P01 · 装箱与覆盖 · 经典问题 · 难

单位正方形内的等圆装箱 · n = 242

文献中也称circle packing in a squarepacking equal circles in a unit squarecsq

在边长 1 的正方形内放置 n 个半径相同、互不重叠的圆,使共同半径尽可能大。

子题n = 242
目标最大化 共同半径

纪录对比

共同半径 · 越大越好
纪录数值 / 区间作者 / 持有人来源
外部已知最好[0.0336101150145, 0.0336101150155]见来源署名packomania.com ↗
本站纪录暂无选手纪录——

严格定义

  • 容器单位正方形:左下角是原点 (0, 0),右上角是 (1, 1)
  • 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 ↗

当前展示:起步布局

1y0
0x1
已验证构造r = 0.033610114

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 = 1–30 已证明最优,适合观察经典接触结构;n = 31–300 接入 Packomania 的公开前沿,除 n = 36 外最优性仍未知。大规模部分集中成一张表,供算法批量挑战。

查看来源
单位正方形内的等圆装箱 n = 242 的当前构型
构型与历史

起步布局

查看构型、求解笔记与纪录历史。

挑战这个纪录 ↗提交证明 / 思路 ↓在讨论区分享证明或思路,审核采纳后可获得证明分。
ANSWER FORMAT

答案怎么写

容器是边长 1 的正方形,左下角是原点 (0, 0),右上角是 (1, 1)。坐标和长度用同一个单位,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 "0.25"。

起步布局答案

{
  "centers": [
    [
      "0.033610115",
      "0.033610115"
    ],
    [
      "0.150038969",
      "0.033610115"
    ],
    [
      "0.266467822",
      "0.033610115"
    ],
    [
      "0.382896676",
      "0.033610115"
    ],
    [
      "0.49932553",
      "0.033610115"
    ],
    [
      "0.615754384",
      "0.033610115"
    ],
    [
      "0.732183239",
      "0.033610115"
    ],
    [
      "0.848627905",
      "0.033610115"
    ],
    [
      "0.966389885",
      "0.033610115"
    ],
    [
      "0.907508895",
      "0.066038318"
    ],
    [
      "0.790405572",
      "0.067206533"
    ],
    [
      "0.673968811",
      "0.067220228"
    ],
    [
      "0.557539957",
      "0.06722023"
    ],
    [
      "0.091824542",
      "0.06722023"
    ],
    [
      "0.208253396",
      "0.06722023"
    ],
    [
      "0.324682249",
      "0.06722023"
    ],
    [
      "0.441111103",
      "0.06722023"
    ],
    [
      "0.965033038",
      "0.10081665"
    ],
    [
      "0.84861209",
      "0.100830343"
    ],
    [
      "0.033610115",
      "0.100830345"
    ],
    [
      "0.150038969",
      "0.100830345"
    ],
    [
      "0.266467822",
      "0.100830345"
    ],
    [
      "0.382896676",
      "0.100830345"
    ],
    [
      "0.49932553",
      "0.100830345"
    ],
    [
      "0.615754384",
      "0.100830345"
    ],
    [
      "0.732183237",
      "0.100830345"
    ],
    [
      "0.906826518",
      "0.134440456"
    ],
    [
      "0.091824542",
      "0.13444046"
    ],
    [
      "0.208253396",
      "0.13444046"
    ],
    [
      "0.324682249",
      "0.13444046"
    ],
    [
      "0.441111103",
      "0.13444046"
    ],
    [
      "0.557539957",
      "0.13444046"
    ],
    [
      "0.67396881",
      "0.13444046"
    ],
    [
      "0.790397664",
      "0.13444046"
    ],
    [
      "0.966389885",
      "0.168023184"
    ],
    [
      "0.848612092",
      "0.168050573"
    ],
    [
      "0.033610115",
      "0.168050575"
    ],
    [
      "0.150038969",
      "0.168050575"
    ],
    [
      "0.266467822",
      "0.168050575"
    ],
    [
      "0.382896676",
      "0.168050575"
    ],
    [
      "0.49932553",
      "0.168050575"
    ],
    [
      "0.615754384",
      "0.168050575"
    ],
    [
      "0.732183237",
      "0.168050575"
    ],
    [
      "0.90682652",
      "0.201660686"
    ],
    [
      "0.091824542",
      "0.20166069"
    ],
    [
      "0.208253396",
      "0.20166069"
    ],
    [
      "0.324682249",
      "0.20166069"
    ],
    [
      "0.441111103",
      "0.20166069"
    ],
    [
      "0.557539957",
      "0.20166069"
    ],
    [
      "0.67396881",
      "0.20166069"
    ],
    [
      "0.790397664",
      "0.20166069"
    ],
    [
      "0.965064287",
      "0.235230342"
    ],
    [
      "0.848612094",
      "0.235270803"
    ],
    [
      "0.033610115",
      "0.235270805"
    ],
    [
      "0.150038969",
      "0.235270805"
    ],
    [
      "0.266467822",
      "0.235270805"
    ],
    [
      "0.382896676",
      "0.235270805"
    ],
    [
      "0.49932553",
      "0.235270805"
    ],
    [
      "0.615754384",
      "0.235270805"
    ],
    [
      "0.732183237",
      "0.235270805"
    ],
    [
      "0.906873229",
      "0.2688809"
    ],
    [
      "0.091824542",
      "0.26888092"
    ],
    [
      "0.208253396",
      "0.26888092"
    ],
    [
      "0.324682249",
      "0.26888092"
    ],
    [
      "0.441111103",
      "0.26888092"
    ],
    [
      "0.557539957",
      "0.26888092"
    ],
    [
      "0.67396881",
      "0.26888092"
    ],
    [
      "0.790397664",
      "0.26888092"
    ],
    [
      "0.966389885",
      "0.302437501"
    ],
    [
      "0.848612092",
      "0.302491033"
    ],
    [
      "0.033610115",
      "0.302491035"
    ],
    [
      "0.150038969",
      "0.302491035"
    ],
    [
      "0.266467822",
      "0.302491035"
    ],
    [
      "0.382896676",
      "0.302491035"
    ],
    [
      "0.49932553",
      "0.302491035"
    ],
    [
      "0.615754384",
      "0.302491035"
    ],
    [
      "0.732183237",
      "0.302491035"
    ],
    [
      "0.906826539",
      "0.336101114"
    ],
    [
      "0.091824542",
      "0.33610115"
    ],
    [
      "0.208253396",
      "0.33610115"
    ],
    [
      "0.324682249",
      "0.33610115"
    ],
    [
      "0.441111103",
      "0.33610115"
    ],
    [
      "0.557539957",
      "0.33610115"
    ],
    [
      "0.67396881",
      "0.33610115"
    ],
    [
      "0.790397664",
      "0.33610115"
    ],
    [
      "0.965079181",
      "0.369644951"
    ],
    [
      "0.848612132",
      "0.369711263"
    ],
    [
      "0.033610115",
      "0.369711265"
    ],
    [
      "0.150038969",
      "0.369711265"
    ],
    [
      "0.266467822",
      "0.369711265"
    ],
    [
      "0.382896676",
      "0.369711265"
    ],
    [
      "0.49932553",
      "0.369711265"
    ],
    [
      "0.615754384",
      "0.369711265"
    ],
    [
      "0.732183237",
      "0.369711265"
    ],
    [
      "0.906903045",
      "0.4033213"
    ],
    [
      "0.091824542",
      "0.40332138"
    ],
    [
      "0.208253396",
      "0.40332138"
    ],
    [
      "0.324682249",
      "0.40332138"
    ],
    [
      "0.441111103",
      "0.40332138"
    ],
    [
      "0.557539957",
      "0.40332138"
    ],
    [
      "0.67396881",
      "0.40332138"
    ],
    [
      "0.790397664",
      "0.40332138"
    ],
    [
      "0.966389885",
      "0.436852401"
    ],
    [
      "0.848612092",
      "0.436931493"
    ],
    [
      "0.033610115",
      "0.436931495"
    ],
    [
      "0.150038969",
      "0.436931495"
    ],
    [
      "0.266467822",
      "0.436931495"
    ],
    [
      "0.382896676",
      "0.436931495"
    ],
    [
      "0.49932553",
      "0.436931495"
    ],
    [
      "0.615754384",
      "0.436931495"
    ],
    [
      "0.732183237",
      "0.436931495"
    ],
    [
      "0.906826589",
      "0.470541487"
    ],
    [
      "0.790397666",
      "0.47054161"
    ],
    [
      "0.091824542",
      "0.47054161"
    ],
    [
      "0.208253396",
      "0.47054161"
    ],
    [
      "0.324682249",
      "0.47054161"
    ],
    [
      "0.441111103",
      "0.47054161"
    ],
    [
      "0.557539957",
      "0.47054161"
    ],
    [
      "0.67396881",
      "0.47054161"
    ],
    [
      "0.965093729",
      "0.504060134"
    ],
    [
      "0.848612232",
      "0.504151723"
    ],
    [
      "0.732183239",
      "0.504151725"
    ],
    [
      "0.033610115",
      "0.504151725"
    ],
    [
      "0.150038969",
      "0.504151725"
    ],
    [
      "0.266467822",
      "0.504151725"
    ],
    [
      "0.382896676",
      "0.504151725"
    ],
    [
      "0.49932553",
      "0.504151725"
    ],
    [
      "0.615754384",
      "0.504151725"
    ],
    [
      "0.90693216",
      "0.537761634"
    ],
    [
      "0.673968813",
      "0.53776184"
    ],
    [
      "0.790397666",
      "0.53776184"
    ],
    [
      "0.091824542",
      "0.53776184"
    ],
    [
      "0.208253396",
      "0.53776184"
    ],
    [
      "0.324682249",
      "0.53776184"
    ],
    [
      "0.441111103",
      "0.53776184"
    ],
    [
      "0.557539957",
      "0.53776184"
    ],
    [
      "0.966389885",
      "0.571267866"
    ],
    [
      "0.848612094",
      "0.571371953"
    ],
    [
      "0.615754386",
      "0.571371955"
    ],
    [
      "0.732183239",
      "0.571371955"
    ],
    [
      "0.033610115",
      "0.571371955"
    ],
    [
      "0.150038969",
      "0.571371955"
    ],
    [
      "0.266467822",
      "0.571371955"
    ],
    [
      "0.382896676",
      "0.571371955"
    ],
    [
      "0.49932553",
      "0.571371955"
    ],
    [
      "0.906826687",
      "0.604981781"
    ],
    [
      "0.790397668",
      "0.60498207"
    ],
    [
      "0.557539959",
      "0.60498207"
    ],
    [
      "0.673968813",
      "0.60498207"
    ],
    [
      "0.091824542",
      "0.60498207"
    ],
    [
      "0.208253396",
      "0.60498207"
    ],
    [
      "0.324682249",
      "0.60498207"
    ],
    [
      "0.441111103",
      "0.60498207"
    ],
    [
      "0.965107947",
      "0.638475871"
    ],
    [
      "0.848612096",
      "0.638592183"
    ],
    [
      "0.732183242",
      "0.638592185"
    ],
    [
      "0.499325532",
      "0.638592185"
    ],
    [
      "0.615754386",
      "0.638592185"
    ],
    [
      "0.033610115",
      "0.638592185"
    ],
    [
      "0.150038969",
      "0.638592185"
    ],
    [
      "0.266467822",
      "0.638592185"
    ],
    [
      "0.382896676",
      "0.638592185"
    ],
    [
      "0.906826689",
      "0.672202011"
    ],
    [
      "0.673968815",
      "0.6722023"
    ],
    [
      "0.790397668",
      "0.6722023"
    ],
    [
      "0.441111105",
      "0.6722023"
    ],
    [
      "0.557539959",
      "0.6722023"
    ],
    [
      "0.091824542",
      "0.6722023"
    ],
    [
      "0.208253396",
      "0.6722023"
    ],
    [
      "0.324682249",
      "0.6722023"
    ],
    [
      "0.966389885",
      "0.705683877"
    ],
    [
      "0.848612096",
      "0.705812413"
    ],
    [
      "0.615754388",
      "0.705812415"
    ],
    [
      "0.732183242",
      "0.705812415"
    ],
    [
      "0.382896678",
      "0.705812415"
    ],
    [
      "0.499325532",
      "0.705812415"
    ],
    [
      "0.033610115",
      "0.705812415"
    ],
    [
      "0.150038969",
      "0.705812415"
    ],
    [
      "0.266467822",
      "0.705812415"
    ],
    [
      "0.908108625",
      "0.739410017"
    ],
    [
      "0.557539961",
      "0.73942253"
    ],
    [
      "0.673968815",
      "0.73942253"
    ],
    [
      "0.324682251",
      "0.73942253"
    ],
    [
      "0.441111105",
      "0.73942253"
    ],
    [
      "0.091824542",
      "0.73942253"
    ],
    [
      "0.208253396",
      "0.73942253"
    ],
    [
      "0.790397862",
      "0.739422866"
    ],
    [
      "0.966389885",
      "0.772904107"
    ],
    [
      "0.849894032",
      "0.773020419"
    ],
    [
      "0.499325534",
      "0.773032645"
    ],
    [
      "0.615754388",
      "0.773032645"
    ],
    [
      "0.732183242",
      "0.773032645"
    ],
    [
      "0.266467825",
      "0.773032645"
    ],
    [
      "0.382896678",
      "0.773032645"
    ],
    [
      "0.033610115",
      "0.773032645"
    ],
    [
      "0.150038969",
      "0.773032645"
    ],
    [
      "0.908108625",
      "0.806630247"
    ],
    [
      "0.791646506",
      "0.806634556"
    ],
    [
      "0.441111107",
      "0.80664276"
    ],
    [
      "0.557539961",
      "0.80664276"
    ],
    [
      "0.091824542",
      "0.80664276"
    ],
    [
      "0.208253396",
      "0.80664276"
    ],
    [
      "0.324682251",
      "0.806642761"
    ],
    [
      "0.674356911",
      "0.807314963"
    ],
    [
      "0.966389885",
      "0.840124337"
    ],
    [
      "0.849894364",
      "0.840240649"
    ],
    [
      "0.733430139",
      "0.84024131"
    ],
    [
      "0.38289668",
      "0.840252875"
    ],
    [
      "0.499325534",
      "0.840252875"
    ],
    [
      "0.615754388",
      "0.840252875"
    ],
    [
      "0.266467822",
      "0.840252875"
    ],
    [
      "0.033610115",
      "0.840252875"
    ],
    [
      "0.150038969",
      "0.840252875"
    ],
    [
      "0.901726383",
      "0.884954328"
    ],
    [
      "0.098408289",
      "0.885962632"
    ],
    [
      "0.435518232",
      "0.885962632"
    ],
    [
      "0.565876531",
      "0.885962632"
    ],
    [
      "0.770585421",
      "0.89625956"
    ],
    [
      "0.229734456",
      "0.896548693"
    ],
    [
      "0.696862367",
      "0.896644832"
    ],
    [
      "0.303013347",
      "0.896670816"
    ],
    [
      "0.63028023",
      "0.905884874"
    ],
    [
      "0.369563632",
      "0.906137541"
    ],
    [
      "0.163206463",
      "0.906170828"
    ],
    [
      "0.837062881",
      "0.906224831"
    ],
    [
      "0.966389885",
      "0.907344567"
    ],
    [
      "0.501472832",
      "0.9074388"
    ],
    [
      "0.033610115",
      "0.907473105"
    ],
    [
      "0.734017649",
      "0.952663082"
    ],
    [
      "0.26627998",
      "0.952966633"
    ],
    [
      "0.466569995",
      "0.964887484"
    ],
    [
      "0.133193441",
      "0.966318794"
    ],
    [
      "0.065973248",
      "0.966389885"
    ],
    [
      "0.200413633",
      "0.966389885"
    ],
    [
      "0.332146327",
      "0.966389885"
    ],
    [
      "0.399366557",
      "0.966389885"
    ],
    [
      "0.533773434",
      "0.966389885"
    ],
    [
      "0.600993664",
      "0.966389885"
    ],
    [
      "0.668213894",
      "0.966389885"
    ],
    [
      "0.799821404",
      "0.966389885"
    ],
    [
      "0.867041634",
      "0.966389885"
    ],
    [
      "0.934261864",
      "0.966389885"
    ]
  ],
  "radius": "0.033610114"
}
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": 242
}

起步布局答案

{
  "centers": [
    [
      "0.033610115",
      "0.033610115"
    ],
    [
      "0.150038969",
      "0.033610115"
    ],
    [
      "0.266467822",
      "0.033610115"
    ],
    [
      "0.382896676",
      "0.033610115"
    ],
    [
      "0.49932553",
      "0.033610115"
    ],
    [
      "0.615754384",
      "0.033610115"
    ],
    [
      "0.732183239",
      "0.033610115"
    ],
    [
      "0.848627905",
      "0.033610115"
    ],
    [
      "0.966389885",
      "0.033610115"
    ],
    [
      "0.907508895",
      "0.066038318"
    ],
    [
      "0.790405572",
      "0.067206533"
    ],
    [
      "0.673968811",
      "0.067220228"
    ],
    [
      "0.557539957",
      "0.06722023"
    ],
    [
      "0.091824542",
      "0.06722023"
    ],
    [
      "0.208253396",
      "0.06722023"
    ],
    [
      "0.324682249",
      "0.06722023"
    ],
    [
      "0.441111103",
      "0.06722023"
    ],
    [
      "0.965033038",
      "0.10081665"
    ],
    [
      "0.84861209",
      "0.100830343"
    ],
    [
      "0.033610115",
      "0.100830345"
    ],
    [
      "0.150038969",
      "0.100830345"
    ],
    [
      "0.266467822",
      "0.100830345"
    ],
    [
      "0.382896676",
      "0.100830345"
    ],
    [
      "0.49932553",
      "0.100830345"
    ],
    [
      "0.615754384",
      "0.100830345"
    ],
    [
      "0.732183237",
      "0.100830345"
    ],
    [
      "0.906826518",
      "0.134440456"
    ],
    [
      "0.091824542",
      "0.13444046"
    ],
    [
      "0.208253396",
      "0.13444046"
    ],
    [
      "0.324682249",
      "0.13444046"
    ],
    [
      "0.441111103",
      "0.13444046"
    ],
    [
      "0.557539957",
      "0.13444046"
    ],
    [
      "0.67396881",
      "0.13444046"
    ],
    [
      "0.790397664",
      "0.13444046"
    ],
    [
      "0.966389885",
      "0.168023184"
    ],
    [
      "0.848612092",
      "0.168050573"
    ],
    [
      "0.033610115",
      "0.168050575"
    ],
    [
      "0.150038969",
      "0.168050575"
    ],
    [
      "0.266467822",
      "0.168050575"
    ],
    [
      "0.382896676",
      "0.168050575"
    ],
    [
      "0.49932553",
      "0.168050575"
    ],
    [
      "0.615754384",
      "0.168050575"
    ],
    [
      "0.732183237",
      "0.168050575"
    ],
    [
      "0.90682652",
      "0.201660686"
    ],
    [
      "0.091824542",
      "0.20166069"
    ],
    [
      "0.208253396",
      "0.20166069"
    ],
    [
      "0.324682249",
      "0.20166069"
    ],
    [
      "0.441111103",
      "0.20166069"
    ],
    [
      "0.557539957",
      "0.20166069"
    ],
    [
      "0.67396881",
      "0.20166069"
    ],
    [
      "0.790397664",
      "0.20166069"
    ],
    [
      "0.965064287",
      "0.235230342"
    ],
    [
      "0.848612094",
      "0.235270803"
    ],
    [
      "0.033610115",
      "0.235270805"
    ],
    [
      "0.150038969",
      "0.235270805"
    ],
    [
      "0.266467822",
      "0.235270805"
    ],
    [
      "0.382896676",
      "0.235270805"
    ],
    [
      "0.49932553",
      "0.235270805"
    ],
    [
      "0.615754384",
      "0.235270805"
    ],
    [
      "0.732183237",
      "0.235270805"
    ],
    [
      "0.906873229",
      "0.2688809"
    ],
    [
      "0.091824542",
      "0.26888092"
    ],
    [
      "0.208253396",
      "0.26888092"
    ],
    [
      "0.324682249",
      "0.26888092"
    ],
    [
      "0.441111103",
      "0.26888092"
    ],
    [
      "0.557539957",
      "0.26888092"
    ],
    [
      "0.67396881",
      "0.26888092"
    ],
    [
      "0.790397664",
      "0.26888092"
    ],
    [
      "0.966389885",
      "0.302437501"
    ],
    [
      "0.848612092",
      "0.302491033"
    ],
    [
      "0.033610115",
      "0.302491035"
    ],
    [
      "0.150038969",
      "0.302491035"
    ],
    [
      "0.266467822",
      "0.302491035"
    ],
    [
      "0.382896676",
      "0.302491035"
    ],
    [
      "0.49932553",
      "0.302491035"
    ],
    [
      "0.615754384",
      "0.302491035"
    ],
    [
      "0.732183237",
      "0.302491035"
    ],
    [
      "0.906826539",
      "0.336101114"
    ],
    [
      "0.091824542",
      "0.33610115"
    ],
    [
      "0.208253396",
      "0.33610115"
    ],
    [
      "0.324682249",
      "0.33610115"
    ],
    [
      "0.441111103",
      "0.33610115"
    ],
    [
      "0.557539957",
      "0.33610115"
    ],
    [
      "0.67396881",
      "0.33610115"
    ],
    [
      "0.790397664",
      "0.33610115"
    ],
    [
      "0.965079181",
      "0.369644951"
    ],
    [
      "0.848612132",
      "0.369711263"
    ],
    [
      "0.033610115",
      "0.369711265"
    ],
    [
      "0.150038969",
      "0.369711265"
    ],
    [
      "0.266467822",
      "0.369711265"
    ],
    [
      "0.382896676",
      "0.369711265"
    ],
    [
      "0.49932553",
      "0.369711265"
    ],
    [
      "0.615754384",
      "0.369711265"
    ],
    [
      "0.732183237",
      "0.369711265"
    ],
    [
      "0.906903045",
      "0.4033213"
    ],
    [
      "0.091824542",
      "0.40332138"
    ],
    [
      "0.208253396",
      "0.40332138"
    ],
    [
      "0.324682249",
      "0.40332138"
    ],
    [
      "0.441111103",
      "0.40332138"
    ],
    [
      "0.557539957",
      "0.40332138"
    ],
    [
      "0.67396881",
      "0.40332138"
    ],
    [
      "0.790397664",
      "0.40332138"
    ],
    [
      "0.966389885",
      "0.436852401"
    ],
    [
      "0.848612092",
      "0.436931493"
    ],
    [
      "0.033610115",
      "0.436931495"
    ],
    [
      "0.150038969",
      "0.436931495"
    ],
    [
      "0.266467822",
      "0.436931495"
    ],
    [
      "0.382896676",
      "0.436931495"
    ],
    [
      "0.49932553",
      "0.436931495"
    ],
    [
      "0.615754384",
      "0.436931495"
    ],
    [
      "0.732183237",
      "0.436931495"
    ],
    [
      "0.906826589",
      "0.470541487"
    ],
    [
      "0.790397666",
      "0.47054161"
    ],
    [
      "0.091824542",
      "0.47054161"
    ],
    [
      "0.208253396",
      "0.47054161"
    ],
    [
      "0.324682249",
      "0.47054161"
    ],
    [
      "0.441111103",
      "0.47054161"
    ],
    [
      "0.557539957",
      "0.47054161"
    ],
    [
      "0.67396881",
      "0.47054161"
    ],
    [
      "0.965093729",
      "0.504060134"
    ],
    [
      "0.848612232",
      "0.504151723"
    ],
    [
      "0.732183239",
      "0.504151725"
    ],
    [
      "0.033610115",
      "0.504151725"
    ],
    [
      "0.150038969",
      "0.504151725"
    ],
    [
      "0.266467822",
      "0.504151725"
    ],
    [
      "0.382896676",
      "0.504151725"
    ],
    [
      "0.49932553",
      "0.504151725"
    ],
    [
      "0.615754384",
      "0.504151725"
    ],
    [
      "0.90693216",
      "0.537761634"
    ],
    [
      "0.673968813",
      "0.53776184"
    ],
    [
      "0.790397666",
      "0.53776184"
    ],
    [
      "0.091824542",
      "0.53776184"
    ],
    [
      "0.208253396",
      "0.53776184"
    ],
    [
      "0.324682249",
      "0.53776184"
    ],
    [
      "0.441111103",
      "0.53776184"
    ],
    [
      "0.557539957",
      "0.53776184"
    ],
    [
      "0.966389885",
      "0.571267866"
    ],
    [
      "0.848612094",
      "0.571371953"
    ],
    [
      "0.615754386",
      "0.571371955"
    ],
    [
      "0.732183239",
      "0.571371955"
    ],
    [
      "0.033610115",
      "0.571371955"
    ],
    [
      "0.150038969",
      "0.571371955"
    ],
    [
      "0.266467822",
      "0.571371955"
    ],
    [
      "0.382896676",
      "0.571371955"
    ],
    [
      "0.49932553",
      "0.571371955"
    ],
    [
      "0.906826687",
      "0.604981781"
    ],
    [
      "0.790397668",
      "0.60498207"
    ],
    [
      "0.557539959",
      "0.60498207"
    ],
    [
      "0.673968813",
      "0.60498207"
    ],
    [
      "0.091824542",
      "0.60498207"
    ],
    [
      "0.208253396",
      "0.60498207"
    ],
    [
      "0.324682249",
      "0.60498207"
    ],
    [
      "0.441111103",
      "0.60498207"
    ],
    [
      "0.965107947",
      "0.638475871"
    ],
    [
      "0.848612096",
      "0.638592183"
    ],
    [
      "0.732183242",
      "0.638592185"
    ],
    [
      "0.499325532",
      "0.638592185"
    ],
    [
      "0.615754386",
      "0.638592185"
    ],
    [
      "0.033610115",
      "0.638592185"
    ],
    [
      "0.150038969",
      "0.638592185"
    ],
    [
      "0.266467822",
      "0.638592185"
    ],
    [
      "0.382896676",
      "0.638592185"
    ],
    [
      "0.906826689",
      "0.672202011"
    ],
    [
      "0.673968815",
      "0.6722023"
    ],
    [
      "0.790397668",
      "0.6722023"
    ],
    [
      "0.441111105",
      "0.6722023"
    ],
    [
      "0.557539959",
      "0.6722023"
    ],
    [
      "0.091824542",
      "0.6722023"
    ],
    [
      "0.208253396",
      "0.6722023"
    ],
    [
      "0.324682249",
      "0.6722023"
    ],
    [
      "0.966389885",
      "0.705683877"
    ],
    [
      "0.848612096",
      "0.705812413"
    ],
    [
      "0.615754388",
      "0.705812415"
    ],
    [
      "0.732183242",
      "0.705812415"
    ],
    [
      "0.382896678",
      "0.705812415"
    ],
    [
      "0.499325532",
      "0.705812415"
    ],
    [
      "0.033610115",
      "0.705812415"
    ],
    [
      "0.150038969",
      "0.705812415"
    ],
    [
      "0.266467822",
      "0.705812415"
    ],
    [
      "0.908108625",
      "0.739410017"
    ],
    [
      "0.557539961",
      "0.73942253"
    ],
    [
      "0.673968815",
      "0.73942253"
    ],
    [
      "0.324682251",
      "0.73942253"
    ],
    [
      "0.441111105",
      "0.73942253"
    ],
    [
      "0.091824542",
      "0.73942253"
    ],
    [
      "0.208253396",
      "0.73942253"
    ],
    [
      "0.790397862",
      "0.739422866"
    ],
    [
      "0.966389885",
      "0.772904107"
    ],
    [
      "0.849894032",
      "0.773020419"
    ],
    [
      "0.499325534",
      "0.773032645"
    ],
    [
      "0.615754388",
      "0.773032645"
    ],
    [
      "0.732183242",
      "0.773032645"
    ],
    [
      "0.266467825",
      "0.773032645"
    ],
    [
      "0.382896678",
      "0.773032645"
    ],
    [
      "0.033610115",
      "0.773032645"
    ],
    [
      "0.150038969",
      "0.773032645"
    ],
    [
      "0.908108625",
      "0.806630247"
    ],
    [
      "0.791646506",
      "0.806634556"
    ],
    [
      "0.441111107",
      "0.80664276"
    ],
    [
      "0.557539961",
      "0.80664276"
    ],
    [
      "0.091824542",
      "0.80664276"
    ],
    [
      "0.208253396",
      "0.80664276"
    ],
    [
      "0.324682251",
      "0.806642761"
    ],
    [
      "0.674356911",
      "0.807314963"
    ],
    [
      "0.966389885",
      "0.840124337"
    ],
    [
      "0.849894364",
      "0.840240649"
    ],
    [
      "0.733430139",
      "0.84024131"
    ],
    [
      "0.38289668",
      "0.840252875"
    ],
    [
      "0.499325534",
      "0.840252875"
    ],
    [
      "0.615754388",
      "0.840252875"
    ],
    [
      "0.266467822",
      "0.840252875"
    ],
    [
      "0.033610115",
      "0.840252875"
    ],
    [
      "0.150038969",
      "0.840252875"
    ],
    [
      "0.901726383",
      "0.884954328"
    ],
    [
      "0.098408289",
      "0.885962632"
    ],
    [
      "0.435518232",
      "0.885962632"
    ],
    [
      "0.565876531",
      "0.885962632"
    ],
    [
      "0.770585421",
      "0.89625956"
    ],
    [
      "0.229734456",
      "0.896548693"
    ],
    [
      "0.696862367",
      "0.896644832"
    ],
    [
      "0.303013347",
      "0.896670816"
    ],
    [
      "0.63028023",
      "0.905884874"
    ],
    [
      "0.369563632",
      "0.906137541"
    ],
    [
      "0.163206463",
      "0.906170828"
    ],
    [
      "0.837062881",
      "0.906224831"
    ],
    [
      "0.966389885",
      "0.907344567"
    ],
    [
      "0.501472832",
      "0.9074388"
    ],
    [
      "0.033610115",
      "0.907473105"
    ],
    [
      "0.734017649",
      "0.952663082"
    ],
    [
      "0.26627998",
      "0.952966633"
    ],
    [
      "0.466569995",
      "0.964887484"
    ],
    [
      "0.133193441",
      "0.966318794"
    ],
    [
      "0.065973248",
      "0.966389885"
    ],
    [
      "0.200413633",
      "0.966389885"
    ],
    [
      "0.332146327",
      "0.966389885"
    ],
    [
      "0.399366557",
      "0.966389885"
    ],
    [
      "0.533773434",
      "0.966389885"
    ],
    [
      "0.600993664",
      "0.966389885"
    ],
    [
      "0.668213894",
      "0.966389885"
    ],
    [
      "0.799821404",
      "0.966389885"
    ],
    [
      "0.867041634",
      "0.966389885"
    ],
    [
      "0.934261864",
      "0.966389885"
    ]
  ],
  "radius": "0.033610114"
}

提交 radius 与 centers。每个数写成十进制字符串,例如 "0.25"。 · 验证器 v1.0.0

DISCUSSION

讨论区

聊思路、贴方法、问为什么卡住。所有登录用户都可以发帖;发言公开署名,与纪录使用同一个名字,署名后的 #编号是账号注册序号,冒不了名。新发言经自动审核后公开。