JavaScript/Data-Structures/Tree/AVLTree.js at master · TheAlgorithms/JavaScript · GitHub

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/**

* Adelson-Velsky and Landis Tree

* [Wikipedia](https://en.wikipedia.org/wiki/AVL_tree)

* [A video lecture](http://www.youtube.com/watch?v=TbvhGcf6UJU)

'use strict'

/**

* A utility class for comparator

* A comparator is expected to have following structure

* comp(a, b) RETURN < 0 if a < b

* RETURN > 0 if a > b

* MUST RETURN 0 if a == b

let utils

;(function (_utils) {

function comparator() {

return function (v1, v2) {

if (v1 < v2) return -1

if (v2 < v1) return 1

return 0

}

_utils.comparator = comparator

})(utils || (utils = {}))

/**

* @constructor

* A class for AVL Tree

* @argument comp - A function used by AVL Tree For Comparison

* If no argument is sent it uses utils.comparator

class AVLTree {

constructor(comp) {

/** @public comparator function */

this._comp = undefined

this._comp = comp !== undefined ? comp : utils.comparator()

/** @public root of the AVL Tree */

this.root = null

/** @public number of elements in AVL Tree */

this.size = 0

}

/* Public Functions */

/**

* For Adding Elements to AVL Tree

* @param {any} _val

* Since in AVL Tree an element can only occur once so

* if a element exists it return false

* @returns {Boolean} element added or not

add(_val) {

const prevSize = this.size

this.root = insert(this.root, _val, this)

return this.size !== prevSize

}

/**

* TO check is a particular element exists or not

* @param {any} _val

* @returns {Boolean} exists or not

find(_val) {

const temp = searchAVLTree(this.root, _val, this)

return temp != null

}

/**

* @param {any} _val

* It is possible that element doesn't exists in tree

* in that case it return false

* @returns {Boolean} if element was found and deleted

remove(_val) {

const prevSize = this.size

this.root = deleteElement(this.root, _val, this)

return prevSize !== this.size

}

// creates new Node Object

class Node {

constructor(val) {

this._val = val

this._left = null

this._right = null

this._height = 1

}

// get height of a node

const getHeight = function (node) {

if (node == null) {

return 0

}

return node._height

}

// height difference or balance factor of a node

const getHeightDifference = function (node) {

return node == null ? 0 : getHeight(node._left) - getHeight(node._right)

}

// update height of a node based on children's heights

const updateHeight = function (node) {

if (node == null) {

return

}

node._height = Math.max(getHeight(node._left), getHeight(node._right)) + 1

}

// Helper: To check if the balanceFactor is valid

const isValidBalanceFactor = (balanceFactor) =>

[0, 1, -1].includes(balanceFactor)

// rotations of AVL Tree

const leftRotate = function (node) {

const temp = node._right

node._right = temp._left

temp._left = node

updateHeight(node)

updateHeight(temp)

return temp

}

const rightRotate = function (node) {

const temp = node._left

node._left = temp._right

temp._right = node

updateHeight(node)

updateHeight(temp)

return temp

}

// check if tree is balanced else balance it for insertion

const insertBalance = function (node, _val, balanceFactor, tree) {

if (balanceFactor > 1 && tree._comp(_val, node._left._val) < 0) {

return rightRotate(node) // Left Left Case

}

if (balanceFactor < 1 && tree._comp(_val, node._right._val) > 0) {

return leftRotate(node) // Right Right Case

}

if (balanceFactor > 1 && tree._comp(_val, node._left._val) > 0) {

node._left = leftRotate(node._left) // Left Right Case

return rightRotate(node)

}

node._right = rightRotate(node._right)

return leftRotate(node)

}

// check if tree is balanced after deletion

const delBalance = function (node) {

const balanceFactor1 = getHeightDifference(node)

if (isValidBalanceFactor(balanceFactor1)) {

return node

}

if (balanceFactor1 > 1) {

if (getHeightDifference(node._left) >= 0) {

return rightRotate(node) // Left Left

}

node._left = leftRotate(node._left)

return rightRotate(node) // Left Right

}

if (getHeightDifference(node._right) > 0) {

node._right = rightRotate(node._right)

return leftRotate(node) // Right Left

}

return leftRotate(node) // Right Right

}

// implement avl tree insertion

const insert = function (root, val, tree) {

if (root == null) {

tree.size++

return new Node(val)

}

if (tree._comp(root._val, val) < 0) {

root._right = insert(root._right, val, tree)

} else if (tree._comp(root._val, val) > 0) {

root._left = insert(root._left, val, tree)

} else {

return root

}

updateHeight(root)

const balanceFactor = getHeightDifference(root)

return isValidBalanceFactor(balanceFactor)

? root

: insertBalance(root, val, balanceFactor, tree)

}

// delete am element

const deleteElement = function (root, _val, tree) {

if (root == null) {

return root

}

if (tree._comp(root._val, _val) === 0) {

// key found case

if (root._left === null && root._right === null) {

root = null

tree.size--

} else if (root._left === null) {

root = root._right

tree.size--

} else if (root._right === null) {

root = root._left

tree.size--

} else {

let temp = root._right

while (temp._left != null) {

temp = temp._left

}

root._val = temp._val

root._right = deleteElement(root._right, temp._val, tree)

}

} else {

if (tree._comp(root._val, _val) < 0) {

root._right = deleteElement(root._right, _val, tree)

} else {

root._left = deleteElement(root._left, _val, tree)

}

updateHeight(root)

root = delBalance(root)

return root

}

// search tree for a element

const searchAVLTree = function (root, val, tree) {

if (root == null) {

return null

}

if (tree._comp(root._val, val) === 0) {

return root

}

if (tree._comp(root._val, val) < 0) {

return searchAVLTree(root._right, val, tree)

}

return searchAVLTree(root._left, val, tree)

}

/**

* A Code for Testing the AVLTree

// (function test () {

// const newAVL = new AVLTree()

// const size = Math.floor(Math.random() * 1000000)

// let uniques = 0

// let i, temp, j

// const array = []

// for (i = 0; i < size; i++) {

// temp = Math.floor(Math.random() * Number.MAX_VALUE)

// if (newAVL.add(temp)) {

// uniques++

// array.push(temp)

// }

// if (newAVL.size !== uniques) {

// throw new Error('elements not inserted properly')

// }

// const findTestSize = Math.floor(Math.random() * uniques)

// for (i = 0; i < findTestSize; i++) {

// j = Math.floor(Math.random() * uniques)

// if (!newAVL.find(array[j])) {

// throw new Error('inserted elements not found')

// }

// const deleteTestSize = Math.floor(uniques * Math.random())

// for (i = 0; i < deleteTestSize; i++) {

// j = Math.floor(Math.random() * uniques)

// temp = array[j]

// if (newAVL.find(temp)) {

// if (!newAVL.remove(temp)) {

// throw new Error('delete not working properly')

// }

// })()

export { AVLTree }

JavaScript/Data-Structures/Tree/AVLTree.js at master · TheAlgorithms/JavaScript · GitHub

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