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 = 225

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 = 225
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[0.0609622137498901866397564440645, 0.0609622137498901866397564440655]见来源署名packomania.com ↗
本站纪录暂无选手纪录——

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:起步布局

2y0
0x2
已验证构造r = 0.060962213

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 = 225 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"。

起步布局答案

{
  "centers": [
    [
      "0.321009577",
      "1.003617602"
    ],
    [
      "0.455070587",
      "1.764750647"
    ],
    [
      "0.496645918",
      "1.183601412"
    ],
    [
      "1.617263299",
      "1.661683922"
    ],
    [
      "1.313776139",
      "1.397009542"
    ],
    [
      "1.017091052",
      "1.697699288"
    ],
    [
      "1.442600936",
      "0.485270013"
    ],
    [
      "1.850810147",
      "0.602615981"
    ],
    [
      "0.065220455",
      "0.910673824"
    ],
    [
      "1.437092033",
      "0.924840269"
    ],
    [
      "1.238255574",
      "0.431981449"
    ],
    [
      "1.627434894",
      "0.301351575"
    ],
    [
      "0.897358324",
      "0.066615174"
    ],
    [
      "1.086127269",
      "1.935079707"
    ],
    [
      "1.342961678",
      "1.760153952"
    ],
    [
      "1.282968748",
      "1.515030152"
    ],
    [
      "0.29024341",
      "1.121596452"
    ],
    [
      "1.182232144",
      "0.228368892"
    ],
    [
      "1.288770102",
      "1.075164262"
    ],
    [
      "0.204925215",
      "1.499647926"
    ],
    [
      "0.681242919",
      "0.475728313"
    ],
    [
      "1.406325866",
      "1.042819119"
    ],
    [
      "1.12069981",
      "0.464326592"
    ],
    [
      "1.140448171",
      "1.225488255"
    ],
    [
      "1.641437395",
      "0.978128834"
    ],
    [
      "1.325045172",
      "0.517615156"
    ],
    [
      "0.276364349",
      "1.598450841"
    ],
    [
      "0.854822114",
      "0.646995727"
    ],
    [
      "1.355811339",
      "0.399636306"
    ],
    [
      "0.964246893",
      "1.938356904"
    ],
    [
      "0.588944418",
      "0.829664862"
    ],
    [
      "1.369758345",
      "1.600663859"
    ],
    [
      "1.937720518",
      "0.950278839"
    ],
    [
      "0.885588281",
      "0.529016877"
    ],
    [
      "1.115190907",
      "0.903896848"
    ],
    [
      "0.440622487",
      "0.979988855"
    ],
    [
      "1.41183477",
      "0.603248863"
    ],
    [
      "1.531395472",
      "0.225783741"
    ],
    [
      "0.715082403",
      "0.354742602"
    ],
    [
      "1.44498821",
      "1.826908373"
    ],
    [
      "1.109430777",
      "1.343720978"
    ],
    [
      "0.681912512",
      "1.832047015"
    ],
    [
      "0.899535288",
      "1.73004443"
    ],
    [
      "0.318732366",
      "1.455904373"
    ],
    [
      "0.259962331",
      "0.646098295"
    ],
    [
      "1.064571697",
      "0.260332875"
    ],
    [
      "0.3901715",
      "1.554707288"
    ],
    [
      "1.02110087",
      "0.06119932"
    ],
    [
      "1.431347467",
      "1.364720978"
    ],
    [
      "0.465879751",
      "1.301580262"
    ],
    [
      "0.628292805",
      "0.269108895"
    ],
    [
      "0.694614484",
      "1.677335333"
    ],
    [
      "0.936102809",
      "1.17219969"
    ],
    [
      "0.79328978",
      "0.882953427"
    ],
    [
      "1.529643881",
      "0.570647263"
    ],
    [
      "1.176723241",
      "0.667939148"
    ],
    [
      "0.549443464",
      "0.176112403"
    ],
    [
      "0.31620549",
      "0.537921249"
    ],
    [
      "1.908715129",
      "1.236698937"
    ],
    [
      "0.43628813",
      "1.42355923"
    ],
    [
      "1.400524512",
      "1.482685009"
    ],
    [
      "0.164078216",
      "0.839310605"
    ],
    [
      "1.165412983",
      "1.547375295"
    ],
    [
      "1.503192311",
      "0.344401394"
    ],
    [
      "0.597526638",
      "0.387087745"
    ],
    [
      "1.729152804",
      "0.610681769"
    ],
    [
      "1.350302436",
      "0.839206562"
    ],
    [
      "1.520980044",
      "1.463816228"
    ],
    [
      "0.473809945",
      "1.643421304"
    ],
    [
      "1.579653835",
      "1.214340407"
    ],
    [
      "0.849313211",
      "1.086565983"
    ],
    [
      "0.972377879",
      "0.614650584"
    ],
    [
      "0.507727265",
      "1.522362145"
    ],
    [
      "0.997635142",
      "0.936241991"
    ],
    [
      "0.061526258",
      "1.032542273"
    ],
    [
      "1.207489407",
      "0.549960299"
    ],
    [
      "1.028401309",
      "0.818263141"
    ],
    [
      "1.616361804",
      "1.539762827"
    ],
    [
      "0.798798683",
      "0.44338317"
    ],
    [
      "1.523881631",
      "1.010473976"
    ],
    [
      "1.201980504",
      "0.989530555"
    ],
    [
      "1.783999197",
      "1.267628971"
    ],
    [
      "1.119325366",
      "1.817761965"
    ],
    [
      "1.75855027",
      "0.94421511"
    ],
    [
      "1.247899981",
      "0.094275117"
    ],
    [
      "1.610671229",
      "1.096107683"
    ],
    [
      "0.232055607",
      "1.305173038"
    ],
    [
      "0.360002794",
      "1.687164857"
    ],
    [
      "1.801452937",
      "0.830088307"
    ],
    [
      "1.493115464",
      "1.128452826"
    ],
    [
      "0.073653189",
      "1.153862113"
    ],
    [
      "1.053658573",
      "1.139854548"
    ],
    [
      "0.725997316",
      "1.558735256"
    ],
    [
      "0.880079378",
      "0.968587134"
    ],
    [
      "0.583435515",
      "1.269235119"
    ],
    [
      "1.232746671",
      "0.871551705"
    ],
    [
      "1.269021741",
      "0.314002599"
    ],
    [
      "1.548887668",
      "1.332319256"
    ],
    [
      "0.266506097",
      "0.41367359"
    ],
    [
      "0.65998898",
      "0.124680361"
    ],
    [
      "0.81274569",
      "1.644410723"
    ],
    [
      "0.262963678",
      "0.767985775"
    ],
    [
      "0.146889737",
      "1.392421766"
    ],
    [
      "0.619710585",
      "0.711686013"
    ],
    [
      "0.608441552",
      "1.591080399"
    ],
    [
      "1.559981026",
      "0.452293043"
    ],
    [
      "1.616180132",
      "0.656537427"
    ],
    [
      "1.226986541",
      "1.311375835"
    ],
    [
      "0.650476752",
      "0.593707163"
    ],
    [
      "1.86164545",
      "0.724057993"
    ],
    [
      "1.252220637",
      "1.633074556"
    ],
    [
      "1.089933643",
      "0.582305442"
    ],
    [
      "1.344542306",
      "1.279030692"
    ],
    [
      "1.446349875",
      "1.695528518"
    ],
    [
      "1.033910212",
      "0.378692885"
    ],
    [
      "1.323515948",
      "1.881549225"
    ],
    [
      "0.855115865",
      "0.181001264"
    ],
    [
      "0.349498532",
      "1.337925523"
    ],
    [
      "0.502154821",
      "0.744031156"
    ],
    [
      "0.930301454",
      "1.612065581"
    ],
    [
      "1.585413965",
      "0.774516277"
    ],
    [
      "1.3755597",
      "1.160797969"
    ],
    [
      "0.314596692",
      "0.879574602"
    ],
    [
      "0.439798217",
      "0.547352144"
    ],
    [
      "0.768032517",
      "0.56136202"
    ],
    [
      "0.824055947",
      "0.764974577"
    ],
    [
      "0.675734016",
      "0.915298569"
    ],
    [
      "1.712632517",
      "0.388586467"
    ],
    [
      "0.614201682",
      "1.151256269"
    ],
    [
      "0.57671972",
      "1.70880589"
    ],
    [
      "1.814765364",
      "1.149650121"
    ],
    [
      "1.492561579",
      "1.582386267"
    ],
    [
      "0.210532657",
      "0.952038378"
    ],
    [
      "1.670493775",
      "0.503795454"
    ],
    [
      "0.874319248",
      "1.408411263"
    ],
    [
      "0.558898667",
      "0.506448149"
    ],
    [
      "0.385990615",
      "0.43794324"
    ],
    [
      "0.56001304",
      "1.829580279"
    ],
    [
      "0.818547044",
      "1.204544833"
    ],
    [
      "1.869554137",
      "1.354496215"
    ],
    [
      "1.713692043",
      "0.73176456"
    ],
    [
      "1.258003935",
      "1.193143112"
    ],
    [
      "1.554647798",
      "0.892495127"
    ],
    [
      "1.697209599",
      "1.181995264"
    ],
    [
      "0.787780877",
      "1.322523683"
    ],
    [
      "1.4678582",
      "0.80686142"
    ],
    [
      "0.670225113",
      "1.354868826"
    ],
    [
      "1.728226993",
      "1.063762541"
    ],
    [
      "0.756763483",
      "1.440756406"
    ],
    [
      "1.751998373",
      "1.386841358"
    ],
    [
      "1.498624367",
      "0.68888257"
    ],
    [
      "0.558178251",
      "0.947643712"
    ],
    [
      "1.047857219",
      "1.579720438"
    ],
    [
      "1.310030407",
      "0.199181628"
    ],
    [
      "1.196220374",
      "1.429354685"
    ],
    [
      "0.471388654",
      "0.862010005"
    ],
    [
      "0.196720972",
      "0.5136516"
    ],
    [
      "0.177725253",
      "1.069465974"
    ],
    [
      "1.059167476",
      "0.700284291"
    ],
    [
      "0.762523613",
      "1.000932276"
    ],
    [
      "1.931878238",
      "1.115736397"
    ],
    [
      "0.644967849",
      "1.033277419"
    ],
    [
      "1.294279005",
      "0.635594006"
    ],
    [
      "1.319536269",
      "0.957185412"
    ],
    [
      "0.189852184",
      "1.190785814"
    ],
    [
      "1.263512838",
      "0.753572855"
    ],
    [
      "0.352206408",
      "0.320431377"
    ],
    [
      "1.206570211",
      "1.916035244"
    ],
    [
      "0.825627919",
      "0.30331056"
    ],
    [
      "1.151465977",
      "0.346347742"
    ],
    [
      "0.905336642",
      "1.29017854"
    ],
    [
      "0.532920988",
      "0.626052306"
    ],
    [
      "0.961108845",
      "1.49404497"
    ],
    [
      "0.70099128",
      "1.236889976"
    ],
    [
      "1.145957074",
      "0.785917998"
    ],
    [
      "0.879845454",
      "1.850368478"
    ],
    [
      "1.666443432",
      "1.299974114"
    ],
    [
      "1.923374139",
      "0.829201395"
    ],
    [
      "1.221377826",
      "1.75104719"
    ],
    [
      "0.774369874",
      "1.911527844"
    ],
    [
      "1.845339867",
      "1.029848817"
    ],
    [
      "1.42660426",
      "0.163459045"
    ],
    [
      "0.478887227",
      "0.35897625"
    ],
    [
      "0.966868976",
      "1.054220841"
    ],
    [
      "0.384599056",
      "0.776376298"
    ],
    [
      "1.634442608",
      "1.419186501"
    ],
    [
      "0.40985632",
      "1.097967705"
    ],
    [
      "0.947120615",
      "0.293059178"
    ],
    [
      "1.681164893",
      "0.849996908"
    ],
    [
      "1.381068603",
      "0.721227713"
    ],
    [
      "0.976883671",
      "0.174823284"
    ],
    [
      "0.140477813",
      "0.621828645"
    ],
    [
      "0.706500183",
      "0.79731972"
    ],
    [
      "0.381597709",
      "0.654488818"
    ],
    [
      "0.781979523",
      "1.762389573"
    ],
    [
      "1.022892406",
      "1.257833397"
    ],
    [
      "1.07866461",
      "1.461699828"
    ],
    [
      "0.73726635",
      "0.67934087"
    ],
    [
      "0.639207719",
      "1.473101549"
    ],
    [
      "1.722399316",
      "1.599942657"
    ],
    [
      "0.991875012",
      "1.376066121"
    ],
    [
      "0.446493593",
      "0.241433839"
    ],
    [
      "1.08442474",
      "1.021875698"
    ],
    [
      "0.997401219",
      "1.818023335"
    ],
    [
      "0.910845545",
      "0.850608284"
    ],
    [
      "0.738838321",
      "0.217676853"
    ],
    [
      "1.46209807",
      "1.246685549"
    ],
    [
      "1.128493548",
      "0.118926079"
    ],
    [
      "0.102818951",
      "1.277232441"
    ],
    [
      "0.098724788",
      "0.736381039"
    ],
    [
      "1.548376408",
      "1.762282939"
    ],
    [
      "0.370016638",
      "1.215175653"
    ],
    [
      "0.552669348",
      "1.387213969"
    ],
    [
      "1.396820005",
      "0.284815335"
    ],
    [
      "1.171214338",
      "1.107509405"
    ],
    [
      "0.731757447",
      "1.118911126"
    ],
    [
      "1.134646816",
      "1.665354145"
    ],
    [
      "0.916354448",
      "0.411038028"
    ],
    [
      "1.792151118",
      "0.495729666"
    ],
    [
      "1.794042161",
      "1.501287354"
    ],
    [
      "1.003144045",
      "0.496671735"
    ],
    [
      "0.843553081",
      "1.526390113"
    ],
    [
      "0.941611712",
      "0.732629434"
    ],
    [
      "0.776266524",
      "0.088004772"
    ],
    [
      "0.527412085",
      "1.065622562"
    ]
  ],
  "radius": "0.060962213"
}
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": 225
}

起步布局答案

{
  "centers": [
    [
      "0.321009577",
      "1.003617602"
    ],
    [
      "0.455070587",
      "1.764750647"
    ],
    [
      "0.496645918",
      "1.183601412"
    ],
    [
      "1.617263299",
      "1.661683922"
    ],
    [
      "1.313776139",
      "1.397009542"
    ],
    [
      "1.017091052",
      "1.697699288"
    ],
    [
      "1.442600936",
      "0.485270013"
    ],
    [
      "1.850810147",
      "0.602615981"
    ],
    [
      "0.065220455",
      "0.910673824"
    ],
    [
      "1.437092033",
      "0.924840269"
    ],
    [
      "1.238255574",
      "0.431981449"
    ],
    [
      "1.627434894",
      "0.301351575"
    ],
    [
      "0.897358324",
      "0.066615174"
    ],
    [
      "1.086127269",
      "1.935079707"
    ],
    [
      "1.342961678",
      "1.760153952"
    ],
    [
      "1.282968748",
      "1.515030152"
    ],
    [
      "0.29024341",
      "1.121596452"
    ],
    [
      "1.182232144",
      "0.228368892"
    ],
    [
      "1.288770102",
      "1.075164262"
    ],
    [
      "0.204925215",
      "1.499647926"
    ],
    [
      "0.681242919",
      "0.475728313"
    ],
    [
      "1.406325866",
      "1.042819119"
    ],
    [
      "1.12069981",
      "0.464326592"
    ],
    [
      "1.140448171",
      "1.225488255"
    ],
    [
      "1.641437395",
      "0.978128834"
    ],
    [
      "1.325045172",
      "0.517615156"
    ],
    [
      "0.276364349",
      "1.598450841"
    ],
    [
      "0.854822114",
      "0.646995727"
    ],
    [
      "1.355811339",
      "0.399636306"
    ],
    [
      "0.964246893",
      "1.938356904"
    ],
    [
      "0.588944418",
      "0.829664862"
    ],
    [
      "1.369758345",
      "1.600663859"
    ],
    [
      "1.937720518",
      "0.950278839"
    ],
    [
      "0.885588281",
      "0.529016877"
    ],
    [
      "1.115190907",
      "0.903896848"
    ],
    [
      "0.440622487",
      "0.979988855"
    ],
    [
      "1.41183477",
      "0.603248863"
    ],
    [
      "1.531395472",
      "0.225783741"
    ],
    [
      "0.715082403",
      "0.354742602"
    ],
    [
      "1.44498821",
      "1.826908373"
    ],
    [
      "1.109430777",
      "1.343720978"
    ],
    [
      "0.681912512",
      "1.832047015"
    ],
    [
      "0.899535288",
      "1.73004443"
    ],
    [
      "0.318732366",
      "1.455904373"
    ],
    [
      "0.259962331",
      "0.646098295"
    ],
    [
      "1.064571697",
      "0.260332875"
    ],
    [
      "0.3901715",
      "1.554707288"
    ],
    [
      "1.02110087",
      "0.06119932"
    ],
    [
      "1.431347467",
      "1.364720978"
    ],
    [
      "0.465879751",
      "1.301580262"
    ],
    [
      "0.628292805",
      "0.269108895"
    ],
    [
      "0.694614484",
      "1.677335333"
    ],
    [
      "0.936102809",
      "1.17219969"
    ],
    [
      "0.79328978",
      "0.882953427"
    ],
    [
      "1.529643881",
      "0.570647263"
    ],
    [
      "1.176723241",
      "0.667939148"
    ],
    [
      "0.549443464",
      "0.176112403"
    ],
    [
      "0.31620549",
      "0.537921249"
    ],
    [
      "1.908715129",
      "1.236698937"
    ],
    [
      "0.43628813",
      "1.42355923"
    ],
    [
      "1.400524512",
      "1.482685009"
    ],
    [
      "0.164078216",
      "0.839310605"
    ],
    [
      "1.165412983",
      "1.547375295"
    ],
    [
      "1.503192311",
      "0.344401394"
    ],
    [
      "0.597526638",
      "0.387087745"
    ],
    [
      "1.729152804",
      "0.610681769"
    ],
    [
      "1.350302436",
      "0.839206562"
    ],
    [
      "1.520980044",
      "1.463816228"
    ],
    [
      "0.473809945",
      "1.643421304"
    ],
    [
      "1.579653835",
      "1.214340407"
    ],
    [
      "0.849313211",
      "1.086565983"
    ],
    [
      "0.972377879",
      "0.614650584"
    ],
    [
      "0.507727265",
      "1.522362145"
    ],
    [
      "0.997635142",
      "0.936241991"
    ],
    [
      "0.061526258",
      "1.032542273"
    ],
    [
      "1.207489407",
      "0.549960299"
    ],
    [
      "1.028401309",
      "0.818263141"
    ],
    [
      "1.616361804",
      "1.539762827"
    ],
    [
      "0.798798683",
      "0.44338317"
    ],
    [
      "1.523881631",
      "1.010473976"
    ],
    [
      "1.201980504",
      "0.989530555"
    ],
    [
      "1.783999197",
      "1.267628971"
    ],
    [
      "1.119325366",
      "1.817761965"
    ],
    [
      "1.75855027",
      "0.94421511"
    ],
    [
      "1.247899981",
      "0.094275117"
    ],
    [
      "1.610671229",
      "1.096107683"
    ],
    [
      "0.232055607",
      "1.305173038"
    ],
    [
      "0.360002794",
      "1.687164857"
    ],
    [
      "1.801452937",
      "0.830088307"
    ],
    [
      "1.493115464",
      "1.128452826"
    ],
    [
      "0.073653189",
      "1.153862113"
    ],
    [
      "1.053658573",
      "1.139854548"
    ],
    [
      "0.725997316",
      "1.558735256"
    ],
    [
      "0.880079378",
      "0.968587134"
    ],
    [
      "0.583435515",
      "1.269235119"
    ],
    [
      "1.232746671",
      "0.871551705"
    ],
    [
      "1.269021741",
      "0.314002599"
    ],
    [
      "1.548887668",
      "1.332319256"
    ],
    [
      "0.266506097",
      "0.41367359"
    ],
    [
      "0.65998898",
      "0.124680361"
    ],
    [
      "0.81274569",
      "1.644410723"
    ],
    [
      "0.262963678",
      "0.767985775"
    ],
    [
      "0.146889737",
      "1.392421766"
    ],
    [
      "0.619710585",
      "0.711686013"
    ],
    [
      "0.608441552",
      "1.591080399"
    ],
    [
      "1.559981026",
      "0.452293043"
    ],
    [
      "1.616180132",
      "0.656537427"
    ],
    [
      "1.226986541",
      "1.311375835"
    ],
    [
      "0.650476752",
      "0.593707163"
    ],
    [
      "1.86164545",
      "0.724057993"
    ],
    [
      "1.252220637",
      "1.633074556"
    ],
    [
      "1.089933643",
      "0.582305442"
    ],
    [
      "1.344542306",
      "1.279030692"
    ],
    [
      "1.446349875",
      "1.695528518"
    ],
    [
      "1.033910212",
      "0.378692885"
    ],
    [
      "1.323515948",
      "1.881549225"
    ],
    [
      "0.855115865",
      "0.181001264"
    ],
    [
      "0.349498532",
      "1.337925523"
    ],
    [
      "0.502154821",
      "0.744031156"
    ],
    [
      "0.930301454",
      "1.612065581"
    ],
    [
      "1.585413965",
      "0.774516277"
    ],
    [
      "1.3755597",
      "1.160797969"
    ],
    [
      "0.314596692",
      "0.879574602"
    ],
    [
      "0.439798217",
      "0.547352144"
    ],
    [
      "0.768032517",
      "0.56136202"
    ],
    [
      "0.824055947",
      "0.764974577"
    ],
    [
      "0.675734016",
      "0.915298569"
    ],
    [
      "1.712632517",
      "0.388586467"
    ],
    [
      "0.614201682",
      "1.151256269"
    ],
    [
      "0.57671972",
      "1.70880589"
    ],
    [
      "1.814765364",
      "1.149650121"
    ],
    [
      "1.492561579",
      "1.582386267"
    ],
    [
      "0.210532657",
      "0.952038378"
    ],
    [
      "1.670493775",
      "0.503795454"
    ],
    [
      "0.874319248",
      "1.408411263"
    ],
    [
      "0.558898667",
      "0.506448149"
    ],
    [
      "0.385990615",
      "0.43794324"
    ],
    [
      "0.56001304",
      "1.829580279"
    ],
    [
      "0.818547044",
      "1.204544833"
    ],
    [
      "1.869554137",
      "1.354496215"
    ],
    [
      "1.713692043",
      "0.73176456"
    ],
    [
      "1.258003935",
      "1.193143112"
    ],
    [
      "1.554647798",
      "0.892495127"
    ],
    [
      "1.697209599",
      "1.181995264"
    ],
    [
      "0.787780877",
      "1.322523683"
    ],
    [
      "1.4678582",
      "0.80686142"
    ],
    [
      "0.670225113",
      "1.354868826"
    ],
    [
      "1.728226993",
      "1.063762541"
    ],
    [
      "0.756763483",
      "1.440756406"
    ],
    [
      "1.751998373",
      "1.386841358"
    ],
    [
      "1.498624367",
      "0.68888257"
    ],
    [
      "0.558178251",
      "0.947643712"
    ],
    [
      "1.047857219",
      "1.579720438"
    ],
    [
      "1.310030407",
      "0.199181628"
    ],
    [
      "1.196220374",
      "1.429354685"
    ],
    [
      "0.471388654",
      "0.862010005"
    ],
    [
      "0.196720972",
      "0.5136516"
    ],
    [
      "0.177725253",
      "1.069465974"
    ],
    [
      "1.059167476",
      "0.700284291"
    ],
    [
      "0.762523613",
      "1.000932276"
    ],
    [
      "1.931878238",
      "1.115736397"
    ],
    [
      "0.644967849",
      "1.033277419"
    ],
    [
      "1.294279005",
      "0.635594006"
    ],
    [
      "1.319536269",
      "0.957185412"
    ],
    [
      "0.189852184",
      "1.190785814"
    ],
    [
      "1.263512838",
      "0.753572855"
    ],
    [
      "0.352206408",
      "0.320431377"
    ],
    [
      "1.206570211",
      "1.916035244"
    ],
    [
      "0.825627919",
      "0.30331056"
    ],
    [
      "1.151465977",
      "0.346347742"
    ],
    [
      "0.905336642",
      "1.29017854"
    ],
    [
      "0.532920988",
      "0.626052306"
    ],
    [
      "0.961108845",
      "1.49404497"
    ],
    [
      "0.70099128",
      "1.236889976"
    ],
    [
      "1.145957074",
      "0.785917998"
    ],
    [
      "0.879845454",
      "1.850368478"
    ],
    [
      "1.666443432",
      "1.299974114"
    ],
    [
      "1.923374139",
      "0.829201395"
    ],
    [
      "1.221377826",
      "1.75104719"
    ],
    [
      "0.774369874",
      "1.911527844"
    ],
    [
      "1.845339867",
      "1.029848817"
    ],
    [
      "1.42660426",
      "0.163459045"
    ],
    [
      "0.478887227",
      "0.35897625"
    ],
    [
      "0.966868976",
      "1.054220841"
    ],
    [
      "0.384599056",
      "0.776376298"
    ],
    [
      "1.634442608",
      "1.419186501"
    ],
    [
      "0.40985632",
      "1.097967705"
    ],
    [
      "0.947120615",
      "0.293059178"
    ],
    [
      "1.681164893",
      "0.849996908"
    ],
    [
      "1.381068603",
      "0.721227713"
    ],
    [
      "0.976883671",
      "0.174823284"
    ],
    [
      "0.140477813",
      "0.621828645"
    ],
    [
      "0.706500183",
      "0.79731972"
    ],
    [
      "0.381597709",
      "0.654488818"
    ],
    [
      "0.781979523",
      "1.762389573"
    ],
    [
      "1.022892406",
      "1.257833397"
    ],
    [
      "1.07866461",
      "1.461699828"
    ],
    [
      "0.73726635",
      "0.67934087"
    ],
    [
      "0.639207719",
      "1.473101549"
    ],
    [
      "1.722399316",
      "1.599942657"
    ],
    [
      "0.991875012",
      "1.376066121"
    ],
    [
      "0.446493593",
      "0.241433839"
    ],
    [
      "1.08442474",
      "1.021875698"
    ],
    [
      "0.997401219",
      "1.818023335"
    ],
    [
      "0.910845545",
      "0.850608284"
    ],
    [
      "0.738838321",
      "0.217676853"
    ],
    [
      "1.46209807",
      "1.246685549"
    ],
    [
      "1.128493548",
      "0.118926079"
    ],
    [
      "0.102818951",
      "1.277232441"
    ],
    [
      "0.098724788",
      "0.736381039"
    ],
    [
      "1.548376408",
      "1.762282939"
    ],
    [
      "0.370016638",
      "1.215175653"
    ],
    [
      "0.552669348",
      "1.387213969"
    ],
    [
      "1.396820005",
      "0.284815335"
    ],
    [
      "1.171214338",
      "1.107509405"
    ],
    [
      "0.731757447",
      "1.118911126"
    ],
    [
      "1.134646816",
      "1.665354145"
    ],
    [
      "0.916354448",
      "0.411038028"
    ],
    [
      "1.792151118",
      "0.495729666"
    ],
    [
      "1.794042161",
      "1.501287354"
    ],
    [
      "1.003144045",
      "0.496671735"
    ],
    [
      "0.843553081",
      "1.526390113"
    ],
    [
      "0.941611712",
      "0.732629434"
    ],
    [
      "0.776266524",
      "0.088004772"
    ],
    [
      "0.527412085",
      "1.065622562"
    ]
  ],
  "radius": "0.060962213"
}

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?