| |
| """ |
| Validator for problem 042: Optimal Difference Basis Construction for n=10000 |
| |
| A set B ⊆ {0, 1, ..., n-1} is a difference basis for [1, n-1] if every integer |
| in [1, n-1] can be written as |a - b| for some a, b ∈ B. |
| |
| For n=10000, the goal is to minimize |B|. |
| |
| Expected input format: |
| {"basis": [b0, b1, b2, ...]} |
| or [b0, b1, b2, ...] |
| """ |
|
|
| import argparse |
| from typing import Any |
|
|
| from . import ValidationResult, load_solution, parse_integer, output_result, success, failure |
|
|
|
|
| TARGET_N = 10000 |
|
|
|
|
| def validate(solution: Any) -> ValidationResult: |
| """ |
| Validate a difference basis for n=10000. |
| |
| Args: |
| solution: Dict with 'basis' key or list of basis elements |
| |
| Returns: |
| ValidationResult with success/failure and basis size |
| """ |
| try: |
| if isinstance(solution, dict) and 'basis' in solution: |
| basis = [parse_integer(b) for b in solution['basis']] |
| elif isinstance(solution, list): |
| basis = [parse_integer(b) for b in solution] |
| else: |
| return failure("Invalid format: expected dict with 'basis' key or list") |
| except (ValueError, TypeError) as e: |
| return failure(f"Failed to parse solution: {e}") |
|
|
| n = TARGET_N |
| B = set(basis) |
|
|
| |
| for b in B: |
| if b < 0 or b >= n: |
| return failure(f"Basis element {b} not in range [0, {n-1}]") |
|
|
| |
| differences = set() |
| for a in B: |
| for b in B: |
| diff = abs(a - b) |
| if diff > 0: |
| differences.add(diff) |
|
|
| |
| missing = set(range(1, n)) - differences |
| if missing: |
| sample = sorted(list(missing))[:5] |
| return failure( |
| f"Not a difference basis: missing {len(missing)} values. Examples: {sample}", |
| missing_count=len(missing) |
| ) |
|
|
| size = len(B) |
| ratio = (size ** 2) / n |
|
|
| return success( |
| f"Verified difference basis for n={n}: |B|={size}, |B|²/n = {ratio:.6f}", |
| n=n, basis_size=size, ratio=ratio |
| ) |
|
|
|
|
| def main(): |
| parser = argparse.ArgumentParser(description='Validate difference basis for n=10000') |
| parser.add_argument('solution', help='Solution as JSON string or path to JSON file') |
| parser.add_argument('--verbose', '-v', action='store_true', help='Verbose output') |
| args = parser.parse_args() |
|
|
| solution = load_solution(args.solution) |
| result = validate(solution) |
| output_result(result) |
|
|
|
|
| if __name__ == '__main__': |
| main() |
|
|
