KombiN - Python 3 Library

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

Installation

Install from PyPI:

pip install kombin-algo-pranavpatel-ca

Usage

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

from kombin import Table

# Initialize Table for sets A (100 elements) and B (80 elements), zero-based indexing
myObj = Table(100, 80, True)

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

# Get combination pair from index value
ai, bi = myObj.GetElementsAtIndex(index)

API Reference

Table Class

Constructor:

Table(lengthOfA: int, lengthOfB: int, zeroBasedIndex: bool)

• 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: int, bi: int) -> int
  Returns the unique index for the pair (ai, bi).

• GetElementsAtIndex(index: int) -> Tuple[int, int]
  Returns the pair (ai, bi) for the given index.

Example: Enumerate All Pairs by Weight

table = Table(3, 3, False)
for i in range(1, 10):
    ai, bi = table.GetElementsAtIndex(i)
    print(f"{i}: ({ai}, {bi})")

Edge Cases & Error Handling

• Raises ValueError for invalid indices or set sizes.
• Large lengthOfA or lengthOfB may cause integer overflows in some environments.

License

MIT License. See LICENSE