Hand permutations to index and vice versa

deal.py

from math import comb
from typing import List


Hand = List[int]

      
def hand_from_index(index: int, deck_indices: List[int], hand_size: int) -> Hand:
    hand = []
    deck_size = len(deck_indices)
    deck_index = 0
    cards_remaining = hand_size
    while 0 < cards_remaining:
        hands_including_this_card = comb(
            deck_size - deck_index - 1, cards_remaining - 1
        )
        if index < hands_including_this_card:
            # we include the card at deck_index
            hand.append(deck_indices[deck_index])
            cards_remaining -= 1
        else:
            index -= hands_including_this_card
        deck_index += 1
    assert index == 0
    return hand


def index_from_hand(hand_index_list, deck_size):
    result = 0
    deck_index = 0
    hand_index = 0
    hand_size = len(hand_index_list)
    for hand_index in hand_index_list:
        while deck_index < hand_index:
            hands_including_this_card = comb(deck_size - deck_index - 1, hand_size - 1)
            result += hands_including_this_card
            deck_index += 1
        deck_index += 1
        hand_size -= 1
    return result