"""
core/wheeling.py
----------------
Full-cover number wheeling.

wheel_count(numbers, k)  — C(n, k) ticket count preview
wheel_full(numbers, k)   — all C(n, k) sorted combinations

Raises ValueError for invalid inputs or if result exceeds MAX_TICKETS.
"""

from itertools import combinations
from math import comb

MAX_TICKETS = 200


def wheel_count(numbers: list | set, k: int) -> int:
    """Return how many tickets a full wheel would produce (C(n, k))."""
    n = len(set(numbers))
    if k < 1 or k > n:
        return 0
    return comb(n, k)


def wheel_full(numbers: list | set, k: int) -> list[list[int]]:
    """
    Generate all C(n, k) combinations from *numbers*, each sorted ascending.
    Duplicates in input are removed before wheeling.
    Raises ValueError if k is out of range or count > MAX_TICKETS.
    """
    pool = sorted(set(numbers))
    n    = len(pool)

    if k < 1:
        raise ValueError("Pick count must be at least 1.")
    if k > n:
        raise ValueError(
            f"Pick count ({k}) exceeds the number pool size ({n})."
        )

    count = comb(n, k)
    if count > MAX_TICKETS:
        raise ValueError(
            f"Wheel would produce {count:,} tickets (max {MAX_TICKETS:,}). "
            f"Reduce your pool or pick count."
        )

    return [sorted(combo) for combo in combinations(pool, k)]