| """21 disjoint circles in a rectangle of perimeter 4, maximize the sum of radii |
| (EinsteinArena circles-rectangle, MIT). |
| |
| Upstream bug fixed: the perimeter test is exact (Fractions) upstream but the disjointness test compares |
| float sqrt distances; both are exact here.""" |
| from fractions import Fraction |
|
|
| from run import Invalid, float_matrix |
|
|
|
|
| def check(inst, ans): |
| n = inst["n"] |
| c = float_matrix(ans.get("circles"), n, 3, "circles") |
| F = [tuple(Fraction(v) for v in row) for row in c] |
| if any(r <= 0 for _, _, r in F): |
| raise Invalid("radii must be positive") |
| w = max(x + r for x, _, r in F) - min(x - r for x, _, r in F) |
| h = max(y + r for _, y, r in F) - min(y - r for _, y, r in F) |
| if w + h > 2: |
| raise Invalid("bounding rectangle violates width + height <= 2") |
| for i in range(n): |
| xi, yi, ri = F[i] |
| for j in range(i + 1, n): |
| xj, yj, rj = F[j] |
| if (xi - xj) ** 2 + (yi - yj) ** 2 < (ri + rj) ** 2: |
| raise Invalid(f"circles {i} and {j} overlap") |
| return sum(r for _, _, r in c), {} |
|
|
