"""Shared helpers: verification of a schedule, and counting facts."""
from itertools import combinations


def all_pairs(n=24):
    return set(combinations(range(n), 2))


def pairs_covered_by_day(day):
    """day: list of 4 boats, each a list of 6 ints. Return set of covered pairs."""
    cov = set()
    for boat in day:
        for a, b in combinations(sorted(boat), 2):
            cov.add((a, b))
    return cov


def verify(schedule, n=24, boats=4, size=6):
    """Validate structure and full pair coverage. Returns (ok, info)."""
    info = {}
    need = all_pairs(n)
    covered = set()
    for d, day in enumerate(schedule):
        assert len(day) == boats, f"day {d}: not {boats} boats"
        flat = [p for boat in day for p in boat]
        assert sorted(flat) == list(range(n)), f"day {d}: not a partition of 0..{n-1}"
        for boat in day:
            assert len(boat) == size, f"day {d}: boat size != {size}"
        covered |= pairs_covered_by_day(day)
    missing = need - covered
    info['days'] = len(schedule)
    info['covered'] = len(covered)
    info['missing'] = len(missing)
    info['missing_pairs'] = sorted(missing)
    # meeting multiplicities
    mult = {}
    for day in schedule:
        for boat in day:
            for a, b in combinations(sorted(boat), 2):
                mult[(a, b)] = mult.get((a, b), 0) + 1
    info['total_meetings'] = sum(mult.values())
    info['repeat_excess'] = sum(m - 1 for m in mult.values())
    return (len(missing) == 0), info


if __name__ == "__main__":
    # Sanity: counting facts
    print("C(24,2) =", len(all_pairs()))
    print("pairs covered per boat C(6,2) =", 15)
    print("pairs covered per day = 4*15 =", 60)
    for d in range(4, 8):
        print(f"d={d}: 60*d = {60*d} meetings, excess if full cover = {60*d - 276}, "
              f"per-person meetings 5*{d}={5*d} (need 23)")