File size: 2,562 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 91 | #!/usr/bin/env python3
"""
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)
# Check all elements are in valid range
for b in B:
if b < 0 or b >= n:
return failure(f"Basis element {b} not in range [0, {n-1}]")
# Compute all differences
differences = set()
for a in B:
for b in B:
diff = abs(a - b)
if diff > 0:
differences.add(diff)
# Check coverage of [1, n-1]
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()
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