P02 · 装箱与覆盖 · 经典问题 · 基线易突破 · 难

单位圆内的等圆装箱 · n = 296

文献中也称circles in a circlepacking equal circles in a circlecci

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 = 296
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[0.0534685722935, 0.0534685722945]见来源署名packomania.com ↗
本站纪录0.053468572游侠纪录详情 ↓

本站纪录尚未确认达到或超越此参考纪录。

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
挑战这个纪录 ↗

当前展示:本站纪录

2y0
0x2
已验证构造r = 0.053468572

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..14 与 19 已证明;其余规模的最优性仍未知。本站接入 Packomania 中 n = 1..300 的公开构型,大规模部分集中成一张表供算法批量挑战。

查看来源
单位圆内的等圆装箱 n = 296 的当前纪录构型,0.053468572
构型与历史

纪录详情

查看构型、求解笔记与纪录历史。

纪录保持者游侠
解题方式AI · OpenAI: GPT-5.6 Sol
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。
纪录保持者的求解笔记暂无求解笔记(点击展开)+

纪录保持者还没有分享求解过程。

历史纪录(1 次易主)
  1. 游侠AI · OpenAI: GPT-5.6 Sol
    0.053468571→0.053468572
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": [
    [
      "0.994135090",
      "0.053530419"
    ],
    [
      "0.865222768",
      "0.063113219"
    ],
    [
      "1.100541128",
      "0.064892277"
    ],
    [
      "1.212220666",
      "0.077566191"
    ],
    [
      "0.759434478",
      "0.084549306"
    ],
    [
      "1.402480127",
      "0.143301984"
    ],
    [
      "0.935583431",
      "0.143642282"
    ],
    [
      "1.295550692",
      "0.144586036"
    ],
    [
      "0.678651889",
      "0.154618744"
    ],
    [
      "0.571722454",
      "0.155902798"
    ],
    [
      "1.147498758",
      "0.162693316"
    ],
    [
      "1.040569323",
      "0.163977368"
    ],
    [
      "0.830662885",
      "0.164311872"
    ],
    [
      "1.512919116",
      "0.204490274"
    ],
    [
      "0.461866730",
      "0.221325276"
    ],
    [
      "1.415868245",
      "0.249397748"
    ],
    [
      "1.308938809",
      "0.250681800"
    ],
    [
      "1.202075497",
      "0.254654897"
    ],
    [
      "0.774392050",
      "0.255504250"
    ],
    [
      "1.095146062",
      "0.255938949"
    ],
    [
      "0.988216627",
      "0.257223001"
    ],
    [
      "0.881287192",
      "0.258507054"
    ],
    [
      "0.667585955",
      "0.260981792"
    ],
    [
      "0.560656520",
      "0.262265846"
    ],
    [
      "1.567495855",
      "0.296451855"
    ],
    [
      "0.409417672",
      "0.314516741"
    ],
    [
      "1.668925420",
      "0.330328046"
    ],
    [
      "1.470444984",
      "0.341359329"
    ],
    [
      "1.363515549",
      "0.342643381"
    ],
    [
      "1.256652237",
      "0.346616478"
    ],
    [
      "1.149722802",
      "0.347900531"
    ],
    [
      "1.042793367",
      "0.349184583"
    ],
    [
      "0.935863932",
      "0.350468635"
    ],
    [
      "0.828934497",
      "0.351752688"
    ],
    [
      "0.309493043",
      "0.352603764"
    ],
    [
      "0.722005062",
      "0.353036741"
    ],
    [
      "0.615075627",
      "0.354320795"
    ],
    [
      "0.508146191",
      "0.355604846"
    ],
    [
      "1.740370249",
      "0.410286313"
    ],
    [
      "1.631925768",
      "0.430660387"
    ],
    [
      "1.525021725",
      "0.433320909"
    ],
    [
      "1.418092288",
      "0.434604962"
    ],
    [
      "1.311228976",
      "0.438578059"
    ],
    [
      "0.238987801",
      "0.438967351"
    ],
    [
      "1.204299541",
      "0.439862112"
    ],
    [
      "1.097370106",
      "0.441146164"
    ],
    [
      "0.990440671",
      "0.442430216"
    ],
    [
      "0.883511236",
      "0.443714269"
    ],
    [
      "0.776581801",
      "0.444998322"
    ],
    [
      "0.669652366",
      "0.446282376"
    ],
    [
      "0.562722931",
      "0.447566428"
    ],
    [
      "0.455793496",
      "0.448850481"
    ],
    [
      "0.348903154",
      "0.452014005"
    ],
    [
      "1.809423478",
      "0.509331704"
    ],
    [
      "1.702499393",
      "0.511002881"
    ],
    [
      "1.579598464",
      "0.525282490"
    ],
    [
      "1.472669029",
      "0.526566542"
    ],
    [
      "0.179563014",
      "0.528213078"
    ],
    [
      "1.365805717",
      "0.530539639"
    ],
    [
      "1.258876282",
      "0.531823693"
    ],
    [
      "1.151946847",
      "0.533107746"
    ],
    [
      "1.045017412",
      "0.534391798"
    ],
    [
      "0.938087977",
      "0.535675850"
    ],
    [
      "0.831158540",
      "0.536959903"
    ],
    [
      "0.724229105",
      "0.538243957"
    ],
    [
      "0.617299670",
      "0.539528009"
    ],
    [
      "0.510370235",
      "0.540812062"
    ],
    [
      "0.403479894",
      "0.543975586"
    ],
    [
      "0.296550459",
      "0.545259639"
    ],
    [
      "1.757408717",
      "0.602766267"
    ],
    [
      "1.650502394",
      "0.605333633"
    ],
    [
      "1.863845527",
      "0.613098657"
    ],
    [
      "1.527245769",
      "0.618528124"
    ],
    [
      "1.420382457",
      "0.622501220"
    ],
    [
      "1.313453021",
      "0.623785274"
    ],
    [
      "1.206523586",
      "0.625069327"
    ],
    [
      "1.099594151",
      "0.626353379"
    ],
    [
      "0.226944451",
      "0.626441882"
    ],
    [
      "0.992664716",
      "0.627637431"
    ],
    [
      "0.885735281",
      "0.628921483"
    ],
    [
      "0.778805846",
      "0.630205537"
    ],
    [
      "0.671876409",
      "0.631489590"
    ],
    [
      "0.564946974",
      "0.632773643"
    ],
    [
      "0.458056633",
      "0.635937167"
    ],
    [
      "0.351127198",
      "0.637221220"
    ],
    [
      "0.121921958",
      "0.646587077"
    ],
    [
      "1.795537160",
      "0.702675099"
    ],
    [
      "1.688630839",
      "0.705242465"
    ],
    [
      "1.581822509",
      "0.710489705"
    ],
    [
      "1.901973970",
      "0.713007489"
    ],
    [
      "1.474959197",
      "0.714462801"
    ],
    [
      "1.368029762",
      "0.715746854"
    ],
    [
      "1.261100327",
      "0.717030908"
    ],
    [
      "1.154170890",
      "0.718314960"
    ],
    [
      "1.047241455",
      "0.719599012"
    ],
    [
      "0.940312020",
      "0.720883064"
    ],
    [
      "0.833382585",
      "0.722167118"
    ],
    [
      "0.726453150",
      "0.723451170"
    ],
    [
      "0.619523715",
      "0.724735224"
    ],
    [
      "0.191879455",
      "0.727466626"
    ],
    [
      "0.512633374",
      "0.727898747"
    ],
    [
      "0.405703939",
      "0.729182801"
    ],
    [
      "0.298774504",
      "0.730466854"
    ],
    [
      "0.087228526",
      "0.749460623"
    ],
    [
      "1.743207578",
      "0.797204046"
    ],
    [
      "1.636399248",
      "0.802451286"
    ],
    [
      "1.849754784",
      "0.806327956"
    ],
    [
      "1.529535936",
      "0.806424382"
    ],
    [
      "1.422606501",
      "0.807708435"
    ],
    [
      "1.315677066",
      "0.808992489"
    ],
    [
      "1.208747631",
      "0.810276541"
    ],
    [
      "1.101818196",
      "0.811560594"
    ],
    [
      "0.994888761",
      "0.812844646"
    ],
    [
      "0.887959326",
      "0.814128698"
    ],
    [
      "0.781029889",
      "0.815412751"
    ],
    [
      "0.674100454",
      "0.816696805"
    ],
    [
      "0.567210113",
      "0.819860328"
    ],
    [
      "0.460280678",
      "0.821144382"
    ],
    [
      "0.353351243",
      "0.822428435"
    ],
    [
      "0.245018403",
      "0.822914878"
    ],
    [
      "0.107264527",
      "0.854504002"
    ],
    [
      "1.937254530",
      "0.867804352"
    ],
    [
      "1.694347657",
      "0.892326393"
    ],
    [
      "1.585067471",
      "0.897840485"
    ],
    [
      "1.477183242",
      "0.899670016"
    ],
    [
      "1.370253807",
      "0.900954069"
    ],
    [
      "1.263324370",
      "0.902238122"
    ],
    [
      "1.156394935",
      "0.903522175"
    ],
    [
      "1.049465500",
      "0.904806228"
    ],
    [
      "0.942536065",
      "0.906090279"
    ],
    [
      "0.835606630",
      "0.907374331"
    ],
    [
      "0.728677195",
      "0.908658385"
    ],
    [
      "1.828212794",
      "0.911664938"
    ],
    [
      "0.621786854",
      "0.911821909"
    ],
    [
      "0.514857419",
      "0.913105962"
    ],
    [
      "0.407927982",
      "0.914390016"
    ],
    [
      "0.300998547",
      "0.915674068"
    ],
    [
      "0.194069112",
      "0.916958120"
    ],
    [
      "0.054911833",
      "0.947749636"
    ],
    [
      "1.946184308",
      "0.974368004"
    ],
    [
      "1.745544582",
      "0.986211577"
    ],
    [
      "1.638690254",
      "0.990419372"
    ],
    [
      "1.531759981",
      "0.991631597"
    ],
    [
      "1.424830546",
      "0.992915650"
    ],
    [
      "1.317901111",
      "0.994199703"
    ],
    [
      "1.210971675",
      "0.995483756"
    ],
    [
      "1.104042240",
      "0.996767809"
    ],
    [
      "0.997112804",
      "0.998051861"
    ],
    [
      "0.890183369",
      "0.999335912"
    ],
    [
      "0.783253934",
      "1.000619966"
    ],
    [
      "0.676363593",
      "1.003783490"
    ],
    [
      "0.569434158",
      "1.005067543"
    ],
    [
      "0.462504723",
      "1.006351596"
    ],
    [
      "0.355575288",
      "1.007635650"
    ],
    [
      "0.248645853",
      "1.008919702"
    ],
    [
      "0.141716418",
      "1.010203754"
    ],
    [
      "1.848018617",
      "1.016783214"
    ],
    [
      "0.056421137",
      "1.074703893"
    ],
    [
      "1.943036980",
      "1.081258824"
    ],
    [
      "1.694765621",
      "1.081475473"
    ],
    [
      "1.586337683",
      "1.083665075"
    ],
    [
      "1.479407286",
      "1.084877231"
    ],
    [
      "1.372477850",
      "1.086161284"
    ],
    [
      "1.265548414",
      "1.087445337"
    ],
    [
      "1.158618979",
      "1.088729390"
    ],
    [
      "1.051689544",
      "1.090013442"
    ],
    [
      "0.944760109",
      "1.091297495"
    ],
    [
      "0.837830674",
      "1.092581547"
    ],
    [
      "0.730940333",
      "1.095745072"
    ],
    [
      "0.624010897",
      "1.097029125"
    ],
    [
      "0.517081462",
      "1.098313178"
    ],
    [
      "0.410152027",
      "1.099597231"
    ],
    [
      "0.303222592",
      "1.100881283"
    ],
    [
      "0.196293157",
      "1.102165335"
    ],
    [
      "1.841861602",
      "1.123542963"
    ],
    [
      "0.110997876",
      "1.166665474"
    ],
    [
      "1.747781980",
      "1.174381704"
    ],
    [
      "1.640852521",
      "1.175663817"
    ],
    [
      "1.533922241",
      "1.176875452"
    ],
    [
      "1.426992805",
      "1.178159504"
    ],
    [
      "1.320063370",
      "1.179443557"
    ],
    [
      "1.213133935",
      "1.180727610"
    ],
    [
      "1.106204500",
      "1.182011662"
    ],
    [
      "0.999275065",
      "1.183295715"
    ],
    [
      "0.892345630",
      "1.184579767"
    ],
    [
      "1.927852721",
      "1.187112455"
    ],
    [
      "0.785455288",
      "1.187743293"
    ],
    [
      "0.678525853",
      "1.189027345"
    ],
    [
      "0.571596418",
      "1.190311398"
    ],
    [
      "0.464666983",
      "1.191595451"
    ],
    [
      "0.357737548",
      "1.192879503"
    ],
    [
      "0.248662327",
      "1.195427737"
    ],
    [
      "1.695427670",
      "1.267626431"
    ],
    [
      "1.588503454",
      "1.269289221"
    ],
    [
      "1.481569544",
      "1.270121085"
    ],
    [
      "1.374640109",
      "1.271405138"
    ],
    [
      "0.093437479",
      "1.272150948"
    ],
    [
      "1.267710674",
      "1.272689191"
    ],
    [
      "1.160781239",
      "1.273973243"
    ],
    [
      "1.053851804",
      "1.275257297"
    ],
    [
      "0.946922369",
      "1.276541348"
    ],
    [
      "0.840032027",
      "1.279704874"
    ],
    [
      "0.733102592",
      "1.280988926"
    ],
    [
      "0.626173157",
      "1.282272979"
    ],
    [
      "0.519243722",
      "1.283557032"
    ],
    [
      "0.412314287",
      "1.284841084"
    ],
    [
      "0.305384852",
      "1.286125138"
    ],
    [
      "1.900825342",
      "1.290577781"
    ],
    [
      "0.198588636",
      "1.291613402"
    ],
    [
      "1.795071501",
      "1.306442146"
    ],
    [
      "1.535756914",
      "1.362312634"
    ],
    [
      "1.428827479",
      "1.363596687"
    ],
    [
      "1.649325803",
      "1.364729082"
    ],
    [
      "1.321898044",
      "1.364880740"
    ],
    [
      "1.214968609",
      "1.366164793"
    ],
    [
      "1.108039174",
      "1.367448846"
    ],
    [
      "1.001109738",
      "1.368732898"
    ],
    [
      "0.894219397",
      "1.371896423"
    ],
    [
      "0.787289962",
      "1.373180476"
    ],
    [
      "0.130534496",
      "1.374100897"
    ],
    [
      "0.680360526",
      "1.374464529"
    ],
    [
      "0.573431091",
      "1.375748582"
    ],
    [
      "0.466501656",
      "1.377032634"
    ],
    [
      "0.359572219",
      "1.378316689"
    ],
    [
      "0.235997832",
      "1.391793764"
    ],
    [
      "1.858829151",
      "1.394431630"
    ],
    [
      "1.751541401",
      "1.404118567"
    ],
    [
      "1.590333653",
      "1.454274215"
    ],
    [
      "1.483404218",
      "1.455558268"
    ],
    [
      "1.376474783",
      "1.456842324"
    ],
    [
      "1.269545348",
      "1.458126374"
    ],
    [
      "1.162615913",
      "1.459410427"
    ],
    [
      "1.055686478",
      "1.460694479"
    ],
    [
      "0.948796137",
      "1.463858004"
    ],
    [
      "0.841866702",
      "1.465142057"
    ],
    [
      "0.734937267",
      "1.466426110"
    ],
    [
      "0.628007832",
      "1.467710163"
    ],
    [
      "0.521078397",
      "1.468994216"
    ],
    [
      "0.414148961",
      "1.470278268"
    ],
    [
      "0.307219526",
      "1.471562324"
    ],
    [
      "0.191197022",
      "1.489851716"
    ],
    [
      "1.690440131",
      "1.491880675"
    ],
    [
      "1.806117920",
      "1.496080279"
    ],
    [
      "1.537980609",
      "1.547520056"
    ],
    [
      "1.431053659",
      "1.548996627"
    ],
    [
      "1.324122083",
      "1.550087958"
    ],
    [
      "1.217192919",
      "1.551394416"
    ],
    [
      "1.110263217",
      "1.552656060"
    ],
    [
      "1.003372876",
      "1.555819585"
    ],
    [
      "0.896443441",
      "1.557103638"
    ],
    [
      "0.789514005",
      "1.558387692"
    ],
    [
      "0.682584570",
      "1.559671745"
    ],
    [
      "0.575655135",
      "1.560955798"
    ],
    [
      "0.468725700",
      "1.562239849"
    ],
    [
      "0.361796265",
      "1.563523905"
    ],
    [
      "0.253305516",
      "1.576981433"
    ],
    [
      "1.745016650",
      "1.583842388"
    ],
    [
      "1.638087212",
      "1.585126184"
    ],
    [
      "1.378532852",
      "1.642147837"
    ],
    [
      "1.164820406",
      "1.644629243"
    ],
    [
      "1.271722722",
      "1.647358308"
    ],
    [
      "1.057930065",
      "1.647792766"
    ],
    [
      "0.951000630",
      "1.649076819"
    ],
    [
      "0.844071195",
      "1.650360873"
    ],
    [
      "0.737141760",
      "1.651644925"
    ],
    [
      "0.630212325",
      "1.652928978"
    ],
    [
      "1.545943663",
      "1.654160305"
    ],
    [
      "0.523282889",
      "1.654213030"
    ],
    [
      "0.325585458",
      "1.664143636"
    ],
    [
      "1.646050266",
      "1.691766433"
    ],
    [
      "0.426465720",
      "1.699622158"
    ],
    [
      "1.457494653",
      "1.714262931"
    ],
    [
      "1.215908123",
      "1.738573897"
    ],
    [
      "1.109017782",
      "1.741737420"
    ],
    [
      "0.898647935",
      "1.742322454"
    ],
    [
      "0.791718500",
      "1.743606507"
    ],
    [
      "0.684789064",
      "1.744890559"
    ],
    [
      "0.577859629",
      "1.746174611"
    ],
    [
      "1.356448618",
      "1.749787030"
    ],
    [
      "1.562904428",
      "1.760449762"
    ],
    [
      "1.003886467",
      "1.761306768"
    ],
    [
      "0.481042460",
      "1.791583739"
    ],
    [
      "1.472545598",
      "1.820135599"
    ],
    [
      "1.279350656",
      "1.824658726"
    ],
    [
      "1.162139590",
      "1.834547046"
    ],
    [
      "0.844513013",
      "1.836602702"
    ],
    [
      "0.695735752",
      "1.851265946"
    ],
    [
      "0.588806317",
      "1.852549998"
    ],
    [
      "0.950071877",
      "1.853716414"
    ],
    [
      "1.057008274",
      "1.854116393"
    ],
    [
      "1.377020555",
      "1.868203457"
    ],
    [
      "1.228253050",
      "1.918598002"
    ],
    [
      "0.777625102",
      "1.920038667"
    ],
    [
      "1.123180180",
      "1.938481044"
    ],
    [
      "0.884904734",
      "1.939488614"
    ],
    [
      "1.003193684",
      "1.946526039"
    ]
  ],
  "radius": "0.053468572"
}
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": 296
}

当前第一名的答案

{
  "centers": [
    [
      "0.994135090",
      "0.053530419"
    ],
    [
      "0.865222768",
      "0.063113219"
    ],
    [
      "1.100541128",
      "0.064892277"
    ],
    [
      "1.212220666",
      "0.077566191"
    ],
    [
      "0.759434478",
      "0.084549306"
    ],
    [
      "1.402480127",
      "0.143301984"
    ],
    [
      "0.935583431",
      "0.143642282"
    ],
    [
      "1.295550692",
      "0.144586036"
    ],
    [
      "0.678651889",
      "0.154618744"
    ],
    [
      "0.571722454",
      "0.155902798"
    ],
    [
      "1.147498758",
      "0.162693316"
    ],
    [
      "1.040569323",
      "0.163977368"
    ],
    [
      "0.830662885",
      "0.164311872"
    ],
    [
      "1.512919116",
      "0.204490274"
    ],
    [
      "0.461866730",
      "0.221325276"
    ],
    [
      "1.415868245",
      "0.249397748"
    ],
    [
      "1.308938809",
      "0.250681800"
    ],
    [
      "1.202075497",
      "0.254654897"
    ],
    [
      "0.774392050",
      "0.255504250"
    ],
    [
      "1.095146062",
      "0.255938949"
    ],
    [
      "0.988216627",
      "0.257223001"
    ],
    [
      "0.881287192",
      "0.258507054"
    ],
    [
      "0.667585955",
      "0.260981792"
    ],
    [
      "0.560656520",
      "0.262265846"
    ],
    [
      "1.567495855",
      "0.296451855"
    ],
    [
      "0.409417672",
      "0.314516741"
    ],
    [
      "1.668925420",
      "0.330328046"
    ],
    [
      "1.470444984",
      "0.341359329"
    ],
    [
      "1.363515549",
      "0.342643381"
    ],
    [
      "1.256652237",
      "0.346616478"
    ],
    [
      "1.149722802",
      "0.347900531"
    ],
    [
      "1.042793367",
      "0.349184583"
    ],
    [
      "0.935863932",
      "0.350468635"
    ],
    [
      "0.828934497",
      "0.351752688"
    ],
    [
      "0.309493043",
      "0.352603764"
    ],
    [
      "0.722005062",
      "0.353036741"
    ],
    [
      "0.615075627",
      "0.354320795"
    ],
    [
      "0.508146191",
      "0.355604846"
    ],
    [
      "1.740370249",
      "0.410286313"
    ],
    [
      "1.631925768",
      "0.430660387"
    ],
    [
      "1.525021725",
      "0.433320909"
    ],
    [
      "1.418092288",
      "0.434604962"
    ],
    [
      "1.311228976",
      "0.438578059"
    ],
    [
      "0.238987801",
      "0.438967351"
    ],
    [
      "1.204299541",
      "0.439862112"
    ],
    [
      "1.097370106",
      "0.441146164"
    ],
    [
      "0.990440671",
      "0.442430216"
    ],
    [
      "0.883511236",
      "0.443714269"
    ],
    [
      "0.776581801",
      "0.444998322"
    ],
    [
      "0.669652366",
      "0.446282376"
    ],
    [
      "0.562722931",
      "0.447566428"
    ],
    [
      "0.455793496",
      "0.448850481"
    ],
    [
      "0.348903154",
      "0.452014005"
    ],
    [
      "1.809423478",
      "0.509331704"
    ],
    [
      "1.702499393",
      "0.511002881"
    ],
    [
      "1.579598464",
      "0.525282490"
    ],
    [
      "1.472669029",
      "0.526566542"
    ],
    [
      "0.179563014",
      "0.528213078"
    ],
    [
      "1.365805717",
      "0.530539639"
    ],
    [
      "1.258876282",
      "0.531823693"
    ],
    [
      "1.151946847",
      "0.533107746"
    ],
    [
      "1.045017412",
      "0.534391798"
    ],
    [
      "0.938087977",
      "0.535675850"
    ],
    [
      "0.831158540",
      "0.536959903"
    ],
    [
      "0.724229105",
      "0.538243957"
    ],
    [
      "0.617299670",
      "0.539528009"
    ],
    [
      "0.510370235",
      "0.540812062"
    ],
    [
      "0.403479894",
      "0.543975586"
    ],
    [
      "0.296550459",
      "0.545259639"
    ],
    [
      "1.757408717",
      "0.602766267"
    ],
    [
      "1.650502394",
      "0.605333633"
    ],
    [
      "1.863845527",
      "0.613098657"
    ],
    [
      "1.527245769",
      "0.618528124"
    ],
    [
      "1.420382457",
      "0.622501220"
    ],
    [
      "1.313453021",
      "0.623785274"
    ],
    [
      "1.206523586",
      "0.625069327"
    ],
    [
      "1.099594151",
      "0.626353379"
    ],
    [
      "0.226944451",
      "0.626441882"
    ],
    [
      "0.992664716",
      "0.627637431"
    ],
    [
      "0.885735281",
      "0.628921483"
    ],
    [
      "0.778805846",
      "0.630205537"
    ],
    [
      "0.671876409",
      "0.631489590"
    ],
    [
      "0.564946974",
      "0.632773643"
    ],
    [
      "0.458056633",
      "0.635937167"
    ],
    [
      "0.351127198",
      "0.637221220"
    ],
    [
      "0.121921958",
      "0.646587077"
    ],
    [
      "1.795537160",
      "0.702675099"
    ],
    [
      "1.688630839",
      "0.705242465"
    ],
    [
      "1.581822509",
      "0.710489705"
    ],
    [
      "1.901973970",
      "0.713007489"
    ],
    [
      "1.474959197",
      "0.714462801"
    ],
    [
      "1.368029762",
      "0.715746854"
    ],
    [
      "1.261100327",
      "0.717030908"
    ],
    [
      "1.154170890",
      "0.718314960"
    ],
    [
      "1.047241455",
      "0.719599012"
    ],
    [
      "0.940312020",
      "0.720883064"
    ],
    [
      "0.833382585",
      "0.722167118"
    ],
    [
      "0.726453150",
      "0.723451170"
    ],
    [
      "0.619523715",
      "0.724735224"
    ],
    [
      "0.191879455",
      "0.727466626"
    ],
    [
      "0.512633374",
      "0.727898747"
    ],
    [
      "0.405703939",
      "0.729182801"
    ],
    [
      "0.298774504",
      "0.730466854"
    ],
    [
      "0.087228526",
      "0.749460623"
    ],
    [
      "1.743207578",
      "0.797204046"
    ],
    [
      "1.636399248",
      "0.802451286"
    ],
    [
      "1.849754784",
      "0.806327956"
    ],
    [
      "1.529535936",
      "0.806424382"
    ],
    [
      "1.422606501",
      "0.807708435"
    ],
    [
      "1.315677066",
      "0.808992489"
    ],
    [
      "1.208747631",
      "0.810276541"
    ],
    [
      "1.101818196",
      "0.811560594"
    ],
    [
      "0.994888761",
      "0.812844646"
    ],
    [
      "0.887959326",
      "0.814128698"
    ],
    [
      "0.781029889",
      "0.815412751"
    ],
    [
      "0.674100454",
      "0.816696805"
    ],
    [
      "0.567210113",
      "0.819860328"
    ],
    [
      "0.460280678",
      "0.821144382"
    ],
    [
      "0.353351243",
      "0.822428435"
    ],
    [
      "0.245018403",
      "0.822914878"
    ],
    [
      "0.107264527",
      "0.854504002"
    ],
    [
      "1.937254530",
      "0.867804352"
    ],
    [
      "1.694347657",
      "0.892326393"
    ],
    [
      "1.585067471",
      "0.897840485"
    ],
    [
      "1.477183242",
      "0.899670016"
    ],
    [
      "1.370253807",
      "0.900954069"
    ],
    [
      "1.263324370",
      "0.902238122"
    ],
    [
      "1.156394935",
      "0.903522175"
    ],
    [
      "1.049465500",
      "0.904806228"
    ],
    [
      "0.942536065",
      "0.906090279"
    ],
    [
      "0.835606630",
      "0.907374331"
    ],
    [
      "0.728677195",
      "0.908658385"
    ],
    [
      "1.828212794",
      "0.911664938"
    ],
    [
      "0.621786854",
      "0.911821909"
    ],
    [
      "0.514857419",
      "0.913105962"
    ],
    [
      "0.407927982",
      "0.914390016"
    ],
    [
      "0.300998547",
      "0.915674068"
    ],
    [
      "0.194069112",
      "0.916958120"
    ],
    [
      "0.054911833",
      "0.947749636"
    ],
    [
      "1.946184308",
      "0.974368004"
    ],
    [
      "1.745544582",
      "0.986211577"
    ],
    [
      "1.638690254",
      "0.990419372"
    ],
    [
      "1.531759981",
      "0.991631597"
    ],
    [
      "1.424830546",
      "0.992915650"
    ],
    [
      "1.317901111",
      "0.994199703"
    ],
    [
      "1.210971675",
      "0.995483756"
    ],
    [
      "1.104042240",
      "0.996767809"
    ],
    [
      "0.997112804",
      "0.998051861"
    ],
    [
      "0.890183369",
      "0.999335912"
    ],
    [
      "0.783253934",
      "1.000619966"
    ],
    [
      "0.676363593",
      "1.003783490"
    ],
    [
      "0.569434158",
      "1.005067543"
    ],
    [
      "0.462504723",
      "1.006351596"
    ],
    [
      "0.355575288",
      "1.007635650"
    ],
    [
      "0.248645853",
      "1.008919702"
    ],
    [
      "0.141716418",
      "1.010203754"
    ],
    [
      "1.848018617",
      "1.016783214"
    ],
    [
      "0.056421137",
      "1.074703893"
    ],
    [
      "1.943036980",
      "1.081258824"
    ],
    [
      "1.694765621",
      "1.081475473"
    ],
    [
      "1.586337683",
      "1.083665075"
    ],
    [
      "1.479407286",
      "1.084877231"
    ],
    [
      "1.372477850",
      "1.086161284"
    ],
    [
      "1.265548414",
      "1.087445337"
    ],
    [
      "1.158618979",
      "1.088729390"
    ],
    [
      "1.051689544",
      "1.090013442"
    ],
    [
      "0.944760109",
      "1.091297495"
    ],
    [
      "0.837830674",
      "1.092581547"
    ],
    [
      "0.730940333",
      "1.095745072"
    ],
    [
      "0.624010897",
      "1.097029125"
    ],
    [
      "0.517081462",
      "1.098313178"
    ],
    [
      "0.410152027",
      "1.099597231"
    ],
    [
      "0.303222592",
      "1.100881283"
    ],
    [
      "0.196293157",
      "1.102165335"
    ],
    [
      "1.841861602",
      "1.123542963"
    ],
    [
      "0.110997876",
      "1.166665474"
    ],
    [
      "1.747781980",
      "1.174381704"
    ],
    [
      "1.640852521",
      "1.175663817"
    ],
    [
      "1.533922241",
      "1.176875452"
    ],
    [
      "1.426992805",
      "1.178159504"
    ],
    [
      "1.320063370",
      "1.179443557"
    ],
    [
      "1.213133935",
      "1.180727610"
    ],
    [
      "1.106204500",
      "1.182011662"
    ],
    [
      "0.999275065",
      "1.183295715"
    ],
    [
      "0.892345630",
      "1.184579767"
    ],
    [
      "1.927852721",
      "1.187112455"
    ],
    [
      "0.785455288",
      "1.187743293"
    ],
    [
      "0.678525853",
      "1.189027345"
    ],
    [
      "0.571596418",
      "1.190311398"
    ],
    [
      "0.464666983",
      "1.191595451"
    ],
    [
      "0.357737548",
      "1.192879503"
    ],
    [
      "0.248662327",
      "1.195427737"
    ],
    [
      "1.695427670",
      "1.267626431"
    ],
    [
      "1.588503454",
      "1.269289221"
    ],
    [
      "1.481569544",
      "1.270121085"
    ],
    [
      "1.374640109",
      "1.271405138"
    ],
    [
      "0.093437479",
      "1.272150948"
    ],
    [
      "1.267710674",
      "1.272689191"
    ],
    [
      "1.160781239",
      "1.273973243"
    ],
    [
      "1.053851804",
      "1.275257297"
    ],
    [
      "0.946922369",
      "1.276541348"
    ],
    [
      "0.840032027",
      "1.279704874"
    ],
    [
      "0.733102592",
      "1.280988926"
    ],
    [
      "0.626173157",
      "1.282272979"
    ],
    [
      "0.519243722",
      "1.283557032"
    ],
    [
      "0.412314287",
      "1.284841084"
    ],
    [
      "0.305384852",
      "1.286125138"
    ],
    [
      "1.900825342",
      "1.290577781"
    ],
    [
      "0.198588636",
      "1.291613402"
    ],
    [
      "1.795071501",
      "1.306442146"
    ],
    [
      "1.535756914",
      "1.362312634"
    ],
    [
      "1.428827479",
      "1.363596687"
    ],
    [
      "1.649325803",
      "1.364729082"
    ],
    [
      "1.321898044",
      "1.364880740"
    ],
    [
      "1.214968609",
      "1.366164793"
    ],
    [
      "1.108039174",
      "1.367448846"
    ],
    [
      "1.001109738",
      "1.368732898"
    ],
    [
      "0.894219397",
      "1.371896423"
    ],
    [
      "0.787289962",
      "1.373180476"
    ],
    [
      "0.130534496",
      "1.374100897"
    ],
    [
      "0.680360526",
      "1.374464529"
    ],
    [
      "0.573431091",
      "1.375748582"
    ],
    [
      "0.466501656",
      "1.377032634"
    ],
    [
      "0.359572219",
      "1.378316689"
    ],
    [
      "0.235997832",
      "1.391793764"
    ],
    [
      "1.858829151",
      "1.394431630"
    ],
    [
      "1.751541401",
      "1.404118567"
    ],
    [
      "1.590333653",
      "1.454274215"
    ],
    [
      "1.483404218",
      "1.455558268"
    ],
    [
      "1.376474783",
      "1.456842324"
    ],
    [
      "1.269545348",
      "1.458126374"
    ],
    [
      "1.162615913",
      "1.459410427"
    ],
    [
      "1.055686478",
      "1.460694479"
    ],
    [
      "0.948796137",
      "1.463858004"
    ],
    [
      "0.841866702",
      "1.465142057"
    ],
    [
      "0.734937267",
      "1.466426110"
    ],
    [
      "0.628007832",
      "1.467710163"
    ],
    [
      "0.521078397",
      "1.468994216"
    ],
    [
      "0.414148961",
      "1.470278268"
    ],
    [
      "0.307219526",
      "1.471562324"
    ],
    [
      "0.191197022",
      "1.489851716"
    ],
    [
      "1.690440131",
      "1.491880675"
    ],
    [
      "1.806117920",
      "1.496080279"
    ],
    [
      "1.537980609",
      "1.547520056"
    ],
    [
      "1.431053659",
      "1.548996627"
    ],
    [
      "1.324122083",
      "1.550087958"
    ],
    [
      "1.217192919",
      "1.551394416"
    ],
    [
      "1.110263217",
      "1.552656060"
    ],
    [
      "1.003372876",
      "1.555819585"
    ],
    [
      "0.896443441",
      "1.557103638"
    ],
    [
      "0.789514005",
      "1.558387692"
    ],
    [
      "0.682584570",
      "1.559671745"
    ],
    [
      "0.575655135",
      "1.560955798"
    ],
    [
      "0.468725700",
      "1.562239849"
    ],
    [
      "0.361796265",
      "1.563523905"
    ],
    [
      "0.253305516",
      "1.576981433"
    ],
    [
      "1.745016650",
      "1.583842388"
    ],
    [
      "1.638087212",
      "1.585126184"
    ],
    [
      "1.378532852",
      "1.642147837"
    ],
    [
      "1.164820406",
      "1.644629243"
    ],
    [
      "1.271722722",
      "1.647358308"
    ],
    [
      "1.057930065",
      "1.647792766"
    ],
    [
      "0.951000630",
      "1.649076819"
    ],
    [
      "0.844071195",
      "1.650360873"
    ],
    [
      "0.737141760",
      "1.651644925"
    ],
    [
      "0.630212325",
      "1.652928978"
    ],
    [
      "1.545943663",
      "1.654160305"
    ],
    [
      "0.523282889",
      "1.654213030"
    ],
    [
      "0.325585458",
      "1.664143636"
    ],
    [
      "1.646050266",
      "1.691766433"
    ],
    [
      "0.426465720",
      "1.699622158"
    ],
    [
      "1.457494653",
      "1.714262931"
    ],
    [
      "1.215908123",
      "1.738573897"
    ],
    [
      "1.109017782",
      "1.741737420"
    ],
    [
      "0.898647935",
      "1.742322454"
    ],
    [
      "0.791718500",
      "1.743606507"
    ],
    [
      "0.684789064",
      "1.744890559"
    ],
    [
      "0.577859629",
      "1.746174611"
    ],
    [
      "1.356448618",
      "1.749787030"
    ],
    [
      "1.562904428",
      "1.760449762"
    ],
    [
      "1.003886467",
      "1.761306768"
    ],
    [
      "0.481042460",
      "1.791583739"
    ],
    [
      "1.472545598",
      "1.820135599"
    ],
    [
      "1.279350656",
      "1.824658726"
    ],
    [
      "1.162139590",
      "1.834547046"
    ],
    [
      "0.844513013",
      "1.836602702"
    ],
    [
      "0.695735752",
      "1.851265946"
    ],
    [
      "0.588806317",
      "1.852549998"
    ],
    [
      "0.950071877",
      "1.853716414"
    ],
    [
      "1.057008274",
      "1.854116393"
    ],
    [
      "1.377020555",
      "1.868203457"
    ],
    [
      "1.228253050",
      "1.918598002"
    ],
    [
      "0.777625102",
      "1.920038667"
    ],
    [
      "1.123180180",
      "1.938481044"
    ],
    [
      "0.884904734",
      "1.939488614"
    ],
    [
      "1.003193684",
      "1.946526039"
    ]
  ],
  "radius": "0.053468572"
}

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

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。

还没有帖子。第一个聊聊这道题的思路?