"""Sinh bộ ca pairwise cho một mô hình cấu hình nhỏ."""
from itertools import combinations, product

DOMAINS = [
    ("web", "desktop"),
    ("password", "oauth"),
    ("online", "offline"),
    ("light", "dark"),
]


def valid(row):
    return not (row[1] == "oauth" and row[2] == "offline")


def pairs(row):
    return {(i, row[i], j, row[j]) for i, j in combinations(range(len(row)), 2)}


def greedy(rows):
    remaining = set().union(*(pairs(row) for row in rows))
    selected = []
    while remaining:
        row = max(rows, key=lambda r: len(pairs(r) & remaining))
        selected.append(row)
        remaining -= pairs(row)
    return selected


if __name__ == "__main__":
    full = [row for row in product(*DOMAINS) if valid(row)]
    selected = greedy(full)
    assert set().union(*(pairs(r) for r in full)) == set().union(*(pairs(r) for r in selected))
    assert all(valid(row) for row in selected)
    first_three = {row[:3] for row in full}
    missed = sorted(first_three - {row[:3] for row in selected})
    assert missed
    print("Tổ hợp khả thi:", len(full), "| Bộ ca pairwise:", len(selected))
    print("Bộ ba hợp lệ chưa xuất hiện:", missed[0])
    for row in selected:
        print(row)