Enclose All

AtCoder

IDabc151_f

Time2000ms

Memory256MB

Difficulty—

Given are $N$ points $(x_i, y_i)$ in a two-dimensional plane. Find the minimum radius of a circle such that all the points are inside or on it. ## Constraints * $2 \leq N \leq 50$ * $0 \leq x_i \leq 1000$ * $0 \leq y_i \leq 1000$ * The given $N$ points are all different. * The values in input are all integers. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $:$ $x_N$ $y_N$ [samples]

Samples

Input #1

2
0 0
1 0

Output #1

0.500000000000000000

Both points are contained in the circle centered at $(0.5,0)$ with a radius of $0.5$.

Input #2

Output #2

0.707106781186497524

Input #3

Output #3

6.726812023536805158

If the absolute or relative error from our answer is at most $10^{-6}$, the output will be considered correct.

API Response (JSON)

{
  "problem": {
    "name": "Enclose All",
    "description": {
      "content": "Given are $N$ points $(x_i, y_i)$ in a two-dimensional plane. Find the minimum radius of a circle such that all the points are inside or on it.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc151_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are $N$ points $(x_i, y_i)$ in a two-dimensional plane.\nFind the minimum radius of a circle such that all the points are inside or on it.\n\n## Constraints\n\n*   $2 \\leq N \\leq 50$\n*   $0 \\leq x_i ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments