Description

ES6 implementation of the binary search tree data structure with TypeScript support.

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Contents

• Description
• Install
• In Depth
• Usage
• API
• Development
• Related
• Team
• License

Install

Yarn

yarn add binstree

NPM

npm install binstree

In Depth

A binary search tree is a rooted binary tree data structure, whose nodes contain a unique key & an associated value, and point to two distinguished left and right sub-trees. The tree satisfies the binary search property, thus the key in each node is greater than any key stored in the left sub-tree, and less than any key stored in the right sub-tree. As an imminent result of this principle, tree operations are greatly benefited, since on average each key comparison allows the operations to skip about half of the tree, so that each insertion, deletion or lookup takes time proportional to the logarithm of the number of nodes stored in the tree.

Usage

Binstree exposes a chainable API, that can be utilized through a simple and minimal syntax, allowing you to combine methods effectively.

Usage examples can be also found at the test directory.

'use strict';
const {Tree, Node} = require('binstree');

const tree = new Tree();
//=> Tree { root: null }

tree.insert(10, 'A');
// => Tree { root: Node { left: null, right: null, key: 10, value: 'A' } }

tree.root;
//=> Node { left: null, right: null, key: 10, value: 'A' }

const node = new Node(10, 'A');

tree.root.key === node.key;
//=> true

tree.root.value === node.value;
//=> true

tree.insert(5, 'B').insert(15, 'C').root;
//=> Node { left: [Node], right: [Node], key: 10, value: 'A' }

tree.root.left;
//=> Node { left: null, right: null, key: 5, value: 'B' }

tree.root.right;
//=> Node { left: null, right: null, key: 15, value: 'C' }

tree.insert(2, 'D').insert(7, 'E').insert(12, 'F').insert(20, 'G');

tree.search(5);
//=> Node { key: 5, value: 'B',
//  left: Node { left: null, right: null, key: 2, value: 'D' },
//  right: Node { left: null, right: null, key: 7, value: 'E' } }

tree.search(15);
//=> Node { key: 15, value: 'C',
//  left: Node { left: null, right: null, key: 12, value: 'F' },
//  right: Node { left: null, right: null, key: 20, value: 'G' } }

tree.includes(12);
//=> true

tree.includes(100);
//=> false

tree.height();
//=> 2

tree.isBalanced();
//=> true

tree.remove(10).root;
//=> Node { key: 12, value: 'F',
//  left: Node { left: [Node], right: [Node], key: 5, value: 'B' },
//  right: Node { left: null, right: [Node], key: 15, value: 'C' } }

tree.isBalanced();
//=> false

API

tree.insert(key, value)

• Return Type: Tree

Mutates the tree by inserting a new node at the appropriate location.

key

• Type: Number

Can be any number that will correspond to the key of the created node. Each node has its own unique key.

value

• Type: Any

Can be any value that will stored in the created node.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A');
// => Tree { root: Node { key: 10, value: 'A', left: null, right: null } }

tree.root

• Return Type: Node | null

Returns the root node of the tree. If the tree is empty null is returned.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A');
// => Tree { root: Node { key: 10, value: 'A', left: null, right: null } }
tree.root;
// => Node { key: 10, value: 'A', left: null, right: null }

tree.isEmpty()

• Return Type: Boolean

Determines whether the tree is empty, returning true or false as appropriate.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A');
tree.isEmpty();
// => false

tree.remove(key)

• Return Type: Tree

Mutates the tree by removing the node corresponding to the key argument.

key

• Type: Number

Can be any number that corresponds to the key of an existing node.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A');
tree.remove(10);
//=> Tree { root: null }

tree.includes(key)

• Return Type: Boolean

Determines whether the tree includes a node with a certain key, returning true or false as appropriate.

key

• Type: Number

Node key to search for.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B');
tree.includes(10);
// => true
tree.includes(25);
// => false
tree.includes(5);
// => true

tree.search(key)

• Return Type: Node | null

Determines whether the tree includes a node with a certain key, returning the targeted node or null as appropriate.

key

• Type: Number

Node key to search for.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B');
tree.search(10);
// => Node { key: 10, value: 'A', left: [Node], right: null }
tree.search(25);
// => null
tree.search(5);
// => Node { key: 5, value: 'B', left: null, right: null }

tree.min()

• Return Type: Node | null

Returns the left-most node in the tree, thus the node corresponding to the minimum key.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(0, 'C');
tree.min();
// => Node { key: 0, value: 'C', left: null, right: null }

tree.max()

• Return Type: Node | null

Returns the right-most node in the tree, thus the node corresponding to the maximum key.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(15, 'B').insert(25, 'C');
tree.max();
// => Node { key: 25, value: 'C', left: null, right: null }

tree.size()

• Return Type: Number

Returns the total number of nodes residing in the tree.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(15, 'B').insert(25, 'C');
tree.size();
// => 3

tree.height()

• Return Type: Number

Returns the maximum distance of any leaf node from the root. If the tree is empty -1 is returned.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A');
tree.height();
// => 0
tree.insert(15, 'B').insert(25, 'C').insert(35, 'D');
tree.height();
//=> 3

tree.inOrder(fn)

• Return Type: Tree

Applies in-order traversal (depth-first traversal - LNR) to the tree and executes the provided fn function on each traversed node without mutating the tree itself.

fn

• Type: Function

Function to execute on each node.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.inOrder(node => console.log(node.key));
// => 5
// 10
// 15

tree.preOrder(fn)

• Return Type: Tree

Applies pre-order traversal (depth-first traversal - NLR) to the tree and executes the provided fn function on each traversed node without mutating the tree itself.

fn

• Type: Function

Function to execute on each node.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.preOrder(node => console.log(node.key));
// => 10
// 5
// 15

tree.postOrder(fn)

• Return Type: Tree

Applies post-order traversal (depth-first traversal - LRN) to the tree and executes the provided fn function on each traversed node without mutating the tree itself.

fn

• Type: Function

Function to execute on each node.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.postOrder(node => console.log(node.key));
// => 5
// 15
// 10

tree.outOrder(fn)

• Return Type: Tree

Applies out-order traversal (depth-first traversal - RNL) to the tree and executes the provided fn function on each traversed node without mutating the tree itself.

fn

• Type: Function

Function to execute on each node.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.outOrder(node => console.log(node.key));
// => 15
// 10
// 5

tree.levelOrder(fn)

• Return Type: Tree

Applies level-order traversal (breadth-first traversal) to the tree and executes the provided fn function on each traversed node without mutating the tree itself.

fn

• Type: Function

Function to execute on each node.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.levelOrder(node => console.log(node.key));
// => 10
// 5
// 15

tree.clear()

• Return Type: Tree

Mutates the tree by removing all residing nodes and returns it empty.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
//=> Tree { root: Node { left: [Node], right: [Node], key: 3, value: 'A' } }
tree.size();
//=> 3
tree.clear();
//=> Tree { root: null } }
tree.size();
//=> 0

tree.toArray()

• Return Type: Array<Node>

Applies in-order traversal to the tree and stores each traversed node in an array. The array is returned at the end of the traversal.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C').insert(3, 'D').insert(20, 'F');
tree.toArray();
//=> [ 
//  Node { left: null, right: null, key: 3, value: 'D' },
//  Node { left: [Node], right: null, key: 5, value: 'B' },
//  Node { left: [Node], right: [Node], key: 10, value: 'A' },
//  Node { left: null, right: [Node], key: 15, value: 'C' },
//  Node { left: null, right: null, key: 20, value: 'F' }
// ]

tree.toPairs()

• Return Type: Array<[Number, Any]>

Applies in-order traversal to the tree and for each traversed node stores in an n-tuple, where n the size of the tree, an ordered-pair/2-tuple, where the first element is a number corresponding to the key of the traversed node, and the last one is a value of type any, corresponding to the value stored in the traversed node. The n-tuple is returned at the end of the traversal.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C').insert(3, 'D').insert(20, 'F');
tree.toPairs();
//=> [ [3, 'D'], [5, 'B'], [10, 'A'], [15, 'C'], [20, 'F'] ]

tree.leafNodes()

• Return Type: Array<Node>

Applies in-order traversal to the tree and stores each traversed leaf node (node without children) in an array. The array is returned at the end of the traversal.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.leafNodes();
//=> [ 
//  Node { left: null, right: null, key: 5, value: 'B' },
//  Node { left: null, right: null, key: 15, value: 'C' } 
// ]

tree.fullNodes()

• Return Type: Array<Node>

Applies in-order traversal to the tree and stores each traversed full node (node with two non-null children) in an array. The array is returned at the end of the traversal.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.fullNodes();
//=> [ 
//  Node { left: [Node], right: [Node], key: 10, value: 'A' } 
// ]

tree.partialNodes()

• Return Type: Array<Node>

Applies in-order traversal to the tree and stores each partial node (node with one non-null child) in an array. The array is returned at the end of the traversal.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C').insert(20, 'D').insert(3, 'E');
tree.partialNodes();
//=> [ 
//  Node { left: [Node], right: null, key: 5, value: 'B' },
//  Node { left: null, right: [Node], key: 15, value: 'C' }
// ]

tree.isBalanced()

• Return Type: Boolean

Returns true if the tree is height-balanced, which implies that its left sub-tree is balanced, its right sub-tree is balanced and the difference between heights of left sub-tree and right sub-tree is not greater than 1. In any other case, the method returns false.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.isBalanced();
//=> true
tree.insert(20, 'D').insert(30, 'E');
tree.isBalanced();
//=> false

tree.isComplete()

• Return Type: Boolean

The method returns true if the tree is a complete binary search tree, which implies that every level, except possibly the last, is completely filled, and all nodes are as far left as possible. In any other case, the method returns false.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.isComplete();
//=> true
tree.insert(3, 'D');
tree.isComplete();
//=> true
tree.insert(20, 'E');
tree.isComplete();
//=> false

tree.isFull()

• Return Type: Boolean

The method returns true if all the nodes residing in the tree are either leaf nodes or full nodes. In any other case (node degree equal to 1) the method returns false.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.isFull();
//=> true
tree.insert(8, 'D');
tree.isFull();
//=> false

tree.isPerfect()

• Return Type: Boolean

The method returns true if all the internal nodes residing in the tree are full nodes (node degree equal to 2) and all leaf nodes are at the same height level. In any other case (node degree equal to 1 or leaf and full nodes are found on the same height level) the method returns false.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(5, 'B').insert(15, 'C');
tree.isPerfect();
//=> true
tree.insert(3, 'D').insert(7, 'E').insert(12, 'F').insert(20, 'G');
tree.isPerfect();
//=> true
tree.insert(1, 'H');
tree.isPerfect();
//=> false

Also available, along with the Tree exposed class, is the Node class, mainly useful for testing purposes, since it can be utilized to compare tree nodes. The class has a binary constructor method, with a key and a value parameter, corresponding to the key and the value stored in the created instance, respectively.

node.key

• Return Type: Number

The key corresponding to the node instance.

const {Node} = require('binstree');

const node = new Node(10, 'A');
// => { key:10, value: 'A', left: null, right: null }
node.key;
//=> 10

node.value

• Return Type: Any

The value that the node contains.

const {Node} = require('binstree');

const node = new Node(10, 'A');

// => { key: 10, value: 'A', left: null, right: null }
node.value;
//=> 'A'
node.value = 'B'
// => { key: 10, value: 'B', left: null, right: null }

node.left

• Return Type: Node | null

The left sub-tree that the node points to.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root;
// => { key: 10, value: 'A', left: null, right: null }
tree.root.left;
//=> null
tree.insert(5, 'B').root;
// => { key: 10, value: 'A', left: { key: 5, value: 'B', left: null, right: null } , right: null }
tree.root.left;
//=> { key: 5, value: 'B', left: null, right: null }

node.right

• Return Type: Node | null

The right sub-tree that the node points to.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root;
// => { key: 10, value: 'A', left: null, right: null }
tree.root.right;
//=> null
tree.insert(15, 'B').root;
// => { key: 10, value: 'A', left: null , right: { key: 15, value: 'B', left: null, right: null } }
tree.root.right;
//=> { key: 15, value: 'B', left: null, right: null }

node.children

• Return Type: Array<Node>

Returns an array contacting the children of the instance, where the left child, if present, is the first element of the array, and the right child, if present, is the last element of the array.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root.children;
//=> []
tree.insert(5, 'B').insert(15, 'C').root.children;
// => [
//  { key: 5, value: 'B', left: null , right: null }, 
//  { key: 15, value: 'C', left: null, right: null }
// ]

node.degree

• Return Type: Number

Returns the number of sub-trees that the node points to.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root.degree;
//=> 0
tree.insert(5, 'B').root.degree;
//=> 1
tree.insert(15, 'C').root.degree;
//=> 2

node.height()

• Return Type: Number

Returns the maximum distance of any leaf node from the node instance.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').insert(15, 'B').insert(25, 'C').insert(35, 'D');
tree.root.height();
//=> 3
tree.root.right.height();
//=> 2

node.isFull()

• Return Type: Boolean

Determines whether a node is a full node (has two non-null children), returning true or false as appropriate.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root.isFull();
//=> false
tree.insert(5, 'B').insert(15, 'C').root.isFull();
//=> true

node.isInternal()

• Return Type: Boolean

Determines whether a node is an internal node (has at least one non-null child), returning true or false as appropriate.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root.isInternal();
//=> false
tree.insert(5, 'B').root.isInternal();
//=> true

node.isLeaf()

• Return Type: Boolean

Determines whether a node is a leaf node (has no children), returning true or false as appropriate.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root.isLeaf();
//=> true
tree.insert(5, 'B').root.isLeaf();
//=> false

node.isLeftPartial()

• Return Type: Boolean

Determines whether a node is a left partial node (has ony one left non-null child), returning true or false as appropriate.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root.isLeftPartial();
//=> false
tree.insert(5, 'B').root.isLeftPartial();
//=> true

node.isPartial()

• Return Type: Boolean

Determines whether a node is a partial node (has ony one non-null child), returning true or false as appropriate.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root.isPartial();
//=> false
tree.insert(15, 'B').root.isPartial();
//=> true

node.isRightPartial()

• Return Type: Boolean

Determines whether a node is a right partial node (has ony one right non-null child), returning true or false as appropriate.

const {Tree} = require('binstree');

const tree = new Tree();

tree.insert(10, 'A').root.isRightPartial();
//=> false
tree.insert(15, 'B').root.isRightPartial();
//=> true

node.toPair()

• Return Type: [Number, Any]

Returns an ordered-pair/2-tuple, where the first element is a number corresponding to the key of the node, and the last one is a value, that can be of any type, corresponding to the value stored in the node.

const {Node, Tree} = require('binstree');

const tree = new Tree();
const node = new Node(5, 'B');

node.toPair();
//=> [5, 'B']
tree.insert(10, 'A').root.toPair();
//=> [10, 'A']

Development

For more info on how to contribute to the project, please read the contributing guidelines.

• Fork the repository and clone it to your machine
• Navigate to your local fork: cd binstree
• Install the project dependencies: npm install or yarn install
• Lint the code and run the tests: npm test or yarn test

Related

• avlbinstree - AVL self-balancing binary search trees for ES6
• doublie - Doubly circular & linear linked lists for ES6
• mheap - Binary min & max heaps for ES6
• prioqueue - Priority queues for ES6
• singlie - Singly circular & linear linked lists for ES6

Team

• Klaus Sinani (@klaussinani)

License

MIT