array-set-ops

Extremely fast set difference, intersection, symmetricDifference, union operations on Sets and Arrays.

All the standard map/reduce/find operations for Sets.

CartesianProduct as a first class object like Set and Array. And, cartesianProduct as a method on both.

Option to use static or iterable/generative approaches for all operations.

API

Direct Calls

Cartesian Product

• CartesianProduct(...iterables) returns an instance of a CartesianProduct which is an iterable and also supports the standard map/reduce methods.

• Creation of the CartesianProduct is O(number of iterables).

• Access to any specific item in a CartesianProduct using at(n) is an O(number of iterables)

• Iteration across an entire CartesianProduct is O(product of lengths of iterables)

A naive Cartesian product implementation that computes all combinations is O(product of lengths of iterables).

const naiveCartesian = (arrays) => arrays.reduce((a, b) => a.reduce((r, v) => r.concat(b.map(w => [].concat(v, w))),[]));

When the typical order of magnitude differences between the number of iterables and the product of their sizes is taken into account, this effectively makes CartesianProduct O(1) for creation and access while maintaining a similar speed for iterating across all combinations. However, the time to get the first item from CartesianProduct will be almost instantaneous and typically orders of magnitude faster than the first item from a naive implementation.

For example assume it takes 1ms to create a CartesianProduct from 5 arrays each having 100 items (it's actually far less, its on the order of .125ms). And assume that access to an item is 1ms (it's actually far less, its on the order of .125ms). Then access to the first item will be 2ms and the last 100^5 ms. For a naive implementation access to the first item will be 100^5 ms!

A generator like the below will solve problem related to accessing the first item.

function* generatorCartesian([head, ...tail]) {
  const remainder = tail.length > 0 ? generatorCartesian(tail) : [[]];
  for (let r of remainder) for (let h of head) yield [h, ...r];
}

However, if there is a desire to sample or split the product for additional processing, bottlenecks will occur because generator access must be sequential. With CartesianProduct you can do something like this:

const cp = CartesianProduct(array1,array2,array3);
cons start = cp.size * .1, end = cp.size * .9
for(let i=start;i<end;i++) {
    doSoemthing(cp.at(i));
}

Even easier, CartesianProduct supports slice and slice as an iterable!

const cp = CartesianProduct(array1,array2,array3);
cons start = cp.size * .1, end = cp.size * .9
for(const item of cp.slice(start,end)) { // iterating over Array but the entire array has to be assembled first
    doSomething(item);
}

const cp = CartesianProduct(array1,array2,array3);
cons start = cp.size * .1, end = cp.size * .9
for(const item of cp.slice.iterable(start,end)) { // on demand iteration as the slice elements are generated
    doSomething(item);
}

Additionally, the generic nature of generators makes them slightly slower than custom iterables and CartesianProduct is a custom iterable.

See the #benchmarks below.

Set Operations

The four functions below return an Array or Set depending on class of the first argument

• difference(base,...iterables) returns items in base but not in the rest of the iterables
• intersection(...iterables)
• symmetricDifference(...iterables) returns all items that exist in at most one of the iterables, i.
• union(...iterables)

Each of the above also has a form:

<operation>.iterable(...iterables) where operation is one of difference, intersection, symmetricDifference, union.

These iterable versions can prevent the blocking of a data processing pipeline by returning values on demand rather than all at once. The gains in performance depend on the nature of the data processed but are typically as follows:

• difference, 3 to 4 orders of magnitude
• intersection, 2x
• symmetricDifference, 2x
• union, 3 to 4 orders of magnitude

The below function return true if the named predicate is true of the base for all the iterables passed in.

import {isDisjointFrom,isSubsetOf,isSupersetOf} from "array-set-ops";

• isDisjointFrom(base,...iterables)
• isSubsetOf(base,...iterables)
• isSupersetOf(base,...iterables)

Set Operations For Arrays and Sets

import {classPrototype} from "array-set-ops";
classPrototype.patch(Set);
classPrototype.patch(Array);

<Array|Set>.

• cartesianProduct(...iterables)
• difference(...iterables)
• intersection(...iterables)
• symmetricDifference(...iterables)
• union(...iterables)

If the method is called on an Array, an Array is returned. If called on a Set, a Set is returned.

• isDisjointFrom(...iterables)
• isSubsetOf(...iterables)
• isSupersetOf(...iterables)

The ...iterables passed as arguments can be Arrays or Sets. Other iterables like Map may work, but have not been tested.

For example:

const set = union(new Set([1,2,2,3]),[2,3,4]) // Set containing 1,2,3,4
    array = union([2,3,4],new Set([1,2,2,3])) // [2,3,4,1]

Loop Functions For Sets and Cartesian Products

The loop functions are built-in to JavaScript for Array.

import {classPrototype} from "array-set-ops";
classPrototype.patch(Set);
import {loopFunctions} from "array-set-ops/src/loop-functions.js",
Object.assign(Set.prototype,loopFunctions);

.

• at(number index)
• cartesianProduct(...iterables)
• every(function f)
• find(function f)
• findIndex(any value)
• filter(function f)
• forEach(function f)
• map(function f)
• reduce(function f)
• reduceRight(function f)
• slice(start,end)
• some(function f)

For example:

const value = new Set([1,2,2,3]).reduce((sum,value) => sum + value); // 6

Aggregate Functions For Arrays, CartesianProducts, and Sets

import {aggregateFunctions} from "array-set-ops/src/aggregate-functions.js",
Object.assign(Set.prototype,aggregateFunctions); // optional
Object.assign(Array.prototype,aggregateFunctions); // optional

<Array|Set>.

• avg()
• product()
• sum()

For example:

const value = new Set([1,2,2,3]).sum(); // 6

Loop And Aggregate Functions For Iterable Versions Of Set Operations

import {classPrototype} from "array-set-ops";
classPrototype.patch(Set);
classPrototype.patch(Array);
import {loopFunctions} from "array-set-ops/src/loop-functions.js",
Object.assign(Set.prototype,loopFunctions);
Object.assign(Array.prototype,loopFunctions);

operation can be one of difference, intersection, symmetricDifference, union, cartesianProduct.

<Array|Set>..iterator(...iterables)

• at(number index)
• cartesianProduct(...iterables)
• every(function f)
• findIndex(any value)
• forEach(function f)
• some(function f)
• reduce(function f)
• reduceRight(function f)
• slice(start,end)

For example:

const union = largeArray1.union.iterable(largeArray2,largeArray3),
    result = union.map((item) => item * 10)

If you are looking for performance on really large data sets, the iterator functions below can return items before they complete.

operation is one of filter, map, slice.

• <operation>.iterable(function f)

For example:

const union = largeArray1.union.iterable(largeArray2,largeArray3);
for(const item of union.map.iterable((item) => item * 10)) {
    doSomething(item);
}

And finally there are aggregate functions.

• avg()
• product()
• sum()

For example:

const union = largeArray1.union.iterable(largeArray2,largeArray3),
    result = union.sum()

By their nature, some of the above force full resolution of the iterable, e.g. map and sum while others do not, e.g. at and findIndex. Some functions may force full resolution based on the data to which they are applied, e.g. some and every. Those that do not require full resolution will typically be faster than calling the same function on a non-iterator version of the same data. For example, the second two lines of code below will typically be more performant.

const staticIntersection = [1,2,3,4,5,6,7,...lots of values].intersection([...lots more values],[...even more values]),
    v1 = staticIntersection[1000]; // or iterableIntersection.at(1000)

const iterableIntersection = [1,2,3,4,5,6,7,...lots of values].intersection.iterable([...lots more values],[...even more values]),
    v2 = iterableIntersection.at(1000); // array index technique not available unless you put a proxy arround iterableIntersection

Installation

npm install array-set-ops

Usage

import {classPrototype} from "array-set-ops";
import {loopFunctions} from "../src/loop-functions.js",
import {aggregateFunctions} from "../src/aggregate-functions.js",
import {cartesianProduct,CartesianProduct} from "../src/cartesian-product.js";

classPrototype.patch(Set);
classPrototype.patch(Array);
Object.assign(Set.prototype,loopFunctions);
Object.assign(Set.prototype,aggregateFunctions); // optional
Set.prototype.cartesianProduct = cartesianProduct; // optional
Object.assign(Array.prototype,aggregateFunctions); // optional
Array.prototype.cartesianProduct = cartesianProduct; // optional

// the class CartesianProduct(...iterables) will also be available

See the file ./test/index.js for more examples.

Unit Testing

Unit testing is conducted with Mocha and C8.

-------------------------|---------|----------|---------|---------|----------------------------------------------------------
File                     | % Stmts | % Branch | % Funcs | % Lines | Uncovered Line #s                                        
-------------------------|---------|----------|---------|---------|----------------------------------------------------------
All files                |   82.67 |    91.62 |   68.96 |   82.67 |                                                         
 aggregate-functions.js  |   45.45 |      100 |       0 |   45.45 | 4-8,11,14-19                                            
 cartesian-product.js    |   79.47 |    90.62 |   78.57 |   79.47 | 51-54,66-67,78-96,130-131,146-149                       
 difference.js           |     100 |       85 |     100 |     100 | 30,43,61                                                
 index.js                |   98.03 |       90 |      70 |   98.03 | 18                                                      
 intersection.js         |   97.77 |    96.15 |     100 |   97.77 | 54-55                                                   
 is-disjoint-from.js     |     100 |      100 |     100 |     100 |                                                         
 is-subset-of.js         |     100 |      100 |     100 |     100 |                                                         
 is-superset-of.js       |     100 |      100 |     100 |     100 |                                                         
 loop-functions.js       |   49.72 |    77.77 |   52.94 |   49.72 | 9-10,23-32,35-39,75,78-96,99-104,112-123,132-143,152-174
 symmetric-difference.js |   80.86 |    90.47 |      50 |   80.86 | 76-78,91-109                                             
 union.js                |     100 |      100 |     100 |     100 |                                                         
-------------------------|---------|----------|---------|---------|----------------------------------------------------------

Benchmarks

Benchmarking involves applying set functions to 3 sequences of random lengths between 1 and 99999 containing random numbers between -99 and 99, 50% of which are randomly negative. The sizes of the results are shown on each line.

Lengths: 16711 73790 9949

Cartesian Product

CartesianProduct first x 129,798 ops/sec ±1.52% (86 runs sampled) 1233104690
bigCartesian first x 102,802 ops/sec ±0.78% (89 runs sampled) 1233104690
generatorCartesian first x 113,300 ops/sec ±0.86% (90 runs sampled) 1233104690
CartesianProduct item at 10% point 123310469 x 130,534 ops/sec ±0.56% (88 runs sampled) 1233104690
bigCartesian item at 10% point 123310469 x 0.05 ops/sec ±8.22% (5 runs sampled) 1233104690
```

## Difference

```
difference x 21.12 ops/sec ±12.06% (40 runs sampled) 8028
Array difference.iterable first x 26.40 ops/sec ±17.64% (46 runs sampled) 1
Array difference.iterable x 27.76 ops/sec ±9.26% (51 runs sampled) 8028
```

## Intersection

```
intersection x 171 ops/sec ±1.87% (76 runs sampled) 4981
intersection.iterable first x 424 ops/sec ±0.91% (85 runs sampled) 1
intersect.iterable x 161 ops/sec ±1.81% (78 runs sampled) 4981
fast_array_intersect x 165 ops/sec ±1.11% (77 runs sampled) 4981
```

## Symmetric Difference

```
symmetricDifference x 11.89 ops/sec ±3.39% (33 runs sampled) 66358
symmetricDifference.iterable first x 36.78 ops/sec ±2.48% (49 runs sampled) 1
symmetricDifference.iterable x 12.04 ops/sec ±1.27% (32 runs sampled) 66358
```

## Union

```
union x 74.73 ops/sec ±2.25% (63 runs sampled) 79910
union.iterable first x 74,245 ops/sec ±0.98% (87 runs sampled) 1
union.iterable x 64.74 ops/sec ±1.61% (64 runs sampled) 79910
```

# Change History (Reverse Chronological Order)

2023-02-22 v0.4.3 More unit tests. Optimized `difference` and `symmetricDifference`.

2023-02-21 v0.4.2 More unit tests. Fixed issue with scoping of iterable looping functions on `CartesianProduct`.

2023-02-20 v0.4.1 More unit tests. Fixed issue with `.map` indexing.

2023-02-20 v0.4.0 More performance and unit tests. More documentation. Iterable versions of `filter`, `map`, `slice`.

2023-02-19 v0.3.0 More unit tests. Performance tests. Simplified patching of Array and Class. Fixed algorithmic issues with `difference`.

2023-02-18 v0.2.0 More documentation, more unit tests, almost complete and standardized API.

2023-02-18 v0.1.0 First public release