| |
| """ |
| Validator for 078_covering_C13_k7_t4 |
| |
| We validate a covering design for C(13,7,4): |
| - Universe: {0,1,...,12} |
| - Blocks: 7-subsets |
| - Coverage: every 4-subset is contained in at least one block |
| |
| Metric (MINIMIZE): |
| - num_blocks = number of blocks |
| |
| Solution format: |
| { |
| "blocks": [[...7 ints...], [...], ...] |
| } |
| """ |
|
|
| import argparse |
| from itertools import combinations |
| from typing import Any, List, Set, Tuple |
|
|
| from . import ( |
| ValidationResult, |
| load_solution, |
| output_result, |
| success, |
| failure, |
| ) |
|
|
| V = 13 |
| K = 7 |
| T = 4 |
|
|
|
|
| def _block_to_mask(block: List[int]) -> int: |
| m = 0 |
| for x in block: |
| m |= 1 << x |
| return m |
|
|
|
|
| def validate(solution: Any) -> ValidationResult: |
| if not isinstance(solution, dict): |
| return failure("Invalid format: expected dict") |
|
|
| blocks = solution.get("blocks", None) |
| if not isinstance(blocks, list) or len(blocks) == 0: |
| return failure("Missing or empty 'blocks' list") |
|
|
| seen_blocks: Set[Tuple[int, ...]] = set() |
| masks: List[int] = [] |
|
|
| for idx, b in enumerate(blocks): |
| if not isinstance(b, list): |
| return failure(f"Block {idx} is not a list") |
|
|
| if len(b) != K: |
| return failure(f"Block {idx} must have exactly {K} elements") |
|
|
| if not all(isinstance(x, int) for x in b): |
| return failure(f"Block {idx} must contain integers only") |
|
|
| if any(x < 0 or x >= V for x in b): |
| return failure(f"Block {idx} has element outside 0..{V-1}") |
|
|
| if len(set(b)) != K: |
| return failure(f"Block {idx} has duplicate elements") |
|
|
| bt = tuple(sorted(b)) |
| if bt in seen_blocks: |
| return failure(f"Duplicate block detected at index {idx}") |
| seen_blocks.add(bt) |
|
|
| masks.append(_block_to_mask(list(bt))) |
|
|
| |
| uncovered = 0 |
| for comb4 in combinations(range(V), T): |
| target = 0 |
| for x in comb4: |
| target |= 1 << x |
| if not any((m & target) == target for m in masks): |
| uncovered += 1 |
| |
| if uncovered >= 5: |
| return failure("Not a valid cover: found uncovered 4-subsets") |
|
|
| if uncovered != 0: |
| return failure(f"Not a valid cover: {uncovered} uncovered 4-subsets") |
|
|
| metrics = { |
| "v": V, |
| "k": K, |
| "t": T, |
| "num_blocks": len(masks), |
| } |
| return success("Valid covering design.", **metrics) |
|
|
|
|
| def main(): |
| parser = argparse.ArgumentParser(description="Validate C(13,7,4) covering design") |
| parser.add_argument("solution", help="Solution as JSON string or path to JSON file") |
| args = parser.parse_args() |
|
|
| sol = load_solution(args.solution) |
| res = validate(sol) |
| output_result(res) |
|
|
|
|
| if __name__ == "__main__": |
| main() |
