| |
| """ |
| Validator for problem 045: 2-Coloring with No Monochromatic 7-Term Arithmetic Progression |
| |
| Find a 2-coloring of {0, 1, ..., n-1} that avoids monochromatic arithmetic |
| progressions of length 7, maximizing n. |
| |
| Expected input format: |
| { |
| "coloring": [0, 1, 0, 1, ...] # list of 0/1 values, one per element |
| } |
| """ |
|
|
| import argparse |
| from typing import Any |
|
|
| from . import ValidationResult, load_solution, output_result, success, failure |
|
|
|
|
| AP_LENGTH = 7 |
|
|
|
|
| def validate(solution: Any) -> ValidationResult: |
| """ |
| Validate a 2-coloring of {0,...,n-1} has no monochromatic 7-AP. |
| |
| Args: |
| solution: Dict with 'coloring' (list of 0/1 values) |
| |
| Returns: |
| ValidationResult with verification status and length metric |
| """ |
| try: |
| if not isinstance(solution, dict): |
| return failure("Invalid format: expected dict") |
|
|
| if 'coloring' not in solution: |
| return failure("Missing 'coloring' key") |
|
|
| coloring = list(solution['coloring']) |
| n = len(coloring) |
|
|
| if n == 0: |
| return failure("Coloring is empty") |
|
|
| |
| for i, c in enumerate(coloring): |
| if c not in (0, 1): |
| return failure(f"coloring[{i}] = {c}, expected 0 or 1") |
|
|
| except (ValueError, TypeError) as e: |
| return failure(f"Failed to parse solution: {e}") |
|
|
| |
| for d in range(1, (n - 1) // (AP_LENGTH - 1) + 1): |
| for a in range(n - (AP_LENGTH - 1) * d): |
| color = coloring[a] |
| mono = True |
| for k in range(1, AP_LENGTH): |
| if coloring[a + k * d] != color: |
| mono = False |
| break |
| if mono: |
| ap = [a + k * d for k in range(AP_LENGTH)] |
| return failure( |
| f"Monochromatic {AP_LENGTH}-AP found: {ap} all color {color}" |
| ) |
|
|
| return success( |
| f"Valid 2-coloring of {{0,...,{n-1}}} with no monochromatic {AP_LENGTH}-AP", |
| length=n, |
| ) |
|
|
|
|
| def main(): |
| parser = argparse.ArgumentParser( |
| description='Validate 2-coloring avoiding monochromatic 7-AP' |
| ) |
| 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() |
|
|
