#!/usr/bin/env python3
"""Exhaustive verifier for covering designs C(v,k,t).

Usage: python verify_covering.py v k t [blockfile]
Block file format: one block per line, ascending 0-based integers separated
by whitespace. Reads stdin if no filename is given.

Checks, with no shortcuts:
  1. every line parses to exactly k distinct integers in {0..v-1};
  2. every t-subset of {0..v-1} is contained in at least one block.
Prints VERDICT: VALID/INVALID and statistics. No dependencies.
"""
import itertools
import sys


def main() -> int:
    if len(sys.argv) < 4:
        print(__doc__)
        return 2
    v, k, t = int(sys.argv[1]), int(sys.argv[2]), int(sys.argv[3])
    data = open(sys.argv[4]).read() if len(sys.argv) > 4 else sys.stdin.read()
    blocks = []
    malformed = 0
    for lineno, line in enumerate(data.splitlines(), 1):
        parts = line.split()
        if not parts or parts[0].startswith("#"):
            continue
        try:
            b = [int(x) for x in parts]
        except ValueError:
            malformed += 1
            continue
        if len(b) != k or any(x < 0 or x >= v for x in b) or any(
            b[i] >= b[i + 1] for i in range(k - 1)
        ):
            malformed += 1
            continue
        blocks.append(b)

    covered = set()
    for b in blocks:
        for ts in itertools.combinations(b, t):
            covered.add(ts)
    total = sum(1 for _ in itertools.combinations(range(v), t))
    uncovered = total - len(covered)
    ok = (malformed == 0) and (uncovered == 0)
    print(f"blocks={len(blocks)} malformed={malformed} "
          f"t_subsets={total} covered={len(covered)} uncovered={uncovered}")
    print("VERDICT: VALID" if ok else "VERDICT: INVALID")
    return 0 if ok else 1


if __name__ == "__main__":
    sys.exit(main())