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.

An earlier implementation, in package flatten-interval-tree, is no longer supported and will be deprecated soon. Please use this package (@flatten-js/interval-tree) instead.

Contacts

Follow me on Twitter @alex_bol_

Installation

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

Usage

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

Notes

Tree stores pairs <key,value> where key is an interval, and value is an object of any type. If value omitted, tree stores only keys.

In a <key,value> tree none of the value can be undefined.

Interval can be simply a pair of numbers or it can be a user-defined object that implements IntervalInterface described in typescript declaration 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 an example of IntervalInterface 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)' ]

Intersect_any(interval)

Returns true if intersection between given and any interval stored in the tree found

let found = tree.intersect_any(interval)

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))

Clear()

Clear tree

tree.clear()

Iterate([interval, outputMapperFn])

Returns an iterator (and iterable). Call next on the iterator to navigate to successor tree nodes and return the corresponding values. In the absence of a starting interval, the iterator will start with the lowest interval.

let iterator = tree.iterate();
let next = iterator.next().value;

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

let iterator = tree.iterate([5,5], (value, key) => key);
let next_key = iterator.next().value;

Supports for .. of syntax. Example:

for (let key of tree.iterate([5,5], (value, key) => key)) {
    if (key[0] > 8) break;
    console.log(key);
}

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

Support