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Interval Tree

The package @flatten-js/interval-tree is an implementation of interval binary search tree according to Cormen et al. Introduction to Algorithms (2009, Section 14.3: Interval trees, pp. 348–354). Cormen shows that insertion, deletion of nodes and range queries take O(log(n)) time where n is the number of items stored in the tree.

This package is a part of flatten-js library.

Package flatten-interval-tree is not supported and will be deprecated soon.

Contacts

Follow me on Twitter @alex_bol_

Installation

npm install --save @flatten-js/interval-tree

Usage

import IntervalTree from '@flatten-js/interval-tree'

What is interval

Tree stores pairs <key, value> where key is an interval, and value is any value Interval is a pair of numbers or a pair of any comparable objects on which may be defined predicates equal, less and method max(p1, p2) that returns maximum in a pair.

When interval is an object rather than pair of numbers, this object should have properties low, high, max and implement methods less_than(), equal_to(), intersect(), not_intersect(), clone(), output(). Two static methods comparable_max(), comparable_less_than() define how to compare values in pair. This interface is described in typescript definition file index.d.ts

Axis aligned rectangle is an example of such interval. We may look at rectangle as an interval between its low left and top right corners. See Box class in flatten-js library as the example of Interval interface implementation

Example

let tree = new IntervalTree();

let intervals = [[6,8],[1,4],[5,12],[1,1],[5,7]];

// Insert interval as a key and string "val0", "val1" etc. as a value 
for (let i=0; i < intervals.length; i++) {
    tree.insert(intervals[i],"val"+i);
}

// Get array of keys sorted in ascendant order
let sorted_intervals = tree.keys;              //  expected array [[1,1],[1,4],[5,7],[5,12],[6,8]]

// Search items which keys intersect with given interval, and return array of values
let values_in_range = tree.search([2,3]);     //  expected array ['val1']

Constructor

Create new instance of interval tree

let tree = new IntervalTree()

Insert(key[, value])

Insert new item into the tree. Key is an interval object or pair of numbers [low, high]. Value may represent any value or reference to any object. If value omitted, tree will store and retrieve keys as values. Method returns reference to the inserted node

let node = tree.insert(key, value)

Exist(key,value)

Method returns true if item {key, value} exists in the tree. Method may be useful if need to support unique items.

let exist = tree.exist(key, value)

Remove(key, value)

Removes item from the tree. Returns true if item was actually deleted, false if not found

let removed = tree.remove(key, value)

Search(interval[, outputMapperFn])

Returns array of values which keys intersected with given interval.

let resp = tree.search(interval)

Optional outputMapperFn(value, key) enables to map search results into custom defined output. Example:

const composers = [
    {name: "Ludwig van Beethoven", period: [1770, 1827]},
    {name: "Johann Sebastian Bach", period: [1685, 1750]},
    {name: "Wolfgang Amadeus Mozart", period: [1756, 1791]},
    {name: "Johannes Brahms", period: [1833, 1897]},
    {name: "Richard Wagner", period: [1813, 1883]},
    {name: "Claude Debussy", period: [1862, 1918]},
    {name: "Pyotr Ilyich Tchaikovsky", period: [1840, 1893]},
    {name: "Frédéric Chopin", period: [1810, 1849]},
    {name: "Joseph Haydn", period: [1732, 1809]},
    {name: "Antonio Vivaldi", period: [1678, 1741]}
];
const tree = new IntervalTree();
for (let composer of composers)
    tree.insert(composer.period, composer.name);

// Great composers who lived in 17th century
const searchRes = tree.search( [1600,1700],
    (name, period) => {return `${name} (${period.low}-${period.high})`});

console.log(searchRes)

// expected to be 
// [ 'Antonio Vivaldi (1678-1741)', 'Johann Sebastian Bach (1685-1750)' ]

Size

Returns number of items stored in the tree (getter)

let size = tree.size

Keys

Returns tree keys in ascendant order (getter)

let keys = tree.keys

Values

Returns tree values in ascendant keys order (getter)

let values = tree.values

Items

Returns items in ascendant keys order (getter)

let items = tree.items

ForEach(visitor)

Enables to traverse the whole tree and perform operation for each item

tree.forEach( (key, value) => console.log(value) )

Map(callback)

Creates new tree with same keys using callback to transform (key,value) to a new value

let tree1 = tree.map((value, key) => (key.high-key.low))

Documentation

Documentation may be found here: https://alexbol99.github.io/flatten-interval-tree

Tests

npm test

Contributors

In lieu of a formal style guide, take care to maintain the existing coding style. Add unit tests for any new or changed functionality. Lint and test your code.

License

MIT