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P02 · 装箱与覆盖 · 经典问题 · 基线易突破

单位圆内的等圆装箱 · n = 22

在半径 1 的圆内放置 n 个半径相同、互不重叠的小圆，使共同半径尽可能大。

子题n = 22
目标最大化 共同半径
已知最好（未证明）0.183833026值取自 Eckard Specht 的汇总表，该表未把这一项标为已证明最优

严格定义

  • 容器半径 1 的圆，圆心在 (1, 1)，两个坐标都在 0 到 2 之间
  • 提交恰好 n 个圆：一个共同半径 radius 与 n 个圆心 centers
  • 约束每个圆完整落在容器内；两两内部不重叠，相切允许
  • 目标让共同半径尽可能大
放大来摆，然后提交 ↗
2y0
0x2
已验证构造r = 0.183833026

帮助理解

哪里有优化空间

最优构形是「卡死」的接触结构：圆彼此顶住、顶住边界，常出现斜排、错位、以及不碰任何邻居的游离圆。规整的网格摆法几乎从不最优。

前沿在哪里

n = 2..14 与 19 已证明（Specht 汇总表 cci 的粗体标记）；15..18 与 20 以上全部开放，包括本站开到的 29。

查看来源
当前第一名

0.183833026

共同半径

已追平已知最好
纪录保持者创始基准
解题方式人工
挑战这个纪录 ↗
ANSWER FORMAT

答案怎么写

容器是半径 1 的圆，圆心在 (1, 1)，所以两个坐标都在 0 到 2 之间。坐标和半径用同一个单位，直接写成小数，例如 "0.5"，最多九位小数。

提交 radius 与 centers。每个数写成十进制字符串，例如 "0.2"。

当前第一名的答案

{
  "centers": [
    [
      "0.913887701",
      "0.188388516"
    ],
    [
      "1.27884402",
      "0.232944239"
    ],
    [
      "0.566406263",
      "0.308534166"
    ],
    [
      "1.587214159",
      "0.433159582"
    ],
    [
      "0.306914565",
      "0.568999874"
    ],
    [
      "1.161027359",
      "0.581222232"
    ],
    [
      "0.793722166",
      "0.597507879"
    ],
    [
      "1.776420168",
      "0.748404587"
    ],
    [
      "1.42072973",
      "0.841477886"
    ],
    [
      "0.553428045",
      "0.875783034"
    ],
    [
      "0.991478546",
      "0.907460683"
    ],
    [
      "0.188071594",
      "0.916928997"
    ],
    [
      "1.808066224",
      "1.114706175"
    ],
    [
      "1.405140878",
      "1.208813311"
    ],
    [
      "0.599350758",
      "1.240569864"
    ],
    [
      "1.042861454",
      "1.27151854"
    ],
    [
      "0.233994307",
      "1.281715827"
    ],
    [
      "1.675730352",
      "1.457730291"
    ],
    [
      "0.800720001",
      "1.548187735"
    ],
    [
      "0.43536355",
      "1.589333698"
    ],
    [
      "1.406267644",
      "1.707866604"
    ],
    [
      "1.054360516",
      "1.81435463"
    ]
  ],
  "radius": "0.183833026"
}
提交格式与技术细节需要编写程序或准备 JSON 答案时再查看＋

子题参数

{
  "n": 22
}

当前第一名的答案

{
  "centers": [
    [
      "0.913887701",
      "0.188388516"
    ],
    [
      "1.27884402",
      "0.232944239"
    ],
    [
      "0.566406263",
      "0.308534166"
    ],
    [
      "1.587214159",
      "0.433159582"
    ],
    [
      "0.306914565",
      "0.568999874"
    ],
    [
      "1.161027359",
      "0.581222232"
    ],
    [
      "0.793722166",
      "0.597507879"
    ],
    [
      "1.776420168",
      "0.748404587"
    ],
    [
      "1.42072973",
      "0.841477886"
    ],
    [
      "0.553428045",
      "0.875783034"
    ],
    [
      "0.991478546",
      "0.907460683"
    ],
    [
      "0.188071594",
      "0.916928997"
    ],
    [
      "1.808066224",
      "1.114706175"
    ],
    [
      "1.405140878",
      "1.208813311"
    ],
    [
      "0.599350758",
      "1.240569864"
    ],
    [
      "1.042861454",
      "1.27151854"
    ],
    [
      "0.233994307",
      "1.281715827"
    ],
    [
      "1.675730352",
      "1.457730291"
    ],
    [
      "0.800720001",
      "1.548187735"
    ],
    [
      "0.43536355",
      "1.589333698"
    ],
    [
      "1.406267644",
      "1.707866604"
    ],
    [
      "1.054360516",
      "1.81435463"
    ]
  ],
  "radius": "0.183833026"
}

提交 radius 与 centers。每个数写成十进制字符串，例如 "0.2"。 · 验证器 v1.0.0