The problem of set of combinations using approximation

set_covering_greedy.py

from typing import Dict


def find_optimal_stations():
    places_to_cover = set(["mt", "wa", "or", "id", "nv", "ut", "ca", "az"])
    hashset_places: Dict[set] = {
        "kone": set(("id", "nv", "uv")),
        "ktwo": set(["wa", "id", "mt"]),
        "k3": set(["or", "nv", "ca"]),
        "k4": set(["nv", "ut"]),
        "k5": set(["ca", "az"]),
    }
    best_station: Optional[str] = None
    is_covered = set()
    stations_to_cover = []
    while places_to_cover:
        for station, places in hashset_places.items():
            if (common_places := places & places_to_cover) and len(
                common_places) > len(is_covered):
                best_station = station
                is_covered = common_places
        stations_to_cover += [best_station]
        places_to_cover -=  is_covered
        is_covered.clear()
    return stations_to_cover

print(find_optimal_stations())