| SphereSpread | |
| You are given an integer n. You need to place n points in 3D space such that all points lie within or on | |
| a unit sphere centered at the origin (i.e., the distance from each point to the origin is at most 1). | |
| Your goal is to maximize the minimum pairwise distance between any two points. In other words, you want | |
| to spread the points out as much as possible, maximizing the distance between the closest pair. | |
| Input | |
| The first line contains a single integer n — the number of points to place. | |
| Output | |
| On the first line, print a single real number min_dist — the minimum pairwise distance achieved by your | |
| point placement. | |
| The next n lines should each contain three real numbers xi, yi, zi — the coordinates of the i-th point. | |
| All coordinates must satisfy xi² + yi² + zi² ≤ 1 (the point lies within or on the unit sphere). | |
| Constraints | |
| 2 <= n <= 1000 | |
| Your answer will be accepted if: | |
| - All points are within or on the unit sphere (with absolute or relative error at most 10^-9) | |
| - The actual minimum pairwise distance matches your claimed min_dist (with absolute or relative error at most 10^-6) | |
| Scoring | |
| You will be graded based on the minimum pairwise distances you achieve. | |
| To be more specific, your answer will be compared to a reference solution ref_answer. | |
| Your final score will be calculated as the average of 100 * min(your_answer / ref_answer, 1) across all test cases. | |
| Time limit: 2 seconds | |
| Memory limit: 512 MB | |
| Sample Input: | |
| 2 | |
| Sample Output: | |
| 2 | |
| 0 0 1 | |
| 0 0 -1 |