combinatorics

This module provides generators for iterating subsets of an input. It is heavily inspired by the combinatoric iterators provided by the itertools package from the Python standard library.

All generators are importable on their own.
These implementations do not build up intermediate results in memory.
All functions iterate subsets lexicographically according to their input indices. If the input is sorted the output will be too.
Likewise, whether the input elements are unique or not does not matter.
The inputs provided are not modified. However, consumable iterables will be consumed.

Usage

combinations(r, iterable)

Yields r length Arrays from the input iterable. Order of selection does not matter and elements are chosen without replacement.

import { assertEquals } from "https://deno.land/std/testing/asserts.ts";
import { combinations } from "https://deno.land/x/combinatorics/combinations.ts";

const sequences = [...combinations(2, [1, 2, 3, 4])];

assertEquals(sequences, [
  [1, 2],
  [1, 3],
  [1, 4],
  [2, 3],
  [2, 4],
  [3, 4],
]);

permutations(r, iterable)

Yields r length Arrays from the input iterable. Order of selection is important and elements are chosen without replacement. If r is undefined, then the length of the iterable is used.

import { assertEquals } from "https://deno.land/std/testing/asserts.ts";
import { permutations } from "https://deno.land/x/combinatorics/permutations.ts";

const sequences = [...permutations(2, [1, 2, 3, 4])];

assertEquals(sequences, [
  [1, 2], [1, 3], [1, 4],
  [2, 1], [2, 3], [2, 4],
  [3, 1], [3, 2], [3, 4],
  [4, 1], [4, 2], [4, 3],
]);

combinationsWithReplacement(r, iterable)

Yields r length Arrays from the input iterable. Order of selection is not important and elements are chosen with replacement.

import { assertEquals } from "https://deno.land/std/testing/asserts.ts";
import { combinationsWithReplacement } from "https://deno.land/x/combinatorics/combinations_with_replacement.ts";

const sequences = [...combinationsWithReplacement(2, [1, 2, 3, 4])];

assertEquals(sequences, [
  [1, 1],
  [1, 2],
  [1, 3],
  [1, 4],
  [2, 2],
  [2, 3],
  [2, 4],
  [3, 3],
  [3, 4],
  [4, 4],
]);

product(r, …iterables)

Yields r * iterables.length length Arrays from the input iterables repeated r times. Order of selection is important and elements are chosen with replacement.

When iterables.length === 1 the output is equivalent to the permutations with replacement of iterables[0] with the given r.

import { assertEquals } from "https://deno.land/std/testing/asserts.ts";
import { product } from "https://deno.land/x/combinatorics/product.ts";

const sequences = [...product(2, [1, 2, 3, 4])];

assertEquals(sequences, [
  [1, 1], [1, 2], [1, 3], [1, 4],
  [2, 1], [2, 2], [2, 3], [2, 4],
  [3, 1], [3, 2], [3, 3], [3, 4],
  [4, 1], [4, 2], [4, 3], [4, 4],
]);

When iterables.length > 1 the output is equivalent to the cartesian product of the iterables repeated r times. This can also be explained as running nested for...of loops using one of the inputs to provide the element at each index for the yielded Array.

import { assertEquals } from "https://deno.land/std/testing/asserts.ts";
import { product } from "https://deno.land/x/combinatorics/product.ts";

const sequences = [...product(1, [1, 2, 3], [4, 5, 6], [7, 8, 9])];

assertEquals(sequences, [
  [1, 4, 7], [1, 4, 8], [1, 4, 9],
  [1, 5, 7], [1, 5, 8], [1, 5, 9],
  [1, 6, 7], [1, 6, 8], [1, 6, 9],
  [2, 4, 7], [2, 4, 8], [2, 4, 9],
  [2, 5, 7], [2, 5, 8], [2, 5, 9],
  [2, 6, 7], [2, 6, 8], [2, 6, 9],
  [3, 4, 7], [3, 4, 8], [3, 4, 9],
  [3, 5, 7], [3, 5, 8], [3, 5, 9],
  [3, 6, 7], [3, 6, 8], [3, 6, 9],
]);

powerSet(iterable)

The set of all subsets of the given iterable. Equivalent to running combinations with 0 <= r <= iterable.length and flattening the results. The first subset is the empty set given when r = 0.

import { assertEquals } from "https://deno.land/std/testing/asserts.ts";
import { powerSet } from "https://deno.land/x/combinatorics/power_set.ts";

const sequences = [...powerSet([1, 2, 3])];

assertEquals(sequences, [
  [],
  [1],
  [2],
  [3],
  [1, 2],
  [1, 3],
  [2, 3],
  [1, 2, 3],
]);