@datastructures-js/binary-search-tree

Binary Search Tree & AVL Tree (Self Balancing Tree) implementation in javascript.

Contents

• Install
• require
• import
• API
  • constructor
  • insert
  • has
  • hasKey
  • find
  • findKey
  • min
  • max
  • lowerBound (floor)
  • lowerBoundKey (floorKey)
  • upperBound (ceil)
  • upperBoundKey (ceilKey)
  • root
  • count
  • traverseInOrder
  • traversePreOrder
  • traversePostOrder
  • remove
  • removeNode
  • clear
  • BinarySearchTreeNode
  • AvlTreeNode
• Build
• License

install

npm install --save @datastructures-js/binary-search-tree

require

const {
  BinarySearchTree,
  BinarySearchTreeNode,
  AvlTree,
  AvlTreeNode
} = require('@datastructures-js/binary-search-tree');

import

import {
  BinarySearchTree,
  BinarySearchTreeNode,
  AvlTree,
  AvlTreeNode
} from '@datastructures-js/binary-search-tree';

API

constructor

constructor accepts a custom compare function to insert new values into the tree based on the returned number.

the compare function must return a number for the 3 cases:

• less than 0 to place a value on the left.
• greater than 0 to place a value on the right.
• 0 for equal values.

There is already a default compare function for primitive values (number, string).

constructor also accepts an options param, where the comparison key prob name can be passed for object types in order to search by that key directly using findKey and hasKey.

JS

BinarySearchTree

const nums = new BinarySearchTree();
const employees = new BinarySearchTree(
  (a, b) => a.id - b.id,
  { key: 'id' }
);

AvlTree

const nums = new AvlTree();
const employees = new AvlTree(
  (a, b) => a.id - b.id,
  { key: 'id' }
);

TS

interface IEmployee {
  id: number;
}

BinarySearchTree

const nums = new BinarySearchTree<number>();
const employees = new BinarySearchTree<IEmployee>((a, b) => a.id - b.id, { key: 'id' });

AvlTree

const nums = new AvlTree<number>();
const employees = new AvlTree<IEmployee>((a, b) => a.id - b.id, { key: 'id' });

insert

O(log(n))

inserts a value into the tree and returns the inserted node. Inserting an node with existing value, will update the existing node's value with the new one.

nums
  .insert(50)
  .insert(80)
  .insert(30)
  .insert(90)
  .insert(60)
  .insert(40)
  .insert(20);

employees
  .insert({ id: 50 })
  .insert({ id: 80 })
  .insert({ id: 30 })
  .insert({ id: 90 })
  .insert({ id: 60 })
  .insert({ id: 40 })
  .insert({ id: 20 });

has

O(log(n))

checks if a value exists.

nums.has(50); // true
nums.has(100); // false

employees.has({ id: 50 }); // true
employees.has({ id: 100 }); // false

hasKey

O(log(n))

checks if an object exists by its key if the comparison key prob is provided in the constructor.

employees.hasKey(50); // true
employees.hasKey(100); // false

find

O(log(n))

finds a value and returns its node.

nums.find(60).getValue(); // 60
nums.find(100); // null

employees.find({ id: 60 }).getValue(); // { id: 60 }
employees.find({ id: 100 }); // null

findKey

O(log(n))

finds a node by its object key if the comparison key prob is provided in the constructor.

employees.findKey(60).getValue(); // { id: 60 }
employees.findKey(100); // null

min

O(log(n))

finds the node with min value in the tree.

nums.min().getValue(); // 20

employees.min().getValue(); // { id: 20 }

max

O(log(n))

finds the node with max value in the tree.

nums.max().getValue(); // 90

employees.max().getValue(); // { id: 90 }

lowerBound (floor)

O(log(n))

finds the node with the biggest value less or equal a given value. You can eliminate equal values by passing second param as false. .floor is an alias to the same function.

nums.lowerBound(60).getValue(); // 60
nums.lowerBound(60, false).getValue(); // 50
nums.lowerBound(10); // null

employees.floor({ id: 60 }).getValue(); // { id: 60 }
employees.floor({ id: 60 }, false).getValue(); // { id: 50 }
employees.floor({ id: 10 }); // null

lowerBoundKey (floorKey)

O(log(n))

finds the node with the biggest key less or equal a given key if the comparison key prob is provided in the constructor. You can eliminate equal values by passing second param as false. .floorKey is an alias to the same function.

employees.floorKey(60).getValue(); // { id: 60 }
employees.floorKey(60, false).getValue(); // { id: 50 }
employees.floorKey(10); // null

upperBound (ceil)

O(log(n))

finds the node with the smallest value bigger or equal a given value. You can eliminate equal values by passing second param as false. .ceil is an alias to the same function.

nums.upperBound(75).getValue(); // 80
nums.upperBound(80).getValue(); // 80
nums.upperBound(80, false).getValue(); // 90
nums.upperBound(110); // null

employees.ceil({ id: 75 }).getValue(); // { id: 80 }
employees.ceil({ id: 80 }).getValue(); // { id: 80 }
employees.ceil({ id: 80 }, false).getValue(); // { id: 90 }
employees.ceil({ id: 110 }); // null

upperBoundKey (ceilKey)

O(log(n))

finds the node with the smallest key bigger or equal a given key if the comparison key prob is provided in the constructor. You can eliminate equal values by passing second param as false. .ceilKey is an alias to the same function.

employees.ceilKey(75).getValue(); // { id: 80 }
employees.ceilKey(80).getValue(); // { id: 80 }
employees.ceilKey(80, false).getValue(); // { id: 90 }
employees.ceilKey(110); // null

root

O(1)

returns the root node of the tree.

nums.root().getValue(); // 50

employees.root().getValue(); // { id: 50 }

count

O(1)

returns the count of nodes in the tree.

nums.count(); // 7

employees.count(); // 7

traverseInOrder

O(n)

traverses the tree in order (left-node-right). it also accepts an optional second param as a callback to abort traversal when it returns true.

nums.traverseInOrder((node) => console.log(node.getValue()));
/*
  20
  30
  40
  50
  60
  80
  90
*/

employees.traverseInOrder((node) => console.log(node.getValue()));
/*
  { id: 20 }
  { id: 30 }
  { id: 40 }
  { id: 50 }
  { id: 60 }
  { id: 80 }
  { id: 90 }
*/

let counter = 0;
const abortCb = () => counter > 1;
employees.traverseInOrder((node) => {
  console.log(node.getValue());
  counter += 1;
}, abortCb);
/*
  { id: 20 }
  { id: 30 }
*/

traversePreOrder

O(n)

traverses the tree pre order (node-left-right). it also accepts an optional second param as a callback to abort traversal when it returns true.

nums.traversePreOrder((node) => console.log(node.getValue()));
/*
  50
  30
  20
  40
  80
  60
  90
*/

employees.traversePreOrder((node) => console.log(node.getValue()));
/*
  { id: 50 }
  { id: 30 }
  { id: 20 }
  { id: 40 }
  { id: 80 }
  { id: 60 }
  { id: 90 }
*/

let counter = 0;
const abortCb = () => counter > 1;
employees.traversePreOrder((node) => {
  console.log(node.getValue());
  counter += 1;
}, abortCb);
/*
  { id: 50 }
  { id: 30 }
*/

traversePostOrder

O(n)

traverses the tree post order (left-right-node). it also accepts an optional second param as a callback to abort traversal when it returns true.

nums.traversePostOrder((node) => console.log(node.getValue()));
/*
  20
  40
  30
  60
  90
  80
  50
*/

employees.traversePostOrder((node) => console.log(node.getValue()));
/*
  { id: 20 }
  { id: 40 }
  { id: 30 }
  { id: 60 }
  { id: 90 }
  { id: 80 }
  { id: 50 }
*/

let counter = 0;
const abortCb = () => counter > 1;
employees.traversePostOrder((node) => {
  console.log(node.getValue());
  counter += 1;
}, abortCb);
/*
  { id: 20 }
  { id: 40 }
*/

remove

O(log(n))

removes a node from the tree by its value. The function will first find the node that corresponds to the value and then remove it. AVL tree will rotate nodes properly if the tree becomes unbalanced.

nums.remove(20); // true
nums.remove(100); // false
nums.count(); // 6

employees.remove({ id: 20 }); // true
employees.remove({ id: 100 }); // false
employees.count(); // 6

removeNode

O(log(n))

removes a node from the tree by its reference.

const n20 = employees.findKey(20);
employees.removeNode(n20); // true

const n50 = employees.findKey(50);
employees.removeNode(n50); // true

clear

O(1)

clears the tree.

nums.clear();
nums.count(); // 0
nums.root(); // null

employees.clear();
employees.count(); // 0
employees.root(); // null

BinarySearchTreeNode<T>

setValue

sets the node's value.

getValue

gets the node's value.

setLeft

sets the node's left child.

getLeft

gets the node's left child.

hasLeft

checks if node has a left child.

setRight

sets the node's right child.

getRight

gets the node's right child.

hasRight

checks if node has a right child.

setParent

sets the node's parent node.

getParent

gets the node's parent node.

hasParent

checks if node has a parent node.

isLeaf

checks if node is a leaf in the tree.

isRoot

check if node is the root node.

AvlTreeNode<T>

setValue

sets the node's value.

getValue

gets the node's value.

setLeft

sets the node's left child.

getLeft

gets the node's left child.

hasLeft

checks if node has a left child.

setRight

sets the node's right child.

getRight

gets the node's right child.

hasRight

checks if node has a right child.

setParent

sets the node's parent node.

getParent

gets the node's parent node.

hasParent

checks if node has a parent node.

isLeaf

checks if node is a leaf in the tree.

isRoot

check if node is the root node.

rotateLeft

Rotates self left (counter-clockwise).

rotateRight

Rotates self right (clockwise).

rotateLeftRight

Rotates left child to left then self to right.

rotateRightLeft

Rotates right child to right then self to left.

getHeight

Gets the height of the node in the tree. root height is 1.

getLeftHeight

Gets the height of left child. 0 if no left child.

getRightHeight

Gets the height of right child. 0 if no right child.

getBalance

returns the node's balance as the diff between left and right heights.

isBalanced

checks if the node is balanced. (height diff is not more/less than 1/-1)

Build

grunt build

License

The MIT License. Full License is here