File size: 2,605 Bytes
848d4b7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 | #!/usr/bin/env python3
"""
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")
# Validate entries are 0 or 1
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}")
# Check all 7-term arithmetic progressions a, a+d, a+2d, ..., a+6d
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()
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