KombiN - JavaScript/TypeScript Library

KombiN is a library for bijectively mapping all ordered pairs $(a_i, b_j)$ from two finite sets A and B into a single linear index. KombiN orders pairs by ascending weight (sum of indices) using a three-region zig-zag algorithm, enabling O(1) bidirectional lookups.

Installation

Available on npm:

npm i @pranavpatel.ca/algo-kombin

Usage

Suppose set A has 100 elements and set B has 80 elements, both using zero-based indexing:

import { Table } from '@pranavpatel.ca/algo-kombin';

// Initialize Table for sets A (100 elements) and B (80 elements), zero-based indexing
const myObj = new Table(100, 80, true);

// Get index for combination pair (ai: 46, bi: 72)
const index = myObj.GetIndexOfElements(46, 72);

// Get combination pair from index value
const [ai, bi] = myObj.GetElementsAtIndex(index);

API Reference

Table Class

Constructor:

new Table(lengthOfA: number, lengthOfB: number, zeroBasedIndex: boolean)

• lengthOfA: Number of elements in set A.
• lengthOfB: Number of elements in set B.
• zeroBasedIndex: true for zero-based, false for one-based indexing.

Methods:

• GetIndexOfElements(ai: number, bi: number): number
  Returns the unique index for the pair (ai, bi).

• GetElementsAtIndex(index: number): [number, number]
  Returns the pair (ai, bi) for the given index as a tuple.

Example: Enumerate All Pairs by Weight

const table = new Table(3, 3, false);
for (let i = 1; i <= 9; i++) {
    const [ai, bi] = table.GetElementsAtIndex(i);
    console.log(`${i}: (${ai}, ${bi})`);
}

Edge Cases & Error Handling

• Throws Error for invalid indices or set sizes.

License

MIT License.