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} else if (d.parent.left === d) {
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d.parent.left = child
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} else if (d.parent.right === d) {
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d.parent.right = child
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} else {
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throw new Error('Impossible!')
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}
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if (d.isBlack()) {
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if (child.isRed()) {
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child.blacken()
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} else {
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this._fixDelete(child)
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}
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}
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this.root.blacken()
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if (isFakeChild) {
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if (child.parent.left === child) {
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child.parent.left = null
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} else if (child.parent.right === child) {
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child.parent.right = null
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} else {
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throw new Error('Impossible #3')
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}
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}
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}
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_fixDelete (n) {
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if (n.parent === null) {
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// this can only be called after the first iteration of fixDelete.
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return
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}
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// d was already replaced by the child
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// d is not the root
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// d and child are black
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let sibling = n.sibling
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if (isRed(sibling)) {
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// make sibling the grandfather
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n.parent.redden()
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sibling.blacken()
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if (n === n.parent.left) {
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n.parent.rotateLeft(this)
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} else if (n === n.parent.right) {
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n.parent.rotateRight(this)
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} else {
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throw new Error('Impossible #2')
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}
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sibling = n.sibling
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}
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// parent, sibling, and children of n are black
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if (n.parent.isBlack() &&
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sibling.isBlack() &&
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isBlack(sibling.left) &&
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isBlack(sibling.right)
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) {
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sibling.redden()
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this._fixDelete(n.parent)
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} else if (n.parent.isRed() &&
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sibling.isBlack() &&
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isBlack(sibling.left) &&
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isBlack(sibling.right)
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) {
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sibling.redden()
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n.parent.blacken()
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} else {
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if (n === n.parent.left &&
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sibling.isBlack() &&
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isRed(sibling.left) &&
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isBlack(sibling.right)
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) {
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sibling.redden()
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sibling.left.blacken()
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sibling.rotateRight(this)
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sibling = n.sibling
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} else if (n === n.parent.right &&
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sibling.isBlack() &&
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isRed(sibling.right) &&
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isBlack(sibling.left)
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) {
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sibling.redden()
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sibling.right.blacken()
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sibling.rotateLeft(this)
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sibling = n.sibling
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}
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sibling.color = n.parent.color
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n.parent.blacken()
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if (n === n.parent.left) {
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sibling.right.blacken()
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n.parent.rotateLeft(this)
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} else {
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sibling.left.blacken()
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n.parent.rotateRight(this)
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}
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}
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}
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put (v) {
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const node = new N(v)
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if (this.root !== null) {
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let p = this.root // p abbrev. parent
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while (true) {
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if (node.val._id.lessThan(p.val._id)) {
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if (p.left === null) {
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p.left = node
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break
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} else {
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p = p.left
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}
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} else if (p.val._id.lessThan(node.val._id)) {
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if (p.right === null) {
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p.right = node
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break
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} else {
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p = p.right
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}
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} else {
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p.val = node.val
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return p
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}
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}
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this._fixInsert(node)
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} else {
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this.root = node
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}
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this.length++
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this.root.blacken()
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return node
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}
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_fixInsert (n) {
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if (n.parent === null) {
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n.blacken()
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return
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} else if (n.parent.isBlack()) {
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return
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}
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const uncle = n.getUncle()
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if (uncle !== null && uncle.isRed()) {
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// Note: parent: red, uncle: red
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n.parent.blacken()
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uncle.blacken()
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n.grandparent.redden()
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this._fixInsert(n.grandparent)
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} else {
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// Note: parent: red, uncle: black or null
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// Now we transform the tree in such a way that
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// either of these holds:
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// 1) grandparent.left.isRed
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// and grandparent.left.left.isRed
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// 2) grandparent.right.isRed
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// and grandparent.right.right.isRed
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if (n === n.parent.right && n.parent === n.grandparent.left) {
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n.parent.rotateLeft(this)
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// Since we rotated and want to use the previous
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// cases, we need to set n in such a way that
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// n.parent.isRed again
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n = n.left
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} else if (n === n.parent.left && n.parent === n.grandparent.right) {
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n.parent.rotateRight(this)
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// see above
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n = n.right
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}
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// Case 1) or 2) hold from here on.
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// Now traverse grandparent, make parent a black node
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// on the highest level which holds two red nodes.
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n.parent.blacken()
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n.grandparent.redden()
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if (n === n.parent.left) {
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// Case 1
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n.grandparent.rotateRight(this)
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} else {
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// Case 2
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n.grandparent.rotateLeft(this)
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}
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}
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}
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}
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