indexed-string-variation

JavaScript module to generate all possible variations of strings over an alphabet using an n-ary virtual tree.

Quick start example:

// generate all strings of max length 3 using the alphabet "ab"
import isv from "indexed-string-variation";

for (const str of isv({ alphabet: "ab", maxLen: 3 })) {
  console.log(str);
}

Output:

(empty string)
a
b
aa
ab
ba
bb
aaa
aab
aba
abb
baa
bab
bba
bbb

Important

Note that the first result is always an empty string! If you want to start from the first non-empty string, you can use the from option to specify the starting index of 1n.

Requirements

• Node.js >= 22

Install

With NPM:

npm install indexed-string-variation

Usage

This library is ESM-only and written in TypeScript. You can import and use it as follows:

import isv from "indexed-string-variation";

// Basic usage: generate the first 23 variations for a given alphabet
for (
  const str of isv({ alphabet: "abc1", maxIterations: 23 })
) {
  console.log(str);
}

// Generate 5 variations starting from a specific index (using BigInt)
for (
  const str of isv({
    alphabet: "abc1",
    from: 20n,
    maxIterations: 5,
  })
) {
  console.log(str);
}

// Generate variations up to a maximum string length of 2 chars
for (const str of isv({ alphabet: "abc1", maxLen: 2 })) {
  console.log(str);
}

// endless variations (careful if you use a `for ... of` loop because it will never end unless you have a break condition!)
const values = isv({
  alphabet: "abc1",
});

// pull values from the iterator one by one
console.log(values.next()); // { value: 'a', done: false }
console.log(values.next()); // { value: 'b', done: false }

// use iterator helpers and the spread operator to pull multiple values
// at once into an array
console.log([...isv({ alphabet: "abc1" }).take(10)]);
// [
//   '',   'a',  'b',
//   'c',  '1',  'aa',
//   'ab', 'ac', 'a1',
//   'ba'
// ]

Tip

Find more about iterator helpers the Iterators MDN page.

Options

The isv generator function accepts options that allow you to configure how the generation will behave:

• alphabet: a string containing the characters that will be used to generate the variations. The order of the characters in the string defines their lexicographic order (defaults to abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789).
• from: a bigintrepresenting the index from which to start generating the variations (defaults to 0n).
• to?: a bigint representing the index at which to stop generating the variations (optional, defaults to undefined, which indicates infinity).
• maxLen: a number representing the maximum length of the generated strings (optional, defaults to undefined, which means no limit).
• maxIterations: a number representing the maximum number of iterations to run (optional, defaults to undefined, which means no limit).

Important

All the options are optional and by default the generator will be endless (it will keep generating variations), so if you use it in a for ... of loop it will never end unless you have an explicit mechanism to break the loop! Alternatively, you can use iterator helpers such as Iterator.prototype.take to limit the number of iterations.

How the algorithm works

The way the generation algorithm work is using an n-ary tree where n is the size of the alphabet. For example, if we have an alphabet containing only a, b and c, and we want to generate all the strings with a maximum length of 3 the algorithm will use the following tree:

The tree is to be considered "virtual", because it's never generated in its integrity, so the used space in memory is minimal.

In summary, we can describe the algorithm as follows:

Given an index i over an alphabet of length n, and it's corresponding n-ary tree, the string associated to i corresponds to the string obtained by concatenating all the characters found in the path that goes from the root node to the i-th node.

Note that since the library exposes a generator/iterator interface, the value of i is managed internally be the iterator.

TypeScript

Type definitions are included. You can use this library with full type safety in TypeScript projects.

Testing

This project uses Vitest:

npm test

Development

• Source code is in src/ (TypeScript)
• Build output is in dist/
• Tests are in src/test.ts

Migration notes

• The library now uses native JavaScript BigInt instead of the big-integer dependency.
• Only ESM is supported (no CommonJS require).
• Node.js 22 or newer is required.

License

Licensed under MIT License. © Luciano Mammino.