| """Difference bases: minimize |B|^2 / v (EinsteinArena difference-bases, MIT). |
| |
| v = largest integer such that 1..v are all differences of elements of B (0 is added to B if missing). |
| Ported from the upstream verifier. Changes: elements must be JSON integers in [0, inst["max_value"]] |
| (upstream cast with int(), so floats/strings were silently truncated) and distinct (upstream deduplicated); |
| at most inst["max_size"] elements after adding 0.""" |
| import numpy as np |
|
|
| from run import Invalid, int_list |
|
|
|
|
| def check(inst, ans): |
| s = ans.get("set") |
| if not isinstance(s, list) or not 1 <= len(s) <= inst["max_size"]: |
| raise Invalid(f"set must be a list of 1..{inst['max_size']} integers") |
| int_list(s, None, 0, inst["max_value"], "set") |
| if len(set(s)) != len(s): |
| raise Invalid("elements must be distinct") |
| B = sorted(set(s) | {0}) |
| if len(B) > inst["max_size"]: |
| raise Invalid(f"at most {inst['max_size']} elements including 0") |
| a = np.array(B, dtype=np.int64) |
| d = (a[None, :] - a[:, None])[np.triu_indices(len(a), 1)] |
| present = np.zeros(int(a[-1]) + 2, dtype=bool) |
| present[d] = True |
| present[0] = True |
| v = int(np.argmin(present)) - 1 |
| if v < 1: |
| raise Invalid("1 is not a difference of the set") |
| return len(B) ** 2 / v, {"size": len(B), "v": v} |
|
|
