Structurae

A collection of data structures for high-performance JavaScript applications that includes:

• Binary Protocol - simple binary protocol based on DataView and defined with JSONSchema
• Bit Structures:
  • BitField & BigBitField - stores and operates on data in Numbers and BigInts treating them as bitfields.
  • BitArray - an array of bits implemented with Uint32Array.
  • Pool - manages availability of objects in object pools.
  • RankedBitArray - extends BitArray with O(1) time rank and O(logN) select methods.
• Graphs:
  • Adjacency Structures - implement adjacency list & matrix data structures.
  • Graph - extends an adjacency list/matrix structure and provides methods for traversal (BFS, DFS), pathfinding (Dijkstra, Bellman-Ford), spanning tree construction (BFS, Prim), etc.
• Grids:
  • BinaryGrid - creates a grid or 2D matrix of bits.
  • Grid - extends built-in indexed collections to handle 2 dimensional data (e.g. nested arrays).
  • SymmetricGrid - a grid to handle symmetric or triangular matrices using half the space required for a normal grid.
• Sorted Structures:
  • BinaryHeap - extends Array to implement the Binary Heap data structure.
  • SortedArray - extends Array to handle sorted data.

Usage

Node.js:

npm i structurae

import {...} from "structurae";

Deno:

import {...} from "https://deno.land/x/[email protected]/index.ts"

Documentation

• Articles:
  • Structurae: Data Structures for Heigh-Performance JavaScript
  • Structurae 1.0: Graphs, Strings, and WebAssembly
  • Binary Protocol for JavaScript

Overview

Binary Protocol

Binary data in JavaScript is represented by ArrayBuffer and accessed through TypedArrays and DataView. However, both of those interfaces are limited to working with numbers. Structurae offers a set of classes that extend the DataView interface to support using ArrayBuffers for strings, objects, and arrays. These classes ("views") form the basis for a simple binary protocol with the following features:

• smaller and faster than schema-less binary formats (e.g. BSON, MessagePack);
• supports zero-copy operations, e.g. reading and changing object fields without decoding the whole object;
• supports static typing through TypeScript;
• uses JSON Schema for schema definitions;
• does not require compilation unlike most other schema-based formats (e.g. FlatBuffers).

The protocol is operated through the View class that handles creation and caching of necessary structures for a given JSON Schema as well as simplifying serialization of tagged objects.

import { View } from "structurae";

// instantiate a view protocol
const view = new View();

// define interface for out animal objects
interface Animal {
  name: string;
  age: number;
}
// create and return a view class (extension of DataView) that handles our Animal objects
const AnimalView = view.create<Animal>({
  $id: "Pet",
  type: "object",
  properties: {
    name: { type: "string", maxLength: 10 },
    // by default, type `number` is treated as int32, but can be further specified usin `btype`
    age: { type: "number", btype: "uint8" },
  },
});
// encode our animal object
const animal = AnimalView.from({ name: "Gaspode", age: 10 });
animal instanceof DataView; //=> true
animal.byteLength; //=> 14
animal.get("age"); //=> 10
animal.set("age", 20);
animal.toJSON(); //=> { name: "Gaspode", age: 20 }

Objects and Maps

Objects by default are treated as C-like structs, the data is laid out sequentially with fixed sizes, all standard JavaScript values are supported, inluding other objects and arrays of fixed size:

interface Friend {
  name: string;
}
interface Person {
  name: string;
  fullName: Array<string>;
  bestFriend: Friend;
  friends: Array<Friend>;
}
const PersonView = view.create<Person>({
  // each object requires a unique id
  $id: "Person",
  type: "object",
  properties: {
    // the size of a string field is required and defined by maxLength
    name: { type: "string", maxLength: 10 },
    fullName: {
      type: "array",
      // the size of an array is required and defined by maxItems
      maxItems: 2,
      // all items have to be the same type
      items: { type: "string", maxLength: 20 },
    },
    // objects can be referenced with $ref using their $id
    bestFriend: { $ref: "#Friend" },
    friends: {
      type: "array",
      maxItems: 3,
      items: {
        $id: "Friend",
        type: "object",
        properties: {
          name: { type: "string", maxLength: 20 },
        },
      },
    },
  },
});
const person = Person.from({
  name: "Carrot",
  fullName: ["Carrot", "Ironfoundersson"],
  bestFriend: { name: "Sam Vimes" },
  friends: [{ name: "Sam Vimes" }],
});
person.get("name"); //=> Carrot
person.getView("name"); //=> StringView [10]
person.get("fullName"); //=> ["Carrot", "Ironfoundersson"]
person.toJSON();
//=> {
//     name: "Carrot",
//     fullName: ["Carrot", "Ironfoundersson"],
//     bestFriend: { name: "Sam Vimes" },
//     friends: [{ name: "Sam Vimes" }]
//    }

Objects that support optional fields and fields of variable size ("maps") should additionally specify btype map and list non-optional (fixed sized) fields as required:

interface Town {
  name: string;
  railstation: boolean;
  clacks?: number;
}
const TownView = view.create<Town>({
    $id: "Town",
    type: "object",
    btype: "map",
    properties: {
      // notice that maxLength is not required for optional fields in maps
      // however, if set, map with truncate longer strings to fit the maxLength
      name: { type: "string" },
      railstation: { type: "boolean" },
      // optional, nullable field
      clacks: { type: "integer" },
    }
    required: ["railstation"],
  });
const lancre = TownView.from({ name: "Lancre", railstation: false });
lancre.get("name") //=> Lancre
lancre.get("clacks") //=> undefined
lancre.byteLength //=> 19
const stoLat = TownView.from({ name: "Sto Lat", railstation: true, clacks: 1 });
stoLat.get("clacks") //=> 1
stoLat.byteLength //=> 24

The size and layout of each map instance is calculated upon creation and stored within the instance (unlike fixed sized objects, where each instance have the same size and layout). Maps are useful for densely packing objects and arrays whose size my vary greatly. There is a limitation, though, since ArrayBuffers cannot be resized, optional fields that were absent upon creation of a map view cannot be set later, and those set cannot be resized, that is, assigned a value that is greater than their current size.

For performance sake, all variable size views are encoded using single global ArrayBuffer that is 8192 bytes long, if you expect to handle bigger views, supply a bigger DataView when instantiating a view protocol:

import { View } from "structurae";

// instantiate a view protocol
const view = new View(new DataView(new ArrayBuffer(65536)));

There are certain requirements for a JSON Schema used for fixed sized objects:

• Each object should have a unique id defined with $id field. Upon initialization, the view class is stored in View.Views and accessed with the id used as the key. References made with $ref are also resolved against the id.
• For fixed sized objects, sizes of strings and arrays should be defined using maxLength and maxItems properties respectfully.
• $ref can be used to reference objects by their $id. The referenced object should be defined either in the same schema or in a schema initialized previously.
• Type number by default resolves to float64 and type integer to int32, you can use any other type by specifying it in btype property.

Objects and maps support setting default values of required fields. Default values are applied upon creation of a view:

interface House {
  size: number;
}
const House = view.create<House>({
  $id: "House",
  type: "object",
  properties: {
    size: { type: "integer", btype: "uint32", default: 100 },
  },
});
const house = House.from({} as House);
house.get("size"); //=> 100

Default values of an object can be overridden when it is nested inside another object:

interface Neighborhood {
  house: House;
  biggerHouse: House;
}
const Neighborhood = view.create<Neighborhood>({
  $id: "Neighborhood",
  type: "object",
  properties: {
    house: { $ref: "#House" },
    biggerHouse: { $ref: "#House", default: { size: 200 } },
  },
});
const neighborhood = Neighborhood.from({} as Neighborhood);
neighborhood.get("house"); //=> { size: 100 }
neighborhood.get("biggerHouse"); //=> { size: 200 }

Dictionaries

Objects and maps described above assume that all properties of encoded objects are known and defined beforehand, however, if the properties are not known, and we are dealing with an object used as a lookup table (also called map, hash map, or records in TypeScript) with varying amount of properties and known type of values, we can use a dictionary view:

const NumberDict = view.create<Record<number, string | undefined>>({
  $id: "NumberDict",
  type: "object",
  btype: "dict", // dictionaries use btype dict
  // the type of keys are defined in the `propertyNames` field of a schema
  // the keys must be either fixed sized strings or numbers
  propertyNames: { type: "number", btype: "uint8" },
  // the type of values defined in `addtionalProperties` field
  // values can be of any supported type
  additionalProperties: { type: "string" },
});
const dict = NumberDict.from({ 1: "a", 2: "bcd", 3: undefined });
dict.get(1); //=> "a"
dict.get(3); //=> undefined
dict.get(10); //=> undefined
dict.get(2); //=> "bcd"

Arrays and Vectors

The protocol supports arrays of non-nullable fixed sized values (numbers, strings of fixed maximum size, objects) and vectors--arrays with nullable or variable sized values. The type of items held by both "container" views is defined in items field of the schema.

const Street = view.create<Array<House>>({
  type: "array",
  items: {
    type: "object",
    // we can also reference previously created class with $ref
    $ref: "#House",
  },
});
const street = Street.from([{ size: 10 }, { size: 20 }]);
street.byteLength; //=> 8
street.get(0); //=> { size: 10 }
street.getView(0).get("size"); //=> 10
street.size; //=> 2
street.set(0, { size: 100 });
street.get(0); //=> { size: 100 }

For vectors set btype to vector:

const Names = view.create<Array<string | undefined>>({
  type: "array",
  btype: "vector",
  items: {
    type: "string",
  },
});
const witches = Names.from([
  "Granny Weatherwax",
  "Nanny Ogg",
  undefined,
  "Magrat Garlick",
]);
witches.byteLength; //=> 64
witches.get(0); //=> "Granny Weatherwax"
witches.get(2); //=> undefined

As with maps, the layout of vectors is calculated upon creation and editing is limited to the items present upon creation.

Strings

The protocol handles strings through StringView, an extension of DataView that handles string serialization. It also offers a handful of convenience methods to operate on encoded strings so that some common operations can be performed without decoding the string:

import { StringView } from "structurae";

let stringView = StringView.from("abc😀a");
//=> StringView [ 97, 98, 99, 240, 159, 152, 128, 97 ]
stringView.toString(); //=> "abc😀a"
stringView == "abc😀a"; //=> true

stringView = StringView.from("abc😀");
// length of the view in bytes
stringView.length; //=> 8
// the amount of characters in the string
stringView.size; //=> 4
// get the first character in the string
stringView.charAt(0); //=> "a"
// get the fourth character in the string
stringView.charAt(3); //=> "😀"
// iterate over characters
[...stringView.characters()]; //=> ["a", "b", "c", "😀"]
stringView.substring(0, 4); //=> "abc😀"

stringView = StringView.from("abc😀a");
const searchValue = StringView.from("😀");
stringView.indexOf(searchValue); //=> 3
const replacement = StringView.from("d");
stringView.replace(searchValue, replacement).toString(); //=> "abcda"
stringView.reverse().toString(); //=> "adcba"

Tagged Objects

When transferring our buffers encoded with views we can often rely on meta information to know what kind of view to use in order to decode a received buffer. However, sometimes we might want our views to carry that information within themselves. To do that, we can prepend or tag each view with a value indicating its class, i.e. add a field that defaults to a certain value for each view class. Now upon receiving a buffer we can read that field using the DataView and convert it into an appropriate view.

The View class offers a few convenience methods to simplify this process:

import { View } from "structurae";
interface Dog {
  tag: 0;
  name: string;
}
interface Cat {
  tag: 1;
  name: string;
}
const DogView = view.create<Dog>({
  type: "object",
  $id: "Dog",
  properties: {
    // the tag field with default value
    tag: { type: "number", btype: "uint8", default: 0 }
    name: { type: "string", maxLength: 10 }
  },
});
const CatView = view.create<Cat>({
  type: "object",
  $id: "Cat",
  properties: {
    // the tag field with default value
    tag: { type: "number", btype: "uint8", default: 1 }
    name: { type: "string", maxLength: 10 }
  },
});

// now we can encode tagged objects without specifying views first:
const animal = view.encode({ tag: 0, name: "Gaspode" });
// and decode them:
view.decode(animal) //=> { tag: 0, name: "Gaspode" }

Extending View Types

The view protocol is designed with extensibility in mind. While built-in view types are ample for most cases, creating a special type can reduce boilerplate in certain situations. You can check out a full example of creating and using a custom view type for BitArray in examples/bit-array-view.

To create a new view type, first create a class extending DataView and implementing one of the view type interfaces, for example PrimitiveView:

export class BitArrayView extends DataView implements PrimitiveView<BitArray> {
  ...
}

To let TypeScript know about our new type, we use module augmentation to add our new type name to ViewSchemaTypeMap interface:

declare module "structurae" {
  interface ViewSchemaTypeMap {
    bitarray: "string";
  }
}

This way, it will be a binary subtype (or btype) of JSONSchema type string.

And finally, we add the new class to the list of views used by our protocol instance:

const protocol = new View();
protocol.Views.set("bitarray", BitArrayView);

Now we can use the new type in our schemas, for example:

class UserSettings {
  id = 0;
  settings = new BitArray(3);
}

const UserSettingsView = protocol.create<UserSettings>({
  $id: "UserSettings",
  type: "object",
  properties: {
    id: { type: "integer" },
    settings: {
      type: "string",
      btype: "bitarray",
      maxLength: 12,
    },
  },
}, UserSettings);

Bit Structures

BitField & BigBitField

BitField and BigBitField use JavaScript Numbers and BigInts respectively as bitfields to store and operate on data using bitwise operations. By default, BitField operates on 31 bit long bitfield where bits are indexed from least significant to most:

import { BitField } from "structurae";

const bitfield = new BitField(29); // 29 === 0b11101
bitfield.get(0); //=> 1
bitfield.get(1); //=> 0
bitfield.has(2, 3, 4); //=> true

You can use BitFieldMixin or BigBitFieldMixin with your own schema by specifying field names and their respective sizes in bits:

const Field = BitFieldMixin({ width: 8, height: 8 });
const field = new Field({ width: 100, height: 200 });
field.get("width"); //=> 100;
field.get("height"); //=> 200
field.set("width", 18);
field.get("width"); //=> 18
field.toObject(); //=> { width: 18, height: 200 }

If the total size of your fields exceeds 31 bits, use BigBitFieldMixin that internally uses a BigInt to represent the resulting number, however, you can still use normal numbers to set each field and get their value as a number as well:

const LargeField = BitFieldMixin({ width: 20, height: 20 });
const largeField = new LargeField([1048576, 1048576]);
largeField.value; //=> 1099512676352n
largeField.set("width", 1000).get("width"); //=> 1000

If you have to add more fields to your schema later on, you do not have to re-encode your existing values, just add new fields at the end of your new schema:

const OldField = BitFieldMixin({ width: 8, height: 8 });
const oldField = OldField.encode([20, 1]);
//=> oldField === 276

const NewField = BitFieldMixin({ width: 8, height: 8, area: 10 });
const newField = new NewField(oldField);
newField.get("width"); //=> 20
newField.get("height"); //=> 1
newField.set("weight", 100).get("weight"); //=> 100

If you only want to encode or decode a set of field values without creating an instance, you can do so by using static methods BitField.encode and BitField.decode respectively:

const Field = BitFieldMixin({ width: 7, height: 1 });

Field.encode([20, 1]); //=> 41
Field.encode({ height: 1, width: 20 }); //=> 41
Field.decode(41); //=> { width: 20, height: 1 }

If you don't know beforehand how many bits you need for your field, you can call BitField.getMinSize with the maximum possible value of your field to find out:

BitField.getMinSize(100); //=> 7
const Field = BitFieldMixin({ width: BitField.getMinSize(250), height: 8 });

For performance sake, BitField doesn't check the size of values being set and setting values that exceed the specified field size will lead to undefined behavior. If you want to check whether values fit their respective fields, you can use BitField.isValid:

const Field = BitFieldMixin({ width: 7, height: 1 });

Field.isValid({ width: 100 }); //=> true
Field.isValid({ width: 100, height: 3 }); //=> false

BitField#match (and its static variation BitField.match) can be used to check values of multiple fields at once:

const Field = BitFieldMixin({ width: 7, height: 1 });
const field = new Field([20, 1]);
field.match({ width: 20 }); //=> true
field.match({ height: 1, width: 20 }); //=> true
field.match({ height: 1, width: 19 }); //=> false
Field.match(field.valueOf(), { height: 1, width: 20 }); //=> true

If you have to check multiple BitField instances for the same values, create a special matcher with BitField.getMatcher and use it in the match method, that way each check will require only one bitwise operation and a comparison:

const Field = BitFieldMixin({ width: 7, height: 1 });
const matcher = Field.getMatcher({ height: 1, width: 20 });
Field.match(new Field([20, 1]).valueOf(), matcher); //=> true
Field.match(new Field([19, 1]).valueOf(), matcher); //=> false

BitArray

BitArray uses Uint32Array as an array or vector of bits. It's a simpler version of BitField that only sets and checks individual bits:

const array = new BitArray(10);
array.getBit(0); //=> 0
array.setBit(0).getBit(0); //=> 1
array.size; //=> 10
array.length; //=> 1

BitArray is the base class for Pool and RankedBitArray classes. It's useful in cases where one needs more bits than can be stored in a number, but doesn't want to use BigInts as it is done by BitField.

Pool

Implements a fast algorithm to manage availability of objects in an object pool using a BitArray.

const { Pool } = require("structurae");

// create a pool of 1600 indexes
const pool = new Pool(100 * 16);

// get the next available index and make it unavailable
pool.get(); //=> 0
pool.get(); //=> 1

// set index available
pool.free(0);
pool.get(); //=> 0
pool.get(); //=> 2

RankedBitArray

RankedBitArray is an extension of BitArray with methods to efficiently calculate rank and select. The rank is calculated in constant time where as select has O(logN) time complexity. This is often used as a basic element in implementing succinct data structures.

const array = new RankedBitArray(10);
array.setBit(1).setBit(3).setBit(7);
array.rank(2); //=> 1
array.rank(7); //=> 2
array.select(2); //=> 3

Graphs

Structurae offers classes that implement adjacency list (AdjacencyList) and adjacency matrix (AdjacencyMatrixUnweightedDirected, AdjacencyMatrixUnweightedUndirected, AdjacencyMatrixWeightedDirected, AdjacencyMatrixWeightedUnirected) as basic primitives to represent graphs using TypedArrays, and the Graph class that extends the adjacency structures to offer methods for traversing graphs (BFS, DFS), pathfinding (Dijkstra, Bellman-Ford), and spanning tree construction (BFS, Prim).

Adjacency Structures

AdjacencyList implements adjacency list data structure extending a TypedArray class. The adjacency list requires less storage space: number of vertices + number of edges * 2 (for a weighted list). However, adding and removing edges is much slower since it involves shifting/unshifting values in the underlying typed array.

import { AdjacencyListMixin } from "structurae";

const List = AdjacencyListMixin(Int32Array);
const graph = List.create(6, 6);

// the length of a weighted graph is vertices + edges * 2 + 1
graph.length; //=> 19
graph.addEdge(0, 1, 5);
graph.addEdge(0, 2, 1);
graph.addEdge(2, 4, 1);
graph.addEdge(2, 5, 2);
graph.hasEdge(0, 1); //=> true
graph.hasEdge(0, 4); //=> false
graph.outEdges(2); //=> [4, 5]
graph.inEdges(2); //=> [0]
graph.hasEdge(0, 1); //=> true
graph.getEdge(0, 1); //=> 5

Since the maximum amount of egdes in AdjacencyList is limited to the number specified at creation, adding edges can overflow throwing a RangeError. If that's a possibility, use AdjacencyList#isFull method to check if the limit is reached before adding an edge.

AdjacencyMatrixUnweightedDirected and AdjacencyMatrixUnweightedUndirected implement adjacency matrix data structure for unweighted graphs representing each edge by a single bit in an underlying ArrayBuffer.

AdjacencyMatrixWeightedDirected and AdjacencyMatrixWeightedUnirected implement adjacency matrix for weighted graphs extending a given TypedArray to store the weights akin to Grid.

import {
  AdjacencyMatrixUnweightedDirected,
  AdjacencyMatrixWeightedDirectedMixin,
} from "structurae";

// creates a class for directed graphs that uses Int32Array for edge weights
const Matrix = AdjacencyMatrixWeightedDirectedMixin(Int32Array);

const unweightedMatrix = new AdjacencyMatrixUnweightedDirected.create(6);
unweightedMatrix.addEdge(0, 1);
unweightedMatrix.addEdge(0, 2);
unweightedMatrix.addEdge(0, 3);
unweightedMatrix.addEdge(2, 4);
unweightedMatrix.addEdge(2, 5);
unweightedMatrix.hasEdge(0, 1); //=> true
unweightedMatrix.hasEdge(0, 4); //=> false
unweightedMatrix.outEdges(2); //=> [4, 5]
unweightedMatrix.inEdges(2); //=> [0]

const weightedMatrix = Matrix.create(6);
weightedMatrix.addEdge(0, 1, 3);
weightedMatrix.hasEdge(0, 1); //=> true
weightedMatrix.hasEdge(1, 0); //=> false
weightedMatrix.getEdge(1, 0); //=> 3

Graph

Graph extends a provided adjacency structure with methods for traversing, pathfinding, and spanning tree construction that use various graph algorithms.

import {
  AdjacencyMatrixUnweightedDirected,
  AdjacencyMatrixWeightedDirectedMixin,
  GraphMixin,
} from "structurae";

// create a graph for directed unweighted graphs that use adjacency list structure
const UnweightedGraph = GraphMixin(AdjacencyMatrixUnweightedDirected);

// for directed weighted graphs that use adjacency matrix structure
const WeightedGraph = GraphMixin(
  AdjacencyMatrixWeightedDirectedMixin(Int32Array),
);

The traversal is done by a generator function Graph#traverse that can be configured to use Breadth-First or Depth-First traversal, as well as returning vertices on various stages of processing, i.e. only return vertices that are fully processed (black), or being processed (gray), or just encountered (white):

const graph = WeightedGraph.create(6);
graph.addEdge(0, 1, 3);
graph.addEdge(0, 2, 2);
graph.addEdge(0, 3, 1);
graph.addEdge(2, 4, 8);
graph.addEdge(2, 5, 6);

// a BFS traversal results
[...graph.traverse()]; //=> [0, 1, 2, 3, 4, 5]

// DFS
[...graph.traverse(true)]; //=> [0, 3, 2, 5, 4, 1]

// BFS yeilding only non-encountered ("white") vertices starting from 0
[...graph.traverse(false, 0, false, true)]; //=> [1, 2, 3, 4, 5]

Graph#path returns the list of vertices constituting the shortest path between two given vertices. By default, the class uses BFS based search for unweighted graphs, and Bellman-Ford algorithm for weighted graphs. However, the method can be configured to use other algorithms by specifying arguments of the function:

graph.path(0, 5); // uses Bellman-Ford by default
graph.path(0, 5, true); // the graph is acyclic, uses DFS
graph.path(0, 5, false, true); // the graph might have cycles, but has no negative edges, uses Dijkstra

Grids

BinaryGrid

BinaryGrid creates a grid or 2D matrix of bits and provides methods to operate on it:

import { BinaryGrid } from "structurae";

// create a grid of 2 rows and 8 columns
const bitGrid = BinaryGrid.create(2, 8);
bitGrid.setValue(0, 0).setValue(0, 2).setValue(0, 5);
bitGrid.getValue(0, 0); //=> 1
bitGrid.getValue(0, 1); //=> 0
bitGrid.getValue(0, 2); //=> 1

BinaryGrid packs bits into numbers like BitField and holds them in an ArrayBuffer, thus occupying the smallest possible space.

Grid

Grid extends a provided Array or TypedArray class to efficiently handle 2 dimensional data without creating nested arrays. Grid "unrolls" nested arrays into a single array and pads its "columns" to the nearest power of 2 in order to employ quick lookups with bitwise operations.

import { GridMixin } from "structurae";

const ArrayGrid = GridMixin(Array);

// create a grid of 5 rows and 4 columns
const grid = ArrayGrid.create(5, 4);
grid.length; //=> 20
grid[0]; //=> 0

// create a grid from existing data:
const dataGrid = new ArrayGrid([
  1,
  2,
  3,
  4,
  5,
  6,
  7,
  8,
]);
// set columns number:
dataGrid.columns = 4;
dataGrid.getValue(1, 0); //=> 5

// you can change dimensions of the grid by setting columns number at any time:
dataGrid.columns = 2;
dataGrid.getValue(1, 0); //=> 3

You can get and set elements using their row and column indexes:

//=> ArrayGrid [1, 2, 3, 4, 5, 6, 7, 8]
grid.getValue(0, 1); //=> 2
grid.setValue(0, 1, 10);
grid.getValue(0, 1); //=> 10

// use `getIndex` to get an array index of an element at given coordinates
grid.getIndex(0, 1); //=> 1

// use `getCoordinates` to find out row and column indexes of a given element by its array index:
grid.getCoordinates(0); //=> [0, 0]
grid.getCoordinates(1); //=> [0, 1]

A grid can be turned to and from an array of nested arrays using respectively Grid.fromArrays and Grid#toArrays methods:

const grid = ArrayGrid.fromArrays([[1, 2], [3, 4]]);
//=> ArrayGrid [ 1, 2, 3, 4 ]
grid.getValue(1, 1); //=> 4

// if arrays are not the same size or their size is not equal to a power two, Grid will pad them with 0 by default
// the value for padding can be specified as the second argument
const grid = ArrayGrid.fromArrays([[1, 2], [3, 4, 5]]);
//=> ArrayGrid [ 1, 2, 0, 0, 3, 4, 5, 0 ]
grid.getValue(1, 1); //=> 4
grid.toArrays(); //=> [ [1, 2], [3, 4, 5] ]

// you can choose to keep the padding values
grid.toArrays(true); //=> [ [1, 2, 0, 0], [3, 4, 5, 0] ]

SymmetricGrid

SymmetricGrid is a Grid that offers a more compact way of encoding symmetric or triangular square matrices using half as much space.

import { SymmetricGrid } from "structurae";

const grid = ArrayGrid.create(100, 100);
grid.length; //=> 12800
const symmetricGrid = SymmetricGrid.create(100);
symmetricGrid.length; //=> 5050

Since the grid is symmetric, it returns the same value for a given pair of coordinates regardless of their position:

symmetricGrid.setValue(0, 5, 10);
symmetricGrid.getValue(0, 5); //=> 10
symmetricGrid.getValue(5, 0); //=> 10

Sorted Structures

BinaryHeap

BinaryHeap extends built-in Array to implement the binary heap data structure. All the mutating methods (push, shift, splice, etc.) do so while maintaining the valid heap structure. By default, BinaryHeap implements min-heap, but it can be changed by providing a different comparator function:

import { BinaryHeap } from "structurae";

class MaxHeap extends BinaryHeap {}
MaxHeap.compare = (a, b) => a > b;

In addition to all array methods, BinaryHeap provides a few methods to traverse or change the heap:

const heap = new BinaryHeap(10, 1, 20, 3, 9, 8);
heap[0]; //=> 1
// the left child of the first (minimal) element of the heap
heap.left(0); //=> 3
// the right child of the first (minimal) element of the heap
heap.right(0); //=> 8
// the parent of the second element of the heap
heap.parent(1); //=> 1
// returns the first element and adds a new element in one operation
heap.replace(4); //=> 1
heap[0]; //=> 3
heap[0] = 6;
// BinaryHeap [ 6, 4, 8, 10, 9, 20 ]
heap.update(0); // updates the position of an element in the heap
// BinaryHeap [ 4, 6, 8, 10, 9, 20 ]

SortedArray

SortedArray extends Array with methods to efficiently handle sorted data. The methods that change the contents of an array do so while preserving the sorted order:

import { SortedArray } from "structurae";

const sortedArray = new SortedArray();
sortedArray.push(1);
//=> SortedArray [ 1, 2, 3, 4, 5, 9 ]
sortedArray.unshift(8);
//=> SortedArray [ 1, 2, 3, 4, 5, 8, 9 ]
sortedArray.splice(0, 2, 6);
//=> SortedArray [ 3, 4, 5, 6, 8, 9 ]

uniquify can be used to remove duplicating elements from the array:

const a = SortedArray.from([1, 1, 2, 2, 3, 4]);
a.uniquify();
//=> SortedArray [ 1, 2, 3, 4 ]

If the instance property unique of an array is set to true, the array will behave as a set and avoid duplicating elements:

const a = new SortedArray();
a.unique = true;
a.push(1); //=> 1
a.push(2); //=> 2
a.push(1); //=> 2
a; //=> SortedArray [ 1, 2 ]

To create a sorted collection from unsorted array-like objects or items use from and of static methods respectively:

SortedArray.from([3, 2, 9, 5, 4]);
//=> SortedArray [ 2, 3, 4, 5, 9 ]
SortedArray.of(8, 5, 6);
//=> SortedArray [ 5, 6, 8 ]

new SortedArray behaves the same way as new Array and should be used with already sorted elements:

new SortedArray(...[1, 2, 3, 4, 8]);
//=> SortedArray [ 1, 2, 3, 4, 8 ];

indexOf and includes use binary search that increasingly outperforms the built-in methods as the size of the array grows.

SortedArray provides isSorted method to check if the collection is sorted, and range method to get elements of the collection whose values are between the specified range:

//=> SortedArray [ 2, 3, 4, 5, 9 ]
sortedArray.range(3, 5);
// => SortedArray [ 3, 4, 5 ]
sortedArray.range(undefined, 4);
// => SortedArray [ 2, 3, 4 ]
sortedArray.range(4);
// => SortedArray [ 4, 5, 8 ]

SortedArray also provides a set of functions to perform common set operations and find statistics of any sorted array-like objects.

License

MIT © Maga D. Zandaqo