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 = 210

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 = 210
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[0.0629771327701164538709275264095, 0.0629771327701164538709275264105]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 = 0.062977132

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 = 210 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": [
    [
      "0.401589528",
      "0.742756831"
    ],
    [
      "0.420829912",
      "1.502090701"
    ],
    [
      "0.744614831",
      "1.300138676"
    ],
    [
      "1.506102506",
      "1.215745721"
    ],
    [
      "0.716215168",
      "0.412907343"
    ],
    [
      "0.537176187",
      "1.684017593"
    ],
    [
      "1.388223947",
      "0.904047173"
    ],
    [
      "0.526541668",
      "1.306264577"
    ],
    [
      "1.173687575",
      "1.036077674"
    ],
    [
      "1.052272225",
      "0.598474527"
    ],
    [
      "0.952077621",
      "0.916298976"
    ],
    [
      "0.619662691",
      "0.73663093"
    ],
    [
      "1.055809016",
      "0.724379127"
    ],
    [
      "1.805954938",
      "0.746298597"
    ],
    [
      "1.247685384",
      "0.09630547"
    ],
    [
      "0.301394924",
      "1.06058128"
    ],
    [
      "0.758786141",
      "1.803796291"
    ],
    [
      "1.304031862",
      "1.886327524"
    ],
    [
      "0.405126319",
      "0.86866143"
    ],
    [
      "0.20237901",
      "0.508255544"
    ],
    [
      "0.595514037",
      "0.278030417"
    ],
    [
      "0.271694616",
      "0.633257555"
    ],
    [
      "1.057883025",
      "1.900218771"
    ],
    [
      "1.507402673",
      "1.477156227"
    ],
    [
      "1.611152966",
      "1.285235848"
    ],
    [
      "1.602760319",
      "0.772016672"
    ],
    [
      "0.508857714",
      "0.676741581"
    ],
    [
      "0.4121999",
      "1.120470629"
    ],
    [
      "1.613370692",
      "1.14973047"
    ],
    [
      "0.083190702",
      "1.193578319"
    ],
    [
      "0.969761576",
      "1.545821973"
    ],
    [
      "0.814584708",
      "0.199848195"
    ],
    [
      "0.734004458",
      "0.922424878"
    ],
    [
      "0.294321342",
      "0.808772082"
    ],
    [
      "1.396516276",
      "1.417417765"
    ],
    [
      "0.840664611",
      "0.07662354"
    ],
    [
      "1.066419389",
      "1.102092924"
    ],
    [
      "1.059345807",
      "0.850283726"
    ],
    [
      "1.187806307",
      "1.539748645"
    ],
    [
      "0.751688413",
      "1.551947874"
    ],
    [
      "0.134794262",
      "1.35976504"
    ],
    [
      "0.600955617",
      "0.152193752"
    ],
    [
      "0.721302932",
      "0.284482628"
    ],
    [
      "0.637346645",
      "1.366153926"
    ],
    [
      "0.519468086",
      "1.054455379"
    ],
    [
      "1.614687035",
      "1.543145187"
    ],
    [
      "0.532873046",
      "0.387303393"
    ],
    [
      "0.379469751",
      "1.621060505"
    ],
    [
      "1.013780464",
      "0.06307847"
    ],
    [
      "1.163077202",
      "0.658363876"
    ],
    [
      "0.6161259",
      "0.61072633"
    ],
    [
      "1.60629711",
      "0.897921272"
    ],
    [
      "1.166613993",
      "0.784268475"
    ],
    [
      "1.827907064",
      "1.017699969"
    ],
    [
      "1.491955342",
      "0.712127323"
    ],
    [
      "0.866054326",
      "1.737781041"
    ],
    [
      "0.084080677",
      "0.802253577"
    ],
    [
      "0.305201613",
      "1.312585274"
    ],
    [
      "0.945004039",
      "0.664489778"
    ],
    [
      "1.288029343",
      "1.221871622"
    ],
    [
      "0.415736691",
      "1.246375228"
    ],
    [
      "1.616425897",
      "1.413881996"
    ],
    [
      "1.717102087",
      "0.95781062"
    ],
    [
      "0.065638457",
      "0.929471064"
    ],
    [
      "0.143634326",
      "0.619671607"
    ],
    [
      "0.630273063",
      "1.114344727"
    ],
    [
      "0.748151622",
      "1.426043275"
    ],
    [
      "0.962687994",
      "1.294012774"
    ],
    [
      "1.54626916",
      "1.761315777"
    ],
    [
      "1.805562105",
      "0.521375357"
    ],
    [
      "1.599223528",
      "0.646112073"
    ],
    [
      "1.19284647",
      "1.667521176"
    ],
    [
      "1.825689338",
      "1.153205347"
    ],
    [
      "1.502565715",
      "1.089841121"
    ],
    [
      "1.506870056",
      "0.336297998"
    ],
    [
      "0.848346226",
      "1.108218826"
    ],
    [
      "1.713565296",
      "0.831906021"
    ],
    [
      "1.06995618",
      "1.227997524"
    ],
    [
      "1.93572272",
      "0.950660637"
    ],
    [
      "1.499028924",
      "0.963936522"
    ],
    [
      "1.932957524",
      "1.087190097"
    ],
    [
      "0.530056586",
      "1.432209664"
    ],
    [
      "1.062882598",
      "0.976188325"
    ],
    [
      "0.523004877",
      "1.180359978"
    ],
    [
      "1.273882179",
      "0.718253225"
    ],
    [
      "0.191348863",
      "0.736238326"
    ],
    [
      "0.261547661",
      "1.576801522"
    ],
    [
      "1.266808597",
      "0.466444026"
    ],
    [
      "1.048735434",
      "0.472569928"
    ],
    [
      "1.429221539",
      "1.711917152"
    ],
    [
      "0.730467667",
      "0.796520278"
    ],
    [
      "1.721957942",
      "1.345125197"
    ],
    [
      "1.263271806",
      "0.340539427"
    ],
    [
      "1.077029762",
      "1.479806722"
    ],
    [
      "1.395297529",
      "1.155856372"
    ],
    [
      "0.858956599",
      "1.485932624"
    ],
    [
      "1.680063794",
      "0.532082869"
    ],
    [
      "0.533639396",
      "1.558112994"
    ],
    [
      "1.530034111",
      "1.636410183"
    ],
    [
      "0.06551156",
      "1.068870961"
    ],
    [
      "0.647981164",
      "1.743906942"
    ],
    [
      "0.623199481",
      "0.862535529"
    ],
    [
      "0.490069115",
      "0.52028955"
    ],
    [
      "1.916759915",
      "0.806187946"
    ],
    [
      "1.284492552",
      "1.095967023"
    ],
    [
      "0.86249339",
      "1.611837223"
    ],
    [
      "1.27741897",
      "0.844157824"
    ],
    [
      "1.291566134",
      "1.347776221"
    ],
    [
      "1.191480689",
      "1.793468036"
    ],
    [
      "0.841272644",
      "0.856409627"
    ],
    [
      "0.410333356",
      "0.416432439"
    ],
    [
      "1.073492971",
      "1.353902123"
    ],
    [
      "0.834199063",
      "0.604600429"
    ],
    [
      "0.959151203",
      "1.168108175"
    ],
    [
      "0.640883436",
      "1.492058525"
    ],
    [
      "0.419273482",
      "1.372279828"
    ],
    [
      "1.824370273",
      "0.89179537"
    ],
    [
      "1.860011758",
      "1.372010255"
    ],
    [
      "1.170150784",
      "0.910173075"
    ],
    [
      "1.649939333",
      "1.674974605"
    ],
    [
      "1.081890347",
      "1.607912319"
    ],
    [
      "0.737541249",
      "1.048329477"
    ],
    [
      "0.855419808",
      "1.360028024"
    ],
    [
      "1.725126677",
      "0.649700102"
    ],
    [
      "1.488418551",
      "0.586222724"
    ],
    [
      "0.485356355",
      "0.21695864"
    ],
    [
      "0.651517955",
      "1.869811541"
    ],
    [
      "1.309919593",
      "1.508880827"
    ],
    [
      "0.644444373",
      "1.618002343"
    ],
    [
      "1.77101052",
      "1.461135204"
    ],
    [
      "0.74107804",
      "1.174234076"
    ],
    [
      "0.96731363",
      "1.812687852"
    ],
    [
      "0.934393667",
      "0.28677598"
    ],
    [
      "0.40866311",
      "0.99456603"
    ],
    [
      "0.626736272",
      "0.988440128"
    ],
    [
      "0.934340341",
      "0.160821726"
    ],
    [
      "1.124585441",
      "0.122967819"
    ],
    [
      "0.937930458",
      "0.412680579"
    ],
    [
      "0.384987679",
      "0.293054671"
    ],
    [
      "1.045145318",
      "0.220711074"
    ],
    [
      "1.420155567",
      "1.837544717"
    ],
    [
      "1.377613574",
      "0.526333375"
    ],
    [
      "1.313097835",
      "1.760699959"
    ],
    [
      "0.723394086",
      "0.54471108"
    ],
    [
      "0.941467248",
      "0.538585178"
    ],
    [
      "0.398052737",
      "0.616852232"
    ],
    [
      "0.534100166",
      "1.812986565"
    ],
    [
      "0.973298367",
      "1.671726572"
    ],
    [
      "1.609833901",
      "1.023825871"
    ],
    [
      "1.39883432",
      "1.281760971"
    ],
    [
      "1.628991697",
      "0.305463248"
    ],
    [
      "1.734592257",
      "1.581709609"
    ],
    [
      "1.422749749",
      "1.570421223"
    ],
    [
      "0.612589109",
      "0.484821731"
    ],
    [
      "0.187053156",
      "0.874787332"
    ],
    [
      "1.374196192",
      "0.400207515"
    ],
    [
      "0.827125481",
      "0.35279123"
    ],
    [
      "0.966224785",
      "1.419917373"
    ],
    [
      "0.286537394",
      "0.392566564"
    ],
    [
      "1.504470932",
      "0.210366583"
    ],
    [
      "0.955614412",
      "1.042203575"
    ],
    [
      "1.07455767",
      "1.746633383"
    ],
    [
      "1.396610689",
      "0.275409993"
    ],
    [
      "0.195968557",
      "1.249664257"
    ],
    [
      "1.177224366",
      "1.161982273"
    ],
    [
      "0.304931714",
      "1.186485879"
    ],
    [
      "0.192431766",
      "1.123759657"
    ],
    [
      "0.837735853",
      "0.730505028"
    ],
    [
      "0.515931296",
      "0.928550779"
    ],
    [
      "1.607003401",
      "0.429483375"
    ],
    [
      "1.285270735",
      "0.216521186"
    ],
    [
      "1.180761157",
      "1.287886872"
    ],
    [
      "0.297858133",
      "0.934676681"
    ],
    [
      "1.045198644",
      "0.346665329"
    ],
    [
      "0.512394505",
      "0.80264618"
    ],
    [
      "1.314463615",
      "1.634753099"
    ],
    [
      "0.423829442",
      "1.738944749"
    ],
    [
      "1.270345388",
      "0.592348626"
    ],
    [
      "0.170761634",
      "0.999683542"
    ],
    [
      "1.720638878",
      "1.08371522"
    ],
    [
      "1.384687156",
      "0.778142574"
    ],
    [
      "1.15600362",
      "0.406554678"
    ],
    [
      "1.182414716",
      "1.919095602"
    ],
    [
      "0.851883017",
      "1.234123425"
    ],
    [
      "1.48488176",
      "0.460318125"
    ],
    [
      "0.75524935",
      "1.677891692"
    ],
    [
      "1.381150365",
      "0.652237975"
    ],
    [
      "0.936794328",
      "1.934888708"
    ],
    [
      "1.902134549",
      "1.253308328"
    ],
    [
      "0.726930877",
      "0.670615679"
    ],
    [
      "0.94854083",
      "0.790394377"
    ],
    [
      "0.328277881",
      "0.511990673"
    ],
    [
      "1.393115694",
      "0.14942865"
    ],
    [
      "1.862475474",
      "0.63373792"
    ],
    [
      "1.159540411",
      "0.532459277"
    ],
    [
      "1.166286566",
      "0.257992799"
    ],
    [
      "1.280955761",
      "0.970062424"
    ],
    [
      "0.633809854",
      "1.240249327"
    ],
    [
      "1.391760738",
      "1.029951772"
    ],
    [
      "1.50388478",
      "1.351251099"
    ],
    [
      "1.733445628",
      "0.416845465"
    ],
    [
      "1.718421152",
      "1.219220598"
    ],
    [
      "0.811982106",
      "1.917965754"
    ],
    [
      "0.190860941",
      "1.472552471"
    ],
    [
      "1.18432927",
      "1.413842381"
    ],
    [
      "1.495492133",
      "0.838031923"
    ],
    [
      "0.312118936",
      "1.438479376"
    ],
    [
      "0.830662272",
      "0.47869583"
    ],
    [
      "0.718264829",
      "0.106334992"
    ],
    [
      "0.844809435",
      "0.982314227"
    ]
  ],
  "radius": "0.062977132"
}
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": 210
}

起步布局答案

{
  "centers": [
    [
      "0.401589528",
      "0.742756831"
    ],
    [
      "0.420829912",
      "1.502090701"
    ],
    [
      "0.744614831",
      "1.300138676"
    ],
    [
      "1.506102506",
      "1.215745721"
    ],
    [
      "0.716215168",
      "0.412907343"
    ],
    [
      "0.537176187",
      "1.684017593"
    ],
    [
      "1.388223947",
      "0.904047173"
    ],
    [
      "0.526541668",
      "1.306264577"
    ],
    [
      "1.173687575",
      "1.036077674"
    ],
    [
      "1.052272225",
      "0.598474527"
    ],
    [
      "0.952077621",
      "0.916298976"
    ],
    [
      "0.619662691",
      "0.73663093"
    ],
    [
      "1.055809016",
      "0.724379127"
    ],
    [
      "1.805954938",
      "0.746298597"
    ],
    [
      "1.247685384",
      "0.09630547"
    ],
    [
      "0.301394924",
      "1.06058128"
    ],
    [
      "0.758786141",
      "1.803796291"
    ],
    [
      "1.304031862",
      "1.886327524"
    ],
    [
      "0.405126319",
      "0.86866143"
    ],
    [
      "0.20237901",
      "0.508255544"
    ],
    [
      "0.595514037",
      "0.278030417"
    ],
    [
      "0.271694616",
      "0.633257555"
    ],
    [
      "1.057883025",
      "1.900218771"
    ],
    [
      "1.507402673",
      "1.477156227"
    ],
    [
      "1.611152966",
      "1.285235848"
    ],
    [
      "1.602760319",
      "0.772016672"
    ],
    [
      "0.508857714",
      "0.676741581"
    ],
    [
      "0.4121999",
      "1.120470629"
    ],
    [
      "1.613370692",
      "1.14973047"
    ],
    [
      "0.083190702",
      "1.193578319"
    ],
    [
      "0.969761576",
      "1.545821973"
    ],
    [
      "0.814584708",
      "0.199848195"
    ],
    [
      "0.734004458",
      "0.922424878"
    ],
    [
      "0.294321342",
      "0.808772082"
    ],
    [
      "1.396516276",
      "1.417417765"
    ],
    [
      "0.840664611",
      "0.07662354"
    ],
    [
      "1.066419389",
      "1.102092924"
    ],
    [
      "1.059345807",
      "0.850283726"
    ],
    [
      "1.187806307",
      "1.539748645"
    ],
    [
      "0.751688413",
      "1.551947874"
    ],
    [
      "0.134794262",
      "1.35976504"
    ],
    [
      "0.600955617",
      "0.152193752"
    ],
    [
      "0.721302932",
      "0.284482628"
    ],
    [
      "0.637346645",
      "1.366153926"
    ],
    [
      "0.519468086",
      "1.054455379"
    ],
    [
      "1.614687035",
      "1.543145187"
    ],
    [
      "0.532873046",
      "0.387303393"
    ],
    [
      "0.379469751",
      "1.621060505"
    ],
    [
      "1.013780464",
      "0.06307847"
    ],
    [
      "1.163077202",
      "0.658363876"
    ],
    [
      "0.6161259",
      "0.61072633"
    ],
    [
      "1.60629711",
      "0.897921272"
    ],
    [
      "1.166613993",
      "0.784268475"
    ],
    [
      "1.827907064",
      "1.017699969"
    ],
    [
      "1.491955342",
      "0.712127323"
    ],
    [
      "0.866054326",
      "1.737781041"
    ],
    [
      "0.084080677",
      "0.802253577"
    ],
    [
      "0.305201613",
      "1.312585274"
    ],
    [
      "0.945004039",
      "0.664489778"
    ],
    [
      "1.288029343",
      "1.221871622"
    ],
    [
      "0.415736691",
      "1.246375228"
    ],
    [
      "1.616425897",
      "1.413881996"
    ],
    [
      "1.717102087",
      "0.95781062"
    ],
    [
      "0.065638457",
      "0.929471064"
    ],
    [
      "0.143634326",
      "0.619671607"
    ],
    [
      "0.630273063",
      "1.114344727"
    ],
    [
      "0.748151622",
      "1.426043275"
    ],
    [
      "0.962687994",
      "1.294012774"
    ],
    [
      "1.54626916",
      "1.761315777"
    ],
    [
      "1.805562105",
      "0.521375357"
    ],
    [
      "1.599223528",
      "0.646112073"
    ],
    [
      "1.19284647",
      "1.667521176"
    ],
    [
      "1.825689338",
      "1.153205347"
    ],
    [
      "1.502565715",
      "1.089841121"
    ],
    [
      "1.506870056",
      "0.336297998"
    ],
    [
      "0.848346226",
      "1.108218826"
    ],
    [
      "1.713565296",
      "0.831906021"
    ],
    [
      "1.06995618",
      "1.227997524"
    ],
    [
      "1.93572272",
      "0.950660637"
    ],
    [
      "1.499028924",
      "0.963936522"
    ],
    [
      "1.932957524",
      "1.087190097"
    ],
    [
      "0.530056586",
      "1.432209664"
    ],
    [
      "1.062882598",
      "0.976188325"
    ],
    [
      "0.523004877",
      "1.180359978"
    ],
    [
      "1.273882179",
      "0.718253225"
    ],
    [
      "0.191348863",
      "0.736238326"
    ],
    [
      "0.261547661",
      "1.576801522"
    ],
    [
      "1.266808597",
      "0.466444026"
    ],
    [
      "1.048735434",
      "0.472569928"
    ],
    [
      "1.429221539",
      "1.711917152"
    ],
    [
      "0.730467667",
      "0.796520278"
    ],
    [
      "1.721957942",
      "1.345125197"
    ],
    [
      "1.263271806",
      "0.340539427"
    ],
    [
      "1.077029762",
      "1.479806722"
    ],
    [
      "1.395297529",
      "1.155856372"
    ],
    [
      "0.858956599",
      "1.485932624"
    ],
    [
      "1.680063794",
      "0.532082869"
    ],
    [
      "0.533639396",
      "1.558112994"
    ],
    [
      "1.530034111",
      "1.636410183"
    ],
    [
      "0.06551156",
      "1.068870961"
    ],
    [
      "0.647981164",
      "1.743906942"
    ],
    [
      "0.623199481",
      "0.862535529"
    ],
    [
      "0.490069115",
      "0.52028955"
    ],
    [
      "1.916759915",
      "0.806187946"
    ],
    [
      "1.284492552",
      "1.095967023"
    ],
    [
      "0.86249339",
      "1.611837223"
    ],
    [
      "1.27741897",
      "0.844157824"
    ],
    [
      "1.291566134",
      "1.347776221"
    ],
    [
      "1.191480689",
      "1.793468036"
    ],
    [
      "0.841272644",
      "0.856409627"
    ],
    [
      "0.410333356",
      "0.416432439"
    ],
    [
      "1.073492971",
      "1.353902123"
    ],
    [
      "0.834199063",
      "0.604600429"
    ],
    [
      "0.959151203",
      "1.168108175"
    ],
    [
      "0.640883436",
      "1.492058525"
    ],
    [
      "0.419273482",
      "1.372279828"
    ],
    [
      "1.824370273",
      "0.89179537"
    ],
    [
      "1.860011758",
      "1.372010255"
    ],
    [
      "1.170150784",
      "0.910173075"
    ],
    [
      "1.649939333",
      "1.674974605"
    ],
    [
      "1.081890347",
      "1.607912319"
    ],
    [
      "0.737541249",
      "1.048329477"
    ],
    [
      "0.855419808",
      "1.360028024"
    ],
    [
      "1.725126677",
      "0.649700102"
    ],
    [
      "1.488418551",
      "0.586222724"
    ],
    [
      "0.485356355",
      "0.21695864"
    ],
    [
      "0.651517955",
      "1.869811541"
    ],
    [
      "1.309919593",
      "1.508880827"
    ],
    [
      "0.644444373",
      "1.618002343"
    ],
    [
      "1.77101052",
      "1.461135204"
    ],
    [
      "0.74107804",
      "1.174234076"
    ],
    [
      "0.96731363",
      "1.812687852"
    ],
    [
      "0.934393667",
      "0.28677598"
    ],
    [
      "0.40866311",
      "0.99456603"
    ],
    [
      "0.626736272",
      "0.988440128"
    ],
    [
      "0.934340341",
      "0.160821726"
    ],
    [
      "1.124585441",
      "0.122967819"
    ],
    [
      "0.937930458",
      "0.412680579"
    ],
    [
      "0.384987679",
      "0.293054671"
    ],
    [
      "1.045145318",
      "0.220711074"
    ],
    [
      "1.420155567",
      "1.837544717"
    ],
    [
      "1.377613574",
      "0.526333375"
    ],
    [
      "1.313097835",
      "1.760699959"
    ],
    [
      "0.723394086",
      "0.54471108"
    ],
    [
      "0.941467248",
      "0.538585178"
    ],
    [
      "0.398052737",
      "0.616852232"
    ],
    [
      "0.534100166",
      "1.812986565"
    ],
    [
      "0.973298367",
      "1.671726572"
    ],
    [
      "1.609833901",
      "1.023825871"
    ],
    [
      "1.39883432",
      "1.281760971"
    ],
    [
      "1.628991697",
      "0.305463248"
    ],
    [
      "1.734592257",
      "1.581709609"
    ],
    [
      "1.422749749",
      "1.570421223"
    ],
    [
      "0.612589109",
      "0.484821731"
    ],
    [
      "0.187053156",
      "0.874787332"
    ],
    [
      "1.374196192",
      "0.400207515"
    ],
    [
      "0.827125481",
      "0.35279123"
    ],
    [
      "0.966224785",
      "1.419917373"
    ],
    [
      "0.286537394",
      "0.392566564"
    ],
    [
      "1.504470932",
      "0.210366583"
    ],
    [
      "0.955614412",
      "1.042203575"
    ],
    [
      "1.07455767",
      "1.746633383"
    ],
    [
      "1.396610689",
      "0.275409993"
    ],
    [
      "0.195968557",
      "1.249664257"
    ],
    [
      "1.177224366",
      "1.161982273"
    ],
    [
      "0.304931714",
      "1.186485879"
    ],
    [
      "0.192431766",
      "1.123759657"
    ],
    [
      "0.837735853",
      "0.730505028"
    ],
    [
      "0.515931296",
      "0.928550779"
    ],
    [
      "1.607003401",
      "0.429483375"
    ],
    [
      "1.285270735",
      "0.216521186"
    ],
    [
      "1.180761157",
      "1.287886872"
    ],
    [
      "0.297858133",
      "0.934676681"
    ],
    [
      "1.045198644",
      "0.346665329"
    ],
    [
      "0.512394505",
      "0.80264618"
    ],
    [
      "1.314463615",
      "1.634753099"
    ],
    [
      "0.423829442",
      "1.738944749"
    ],
    [
      "1.270345388",
      "0.592348626"
    ],
    [
      "0.170761634",
      "0.999683542"
    ],
    [
      "1.720638878",
      "1.08371522"
    ],
    [
      "1.384687156",
      "0.778142574"
    ],
    [
      "1.15600362",
      "0.406554678"
    ],
    [
      "1.182414716",
      "1.919095602"
    ],
    [
      "0.851883017",
      "1.234123425"
    ],
    [
      "1.48488176",
      "0.460318125"
    ],
    [
      "0.75524935",
      "1.677891692"
    ],
    [
      "1.381150365",
      "0.652237975"
    ],
    [
      "0.936794328",
      "1.934888708"
    ],
    [
      "1.902134549",
      "1.253308328"
    ],
    [
      "0.726930877",
      "0.670615679"
    ],
    [
      "0.94854083",
      "0.790394377"
    ],
    [
      "0.328277881",
      "0.511990673"
    ],
    [
      "1.393115694",
      "0.14942865"
    ],
    [
      "1.862475474",
      "0.63373792"
    ],
    [
      "1.159540411",
      "0.532459277"
    ],
    [
      "1.166286566",
      "0.257992799"
    ],
    [
      "1.280955761",
      "0.970062424"
    ],
    [
      "0.633809854",
      "1.240249327"
    ],
    [
      "1.391760738",
      "1.029951772"
    ],
    [
      "1.50388478",
      "1.351251099"
    ],
    [
      "1.733445628",
      "0.416845465"
    ],
    [
      "1.718421152",
      "1.219220598"
    ],
    [
      "0.811982106",
      "1.917965754"
    ],
    [
      "0.190860941",
      "1.472552471"
    ],
    [
      "1.18432927",
      "1.413842381"
    ],
    [
      "1.495492133",
      "0.838031923"
    ],
    [
      "0.312118936",
      "1.438479376"
    ],
    [
      "0.830662272",
      "0.47869583"
    ],
    [
      "0.718264829",
      "0.106334992"
    ],
    [
      "0.844809435",
      "0.982314227"
    ]
  ],
  "radius": "0.062977132"
}

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?