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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 92 93 94 95 96 97 98 99 100 101 102 103 104 | #!/usr/bin/env python3
"""
Validator for problem 059: Thomson Problem for n=50
The Thomson problem asks for n points on a unit sphere that minimize
the electrostatic potential energy E = Σᵢ<ⱼ 1/|xᵢ - xⱼ|.
For n=50, this validator:
1. Checks all points are on the unit sphere S²
2. Computes the electrostatic energy
3. Reports the configuration quality
Expected input format:
{"points": [[x, y, z], ...]} 50 points on S²
or [[x, y, z], ...]
"""
import argparse
from typing import Any
import numpy as np
from . import ValidationResult, load_solution, output_result, success, failure
TARGET_N = 50
TOLERANCE = 1e-9
def validate(solution: Any) -> ValidationResult:
"""
Validate a Thomson configuration for n=50.
Args:
solution: Dict with 'points' key or list of 50 3D points
Returns:
ValidationResult with energy and configuration properties
"""
try:
if isinstance(solution, dict) and 'points' in solution:
points_data = solution['points']
elif isinstance(solution, list):
points_data = solution
else:
return failure("Invalid format: expected dict with 'points' or list")
points = np.array(points_data, dtype=np.float64)
except (ValueError, TypeError) as e:
return failure(f"Failed to parse points: {e}")
if points.ndim != 2:
return failure(f"Points must be 2D array, got {points.ndim}D")
n, d = points.shape
if d != 3:
return failure(f"Points must be in ℝ³, got dimension {d}")
if n != TARGET_N:
return failure(f"Expected {TARGET_N} points, got {n}")
# Check all points are on unit sphere
norms = np.linalg.norm(points, axis=1)
off_sphere = np.abs(norms - 1.0) > TOLERANCE
if np.any(off_sphere):
worst_idx = np.argmax(np.abs(norms - 1.0))
return failure(
f"Point {worst_idx} not on unit sphere: |x| = {norms[worst_idx]:.10f}",
off_sphere_count=int(np.sum(off_sphere))
)
# Compute electrostatic energy
energy = 0.0
min_dist = float('inf')
for i in range(n):
for j in range(i + 1, n):
dist = np.linalg.norm(points[i] - points[j])
if dist < TOLERANCE:
return failure(f"Points {i} and {j} are coincident")
energy += 1.0 / dist
min_dist = min(min_dist, dist)
return success(
f"Thomson configuration for n={n}: energy = {energy:.10f}, min distance = {min_dist:.6f}",
num_points=n,
energy=energy,
min_distance=min_dist
)
def main():
parser = argparse.ArgumentParser(description='Validate Thomson configuration for n=50')
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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