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 = 246

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 = 246
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[0.0584524509712815833794373645735, 0.0584524509712815833794373645745]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 = 0.058452450

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 = 246 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": [
    [
      "0.4889363",
      "1.656745543"
    ],
    [
      "1.448184849",
      "1.293755698"
    ],
    [
      "0.332593347",
      "1.162645679"
    ],
    [
      "0.897656633",
      "1.013608008"
    ],
    [
      "1.252041531",
      "0.50657693"
    ],
    [
      "0.752382787",
      "1.154660403"
    ],
    [
      "0.440194131",
      "1.460437882"
    ],
    [
      "1.057249651",
      "0.451292286"
    ],
    [
      "0.242071109",
      "0.441380645"
    ],
    [
      "0.9404764",
      "1.939664157"
    ],
    [
      "0.653346718",
      "0.761986326"
    ],
    [
      "0.760663011",
      "0.090132117"
    ],
    [
      "0.57191008",
      "0.678112433"
    ],
    [
      "1.27083169",
      "1.547426978"
    ],
    [
      "1.528270049",
      "0.645735467"
    ],
    [
      "1.189555762",
      "1.463397343"
    ],
    [
      "1.414914807",
      "0.674324717"
    ],
    [
      "0.426636234",
      "0.819164827"
    ],
    [
      "1.025331047",
      "0.563755431"
    ],
    [
      "0.219238105",
      "1.19123493"
    ],
    [
      "0.155418803",
      "1.416166299"
    ],
    [
      "1.380693021",
      "0.138846929"
    ],
    [
      "0.38791335",
      "0.492784346"
    ],
    [
      "1.221474365",
      "1.350934199"
    ],
    [
      "0.283785065",
      "0.834764606"
    ],
    [
      "1.173885151",
      "1.152766545"
    ],
    [
      "0.608363195",
      "0.240938932"
    ],
    [
      "1.319158996",
      "1.01171415"
    ],
    [
      "1.253392969",
      "1.238471054"
    ],
    [
      "1.092448512",
      "1.068892651"
    ],
    [
      "0.253925567",
      "0.662244321"
    ],
    [
      "1.044121206",
      "1.604605479"
    ],
    [
      "1.788627009",
      "0.485627345"
    ],
    [
      "1.510670618",
      "0.336935284"
    ],
    [
      "1.366748211",
      "1.209881804"
    ],
    [
      "0.734392777",
      "1.577245293"
    ],
    [
      "0.913327243",
      "1.324238806"
    ],
    [
      "0.843746822",
      "1.874012464"
    ],
    [
      "1.007731617",
      "0.254955248"
    ],
    [
      "1.432514238",
      "0.9831249"
    ],
    [
      "1.042930478",
      "0.872555613"
    ],
    [
      "0.414029985",
      "1.246519573"
    ],
    [
      "1.627306118",
      "1.038409543"
    ],
    [
      "1.074849082",
      "0.760092469"
    ],
    [
      "0.943894409",
      "0.479881537"
    ],
    [
      "1.334829607",
      "1.322344948"
    ],
    [
      "1.561540091",
      "1.265166447"
    ],
    [
      "1.033497987",
      "0.059048528"
    ],
    [
      "1.419446286",
      "1.726976773"
    ],
    [
      "0.816219994",
      "0.929734114"
    ],
    [
      "1.416353314",
      "0.250180211"
    ],
    [
      "0.734783356",
      "0.84586022"
    ],
    [
      "1.885307854",
      "1.320533602"
    ],
    [
      "1.529708556",
      "0.22159096"
    ],
    [
      "0.669880989",
      "1.801978251"
    ],
    [
      "1.060529909",
      "1.181355796"
    ],
    [
      "1.706813936",
      "1.124114052"
    ],
    [
      "0.929575236",
      "0.901144864"
    ],
    [
      "1.593458695",
      "1.152703303"
    ],
    [
      "1.838762268",
      "1.427772889"
    ],
    [
      "1.106767686",
      "0.647629324"
    ],
    [
      "1.816455223",
      "0.819978854"
    ],
    [
      "0.192511036",
      "0.761717993"
    ],
    [
      "0.958651091",
      "0.148852194"
    ],
    [
      "1.07620052",
      "1.491986594"
    ],
    [
      "1.188204324",
      "0.731503218"
    ],
    [
      "1.317298998",
      "1.783833502"
    ],
    [
      "1.302911003",
      "1.434808093"
    ],
    [
      "0.284117127",
      "1.610790265"
    ],
    [
      "1.697161963",
      "1.632832509"
    ],
    [
      "1.220122927",
      "0.619040074"
    ],
    [
      "1.931032242",
      "0.859676261"
    ],
    [
      "1.271041898",
      "0.098308214"
    ],
    [
      "1.29956127",
      "0.245044595"
    ],
    [
      "1.770210632",
      "1.541560126"
    ],
    [
      "0.089478762",
      "1.239714125"
    ],
    [
      "1.500595166",
      "1.508073016"
    ],
    [
      "0.729004103",
      "0.207439028"
    ],
    [
      "1.416295621",
      "1.406335518"
    ],
    [
      "0.68661676",
      "1.381417307"
    ],
    [
      "0.911975806",
      "0.592344681"
    ],
    [
      "0.730261938",
      "1.902082682"
    ],
    [
      "0.617248395",
      "0.449517176"
    ],
    [
      "0.947174667",
      "1.209945046"
    ],
    [
      "0.620985036",
      "1.60581963"
    ],
    [
      "1.301559565",
      "0.702913968"
    ],
    [
      "0.062609654",
      "0.911619424"
    ],
    [
      "1.464432842",
      "0.870661755"
    ],
    [
      "0.187319501",
      "1.303698074"
    ],
    [
      "1.722082322",
      "1.435021767"
    ],
    [
      "0.781021133",
      "0.312133749"
    ],
    [
      "0.300674743",
      "1.275108824"
    ],
    [
      "1.237722358",
      "0.927840256"
    ],
    [
      "0.865738029",
      "1.126071152"
    ],
    [
      "0.121397365",
      "1.12725098"
    ],
    [
      "0.833819425",
      "1.238534297"
    ],
    [
      "1.765505522",
      "0.714760585"
    ],
    [
      "1.644176963",
      "1.347858063"
    ],
    [
      "1.157476448",
      "1.576016228"
    ],
    [
      "0.862457771",
      "0.396007643"
    ],
    [
      "0.3771182",
      "0.622827789"
    ],
    [
      "0.96149384",
      "0.788681719"
    ],
    [
      "0.213501552",
      "1.517621463"
    ],
    [
      "0.457017697",
      "1.769208688"
    ],
    [
      "0.362799027",
      "1.044091116"
    ],
    [
      "0.670946149",
      "1.070786509"
    ],
    [
      "1.936947282",
      "1.092960092"
    ],
    [
      "1.011011874",
      "0.985018757"
    ],
    [
      "1.513950876",
      "1.066998794"
    ],
    [
      "1.473460381",
      "1.622951318"
    ],
    [
      "1.529621487",
      "1.377629592"
    ],
    [
      "0.642267525",
      "0.129058404"
    ],
    [
      "1.057381226",
      "1.939797415"
    ],
    [
      "0.345199596",
      "0.735290934"
    ],
    [
      "1.287240392",
      "1.124177295"
    ],
    [
      "1.66392782",
      "0.921108585"
    ],
    [
      "1.672918272",
      "0.502308004"
    ],
    [
      "0.798620564",
      "0.620933932"
    ],
    [
      "0.607108941",
      "1.295712798"
    ],
    [
      "1.598984953",
      "1.69629928"
    ],
    [
      "0.251156709",
      "1.078771786"
    ],
    [
      "1.384186932",
      "1.518837727"
    ],
    [
      "0.784301391",
      "1.042197258"
    ],
    [
      "0.490473442",
      "0.594238539"
    ],
    [
      "0.702421674",
      "1.689693524"
    ],
    [
      "1.641625291",
      "0.617146216"
    ],
    [
      "1.200530991",
      "1.778177664"
    ],
    [
      "0.652956139",
      "1.493371399"
    ],
    [
      "0.556525747",
      "1.830567501"
    ],
    [
      "1.496351445",
      "0.758198611"
    ],
    [
      "1.286970273",
      "1.89674929"
    ],
    [
      "1.3510776",
      "0.899251006"
    ],
    [
      "0.665396473",
      "0.34298775"
    ],
    [
      "0.768053398",
      "1.465291201"
    ],
    [
      "0.503893153",
      "0.478106427"
    ],
    [
      "1.026682485",
      "1.295649555"
    ],
    [
      "1.400595634",
      "1.095588044"
    ],
    [
      "0.548347848",
      "0.341345413"
    ],
    [
      "0.88140864",
      "1.43670195"
    ],
    [
      "1.831476429",
      "0.935914696"
    ],
    [
      "1.906466353",
      "0.745381584"
    ],
    [
      "1.124367116",
      "0.956429507"
    ],
    [
      "0.508072873",
      "0.903038721"
    ],
    [
      "0.497537257",
      "0.203731843"
    ],
    [
      "1.521561414",
      "1.783891241"
    ],
    [
      "0.962845278",
      "1.520575844"
    ],
    [
      "0.444235665",
      "1.12796501"
    ],
    [
      "0.639027545",
      "1.183249653"
    ],
    [
      "1.622088265",
      "0.293234142"
    ],
    [
      "0.930765965",
      "1.633194729"
    ],
    [
      "0.994763882",
      "1.4081127"
    ],
    [
      "0.603828684",
      "0.565649288"
    ],
    [
      "0.557590907",
      "1.099375759"
    ],
    [
      "1.603050327",
      "0.408578466"
    ],
    [
      "0.058882825",
      "1.028464907"
    ],
    [
      "1.240727936",
      "1.666992484"
    ],
    [
      "0.993412444",
      "0.676218575"
    ],
    [
      "0.458554838",
      "0.706701683"
    ],
    [
      "0.525672303",
      "1.211838904"
    ],
    [
      "1.095365046",
      "1.829235281"
    ],
    [
      "1.089168255",
      "0.338829142"
    ],
    [
      "1.382996204",
      "0.786787862"
    ],
    [
      "1.283960135",
      "0.394113785"
    ],
    [
      "0.269100843",
      "1.388905525"
    ],
    [
      "1.593109623",
      "1.57954211"
    ],
    [
      "1.352268328",
      "1.631300872"
    ],
    [
      "1.801319989",
      "1.21049603"
    ],
    [
      "0.749102529",
      "0.424596893"
    ],
    [
      "1.688071899",
      "1.239506826"
    ],
    [
      "1.125557845",
      "1.688479373"
    ],
    [
      "0.521476986",
      "1.544460817"
    ],
    [
      "1.15628572",
      "0.843966363"
    ],
    [
      "0.402734377",
      "0.272136302"
    ],
    [
      "0.702864753",
      "0.958323365"
    ],
    [
      "1.397315377",
      "0.365524535"
    ],
    [
      "0.894376375",
      "0.283544499"
    ],
    [
      "1.012174966",
      "1.717095855"
    ],
    [
      "1.269640962",
      "0.815377112"
    ],
    [
      "1.577788084",
      "0.842072505"
    ],
    [
      "0.76670196",
      "0.733397076"
    ],
    [
      "1.941245033",
      "0.976134215"
    ],
    [
      "0.589509511",
      "0.986912615"
    ],
    [
      "0.685265322",
      "0.649523182"
    ],
    [
      "0.28584417",
      "0.549781177"
    ],
    [
      "0.842359345",
      "0.178849777"
    ],
    [
      "0.799972002",
      "1.352828056"
    ],
    [
      "0.849490036",
      "1.549165095"
    ],
    [
      "1.140037727",
      "1.267060305"
    ],
    [
      "1.197061032",
      "0.188826651"
    ],
    [
      "1.608746446",
      "1.463687694"
    ],
    [
      "0.365880439",
      "1.695991501"
    ],
    [
      "0.897105343",
      "1.745148821"
    ],
    [
      "0.720464183",
      "1.267123547"
    ],
    [
      "0.975813013",
      "0.367418392"
    ],
    [
      "0.394717631",
      "0.931627972"
    ],
    [
      "0.279529993",
      "0.951592045"
    ],
    [
      "0.979093271",
      "1.097481902"
    ],
    [
      "0.168900162",
      "0.557727132"
    ],
    [
      "1.108119123",
      "1.379523449"
    ],
    [
      "0.080787599",
      "0.796136445"
    ],
    [
      "1.740554208",
      "1.009398747"
    ],
    [
      "1.609706687",
      "0.729609361"
    ],
    [
      "1.54586948",
      "0.954535649"
    ],
    [
      "0.397799043",
      "1.583528357"
    ],
    [
      "1.446833411",
      "0.561861573"
    ],
    [
      "0.495466623",
      "1.330393467"
    ],
    [
      "0.978460221",
      "1.829102023"
    ],
    [
      "1.756979295",
      "0.59816702"
    ],
    [
      "1.365396773",
      "0.477987679"
    ],
    [
      "1.480103453",
      "1.181292553"
    ],
    [
      "1.820062026",
      "1.095103257"
    ],
    [
      "1.170604893",
      "0.422703036"
    ],
    [
      "0.539991476",
      "0.790575577"
    ],
    [
      "1.417612014",
      "1.843867284"
    ],
    [
      "0.120936212",
      "0.664454977"
    ],
    [
      "0.433191801",
      "0.38500393"
    ],
    [
      "0.170606262",
      "0.994046455"
    ],
    [
      "1.560188653",
      "0.533272322"
    ],
    [
      "1.138686289",
      "0.53516618"
    ],
    [
      "1.173620738",
      "1.925363203"
    ],
    [
      "1.082578512",
      "0.165151583"
    ],
    [
      "1.205803754",
      "1.040303401"
    ],
    [
      "0.78373679",
      "1.773685238"
    ],
    [
      "0.880057202",
      "0.704807825"
    ],
    [
      "0.327183593",
      "1.490360689"
    ],
    [
      "0.382111381",
      "1.358982718"
    ],
    [
      "0.553549373",
      "1.431848631"
    ],
    [
      "0.875451835",
      "0.066726438"
    ],
    [
      "1.154289288",
      "0.071768044"
    ],
    [
      "0.717183926",
      "0.537060038"
    ],
    [
      "0.830539167",
      "0.508470787"
    ],
    [
      "1.333478169",
      "0.590450823"
    ],
    [
      "1.867926082",
      "0.635012188"
    ],
    [
      "0.31713914",
      "0.351761747"
    ],
    [
      "1.918205244",
      "1.208352865"
    ],
    [
      "0.588444351",
      "1.718104357"
    ],
    [
      "0.476154269",
      "1.015501866"
    ],
    [
      "1.718771456",
      "0.391885787"
    ],
    [
      "1.768417094",
      "1.325420755"
    ],
    [
      "1.695846424",
      "0.80864544"
    ],
    [
      "0.815829415",
      "1.661119186"
    ],
    [
      "1.478752015",
      "0.449398429"
    ],
    [
      "1.202523497",
      "0.310239891"
    ],
    [
      "0.174333091",
      "0.877200972"
    ],
    [
      "0.621428114",
      "0.874449471"
    ],
    [
      "0.848138598",
      "0.81727097"
    ]
  ],
  "radius": "0.05845245"
}
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": 246
}

起步布局答案

{
  "centers": [
    [
      "0.4889363",
      "1.656745543"
    ],
    [
      "1.448184849",
      "1.293755698"
    ],
    [
      "0.332593347",
      "1.162645679"
    ],
    [
      "0.897656633",
      "1.013608008"
    ],
    [
      "1.252041531",
      "0.50657693"
    ],
    [
      "0.752382787",
      "1.154660403"
    ],
    [
      "0.440194131",
      "1.460437882"
    ],
    [
      "1.057249651",
      "0.451292286"
    ],
    [
      "0.242071109",
      "0.441380645"
    ],
    [
      "0.9404764",
      "1.939664157"
    ],
    [
      "0.653346718",
      "0.761986326"
    ],
    [
      "0.760663011",
      "0.090132117"
    ],
    [
      "0.57191008",
      "0.678112433"
    ],
    [
      "1.27083169",
      "1.547426978"
    ],
    [
      "1.528270049",
      "0.645735467"
    ],
    [
      "1.189555762",
      "1.463397343"
    ],
    [
      "1.414914807",
      "0.674324717"
    ],
    [
      "0.426636234",
      "0.819164827"
    ],
    [
      "1.025331047",
      "0.563755431"
    ],
    [
      "0.219238105",
      "1.19123493"
    ],
    [
      "0.155418803",
      "1.416166299"
    ],
    [
      "1.380693021",
      "0.138846929"
    ],
    [
      "0.38791335",
      "0.492784346"
    ],
    [
      "1.221474365",
      "1.350934199"
    ],
    [
      "0.283785065",
      "0.834764606"
    ],
    [
      "1.173885151",
      "1.152766545"
    ],
    [
      "0.608363195",
      "0.240938932"
    ],
    [
      "1.319158996",
      "1.01171415"
    ],
    [
      "1.253392969",
      "1.238471054"
    ],
    [
      "1.092448512",
      "1.068892651"
    ],
    [
      "0.253925567",
      "0.662244321"
    ],
    [
      "1.044121206",
      "1.604605479"
    ],
    [
      "1.788627009",
      "0.485627345"
    ],
    [
      "1.510670618",
      "0.336935284"
    ],
    [
      "1.366748211",
      "1.209881804"
    ],
    [
      "0.734392777",
      "1.577245293"
    ],
    [
      "0.913327243",
      "1.324238806"
    ],
    [
      "0.843746822",
      "1.874012464"
    ],
    [
      "1.007731617",
      "0.254955248"
    ],
    [
      "1.432514238",
      "0.9831249"
    ],
    [
      "1.042930478",
      "0.872555613"
    ],
    [
      "0.414029985",
      "1.246519573"
    ],
    [
      "1.627306118",
      "1.038409543"
    ],
    [
      "1.074849082",
      "0.760092469"
    ],
    [
      "0.943894409",
      "0.479881537"
    ],
    [
      "1.334829607",
      "1.322344948"
    ],
    [
      "1.561540091",
      "1.265166447"
    ],
    [
      "1.033497987",
      "0.059048528"
    ],
    [
      "1.419446286",
      "1.726976773"
    ],
    [
      "0.816219994",
      "0.929734114"
    ],
    [
      "1.416353314",
      "0.250180211"
    ],
    [
      "0.734783356",
      "0.84586022"
    ],
    [
      "1.885307854",
      "1.320533602"
    ],
    [
      "1.529708556",
      "0.22159096"
    ],
    [
      "0.669880989",
      "1.801978251"
    ],
    [
      "1.060529909",
      "1.181355796"
    ],
    [
      "1.706813936",
      "1.124114052"
    ],
    [
      "0.929575236",
      "0.901144864"
    ],
    [
      "1.593458695",
      "1.152703303"
    ],
    [
      "1.838762268",
      "1.427772889"
    ],
    [
      "1.106767686",
      "0.647629324"
    ],
    [
      "1.816455223",
      "0.819978854"
    ],
    [
      "0.192511036",
      "0.761717993"
    ],
    [
      "0.958651091",
      "0.148852194"
    ],
    [
      "1.07620052",
      "1.491986594"
    ],
    [
      "1.188204324",
      "0.731503218"
    ],
    [
      "1.317298998",
      "1.783833502"
    ],
    [
      "1.302911003",
      "1.434808093"
    ],
    [
      "0.284117127",
      "1.610790265"
    ],
    [
      "1.697161963",
      "1.632832509"
    ],
    [
      "1.220122927",
      "0.619040074"
    ],
    [
      "1.931032242",
      "0.859676261"
    ],
    [
      "1.271041898",
      "0.098308214"
    ],
    [
      "1.29956127",
      "0.245044595"
    ],
    [
      "1.770210632",
      "1.541560126"
    ],
    [
      "0.089478762",
      "1.239714125"
    ],
    [
      "1.500595166",
      "1.508073016"
    ],
    [
      "0.729004103",
      "0.207439028"
    ],
    [
      "1.416295621",
      "1.406335518"
    ],
    [
      "0.68661676",
      "1.381417307"
    ],
    [
      "0.911975806",
      "0.592344681"
    ],
    [
      "0.730261938",
      "1.902082682"
    ],
    [
      "0.617248395",
      "0.449517176"
    ],
    [
      "0.947174667",
      "1.209945046"
    ],
    [
      "0.620985036",
      "1.60581963"
    ],
    [
      "1.301559565",
      "0.702913968"
    ],
    [
      "0.062609654",
      "0.911619424"
    ],
    [
      "1.464432842",
      "0.870661755"
    ],
    [
      "0.187319501",
      "1.303698074"
    ],
    [
      "1.722082322",
      "1.435021767"
    ],
    [
      "0.781021133",
      "0.312133749"
    ],
    [
      "0.300674743",
      "1.275108824"
    ],
    [
      "1.237722358",
      "0.927840256"
    ],
    [
      "0.865738029",
      "1.126071152"
    ],
    [
      "0.121397365",
      "1.12725098"
    ],
    [
      "0.833819425",
      "1.238534297"
    ],
    [
      "1.765505522",
      "0.714760585"
    ],
    [
      "1.644176963",
      "1.347858063"
    ],
    [
      "1.157476448",
      "1.576016228"
    ],
    [
      "0.862457771",
      "0.396007643"
    ],
    [
      "0.3771182",
      "0.622827789"
    ],
    [
      "0.96149384",
      "0.788681719"
    ],
    [
      "0.213501552",
      "1.517621463"
    ],
    [
      "0.457017697",
      "1.769208688"
    ],
    [
      "0.362799027",
      "1.044091116"
    ],
    [
      "0.670946149",
      "1.070786509"
    ],
    [
      "1.936947282",
      "1.092960092"
    ],
    [
      "1.011011874",
      "0.985018757"
    ],
    [
      "1.513950876",
      "1.066998794"
    ],
    [
      "1.473460381",
      "1.622951318"
    ],
    [
      "1.529621487",
      "1.377629592"
    ],
    [
      "0.642267525",
      "0.129058404"
    ],
    [
      "1.057381226",
      "1.939797415"
    ],
    [
      "0.345199596",
      "0.735290934"
    ],
    [
      "1.287240392",
      "1.124177295"
    ],
    [
      "1.66392782",
      "0.921108585"
    ],
    [
      "1.672918272",
      "0.502308004"
    ],
    [
      "0.798620564",
      "0.620933932"
    ],
    [
      "0.607108941",
      "1.295712798"
    ],
    [
      "1.598984953",
      "1.69629928"
    ],
    [
      "0.251156709",
      "1.078771786"
    ],
    [
      "1.384186932",
      "1.518837727"
    ],
    [
      "0.784301391",
      "1.042197258"
    ],
    [
      "0.490473442",
      "0.594238539"
    ],
    [
      "0.702421674",
      "1.689693524"
    ],
    [
      "1.641625291",
      "0.617146216"
    ],
    [
      "1.200530991",
      "1.778177664"
    ],
    [
      "0.652956139",
      "1.493371399"
    ],
    [
      "0.556525747",
      "1.830567501"
    ],
    [
      "1.496351445",
      "0.758198611"
    ],
    [
      "1.286970273",
      "1.89674929"
    ],
    [
      "1.3510776",
      "0.899251006"
    ],
    [
      "0.665396473",
      "0.34298775"
    ],
    [
      "0.768053398",
      "1.465291201"
    ],
    [
      "0.503893153",
      "0.478106427"
    ],
    [
      "1.026682485",
      "1.295649555"
    ],
    [
      "1.400595634",
      "1.095588044"
    ],
    [
      "0.548347848",
      "0.341345413"
    ],
    [
      "0.88140864",
      "1.43670195"
    ],
    [
      "1.831476429",
      "0.935914696"
    ],
    [
      "1.906466353",
      "0.745381584"
    ],
    [
      "1.124367116",
      "0.956429507"
    ],
    [
      "0.508072873",
      "0.903038721"
    ],
    [
      "0.497537257",
      "0.203731843"
    ],
    [
      "1.521561414",
      "1.783891241"
    ],
    [
      "0.962845278",
      "1.520575844"
    ],
    [
      "0.444235665",
      "1.12796501"
    ],
    [
      "0.639027545",
      "1.183249653"
    ],
    [
      "1.622088265",
      "0.293234142"
    ],
    [
      "0.930765965",
      "1.633194729"
    ],
    [
      "0.994763882",
      "1.4081127"
    ],
    [
      "0.603828684",
      "0.565649288"
    ],
    [
      "0.557590907",
      "1.099375759"
    ],
    [
      "1.603050327",
      "0.408578466"
    ],
    [
      "0.058882825",
      "1.028464907"
    ],
    [
      "1.240727936",
      "1.666992484"
    ],
    [
      "0.993412444",
      "0.676218575"
    ],
    [
      "0.458554838",
      "0.706701683"
    ],
    [
      "0.525672303",
      "1.211838904"
    ],
    [
      "1.095365046",
      "1.829235281"
    ],
    [
      "1.089168255",
      "0.338829142"
    ],
    [
      "1.382996204",
      "0.786787862"
    ],
    [
      "1.283960135",
      "0.394113785"
    ],
    [
      "0.269100843",
      "1.388905525"
    ],
    [
      "1.593109623",
      "1.57954211"
    ],
    [
      "1.352268328",
      "1.631300872"
    ],
    [
      "1.801319989",
      "1.21049603"
    ],
    [
      "0.749102529",
      "0.424596893"
    ],
    [
      "1.688071899",
      "1.239506826"
    ],
    [
      "1.125557845",
      "1.688479373"
    ],
    [
      "0.521476986",
      "1.544460817"
    ],
    [
      "1.15628572",
      "0.843966363"
    ],
    [
      "0.402734377",
      "0.272136302"
    ],
    [
      "0.702864753",
      "0.958323365"
    ],
    [
      "1.397315377",
      "0.365524535"
    ],
    [
      "0.894376375",
      "0.283544499"
    ],
    [
      "1.012174966",
      "1.717095855"
    ],
    [
      "1.269640962",
      "0.815377112"
    ],
    [
      "1.577788084",
      "0.842072505"
    ],
    [
      "0.76670196",
      "0.733397076"
    ],
    [
      "1.941245033",
      "0.976134215"
    ],
    [
      "0.589509511",
      "0.986912615"
    ],
    [
      "0.685265322",
      "0.649523182"
    ],
    [
      "0.28584417",
      "0.549781177"
    ],
    [
      "0.842359345",
      "0.178849777"
    ],
    [
      "0.799972002",
      "1.352828056"
    ],
    [
      "0.849490036",
      "1.549165095"
    ],
    [
      "1.140037727",
      "1.267060305"
    ],
    [
      "1.197061032",
      "0.188826651"
    ],
    [
      "1.608746446",
      "1.463687694"
    ],
    [
      "0.365880439",
      "1.695991501"
    ],
    [
      "0.897105343",
      "1.745148821"
    ],
    [
      "0.720464183",
      "1.267123547"
    ],
    [
      "0.975813013",
      "0.367418392"
    ],
    [
      "0.394717631",
      "0.931627972"
    ],
    [
      "0.279529993",
      "0.951592045"
    ],
    [
      "0.979093271",
      "1.097481902"
    ],
    [
      "0.168900162",
      "0.557727132"
    ],
    [
      "1.108119123",
      "1.379523449"
    ],
    [
      "0.080787599",
      "0.796136445"
    ],
    [
      "1.740554208",
      "1.009398747"
    ],
    [
      "1.609706687",
      "0.729609361"
    ],
    [
      "1.54586948",
      "0.954535649"
    ],
    [
      "0.397799043",
      "1.583528357"
    ],
    [
      "1.446833411",
      "0.561861573"
    ],
    [
      "0.495466623",
      "1.330393467"
    ],
    [
      "0.978460221",
      "1.829102023"
    ],
    [
      "1.756979295",
      "0.59816702"
    ],
    [
      "1.365396773",
      "0.477987679"
    ],
    [
      "1.480103453",
      "1.181292553"
    ],
    [
      "1.820062026",
      "1.095103257"
    ],
    [
      "1.170604893",
      "0.422703036"
    ],
    [
      "0.539991476",
      "0.790575577"
    ],
    [
      "1.417612014",
      "1.843867284"
    ],
    [
      "0.120936212",
      "0.664454977"
    ],
    [
      "0.433191801",
      "0.38500393"
    ],
    [
      "0.170606262",
      "0.994046455"
    ],
    [
      "1.560188653",
      "0.533272322"
    ],
    [
      "1.138686289",
      "0.53516618"
    ],
    [
      "1.173620738",
      "1.925363203"
    ],
    [
      "1.082578512",
      "0.165151583"
    ],
    [
      "1.205803754",
      "1.040303401"
    ],
    [
      "0.78373679",
      "1.773685238"
    ],
    [
      "0.880057202",
      "0.704807825"
    ],
    [
      "0.327183593",
      "1.490360689"
    ],
    [
      "0.382111381",
      "1.358982718"
    ],
    [
      "0.553549373",
      "1.431848631"
    ],
    [
      "0.875451835",
      "0.066726438"
    ],
    [
      "1.154289288",
      "0.071768044"
    ],
    [
      "0.717183926",
      "0.537060038"
    ],
    [
      "0.830539167",
      "0.508470787"
    ],
    [
      "1.333478169",
      "0.590450823"
    ],
    [
      "1.867926082",
      "0.635012188"
    ],
    [
      "0.31713914",
      "0.351761747"
    ],
    [
      "1.918205244",
      "1.208352865"
    ],
    [
      "0.588444351",
      "1.718104357"
    ],
    [
      "0.476154269",
      "1.015501866"
    ],
    [
      "1.718771456",
      "0.391885787"
    ],
    [
      "1.768417094",
      "1.325420755"
    ],
    [
      "1.695846424",
      "0.80864544"
    ],
    [
      "0.815829415",
      "1.661119186"
    ],
    [
      "1.478752015",
      "0.449398429"
    ],
    [
      "1.202523497",
      "0.310239891"
    ],
    [
      "0.174333091",
      "0.877200972"
    ],
    [
      "0.621428114",
      "0.874449471"
    ],
    [
      "0.848138598",
      "0.81727097"
    ]
  ],
  "radius": "0.05845245"
}

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?