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 = 288

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 = 288
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[0.0540707539695, 0.0540707539705]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 = 0.054070753

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 = 288 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": [
    [
      "1.012375484",
      "0.054151711"
    ],
    [
      "0.894565146",
      "0.060047413"
    ],
    [
      "1.192676593",
      "0.073901804"
    ],
    [
      "0.785067297",
      "0.078812684"
    ],
    [
      "1.297118727",
      "0.101945101"
    ],
    [
      "1.096111844",
      "0.122582754"
    ],
    [
      "0.608079113",
      "0.139081794"
    ],
    [
      "0.9618124",
      "0.14974439"
    ],
    [
      "0.714096938",
      "0.160407989"
    ],
    [
      "0.854350106",
      "0.161845678"
    ],
    [
      "1.450928732",
      "0.16846803"
    ],
    [
      "0.512378408",
      "0.189440118"
    ],
    [
      "1.238854817",
      "0.193048903"
    ],
    [
      "1.346884978",
      "0.197955028"
    ],
    [
      "1.135077475",
      "0.223460231"
    ],
    [
      "1.542889797",
      "0.225369245"
    ],
    [
      "1.027615181",
      "0.235561519"
    ],
    [
      "0.918561276",
      "0.24886011"
    ],
    [
      "0.797242749",
      "0.253678872"
    ],
    [
      "0.689780455",
      "0.26578016"
    ],
    [
      "0.581736752",
      "0.272427659"
    ],
    [
      "1.422524109",
      "0.275453879"
    ],
    [
      "0.474069267",
      "0.290568727"
    ],
    [
      "0.36617176",
      "0.297829151"
    ],
    [
      "1.306750938",
      "0.298373376"
    ],
    [
      "1.199288644",
      "0.310474664"
    ],
    [
      "1.091826351",
      "0.322575952"
    ],
    [
      "1.576672263",
      "0.32809865"
    ],
    [
      "0.984364057",
      "0.33467724"
    ],
    [
      "0.861453918",
      "0.340693304"
    ],
    [
      "1.683336788",
      "0.345910577"
    ],
    [
      "0.753991625",
      "0.352794592"
    ],
    [
      "0.646529331",
      "0.36489588"
    ],
    [
      "1.478424401",
      "0.37328652"
    ],
    [
      "0.290170697",
      "0.374760447"
    ],
    [
      "0.539067037",
      "0.376997168"
    ],
    [
      "1.370962108",
      "0.385387808"
    ],
    [
      "0.426408226",
      "0.387640921"
    ],
    [
      "1.263499814",
      "0.397489096"
    ],
    [
      "1.15603752",
      "0.409590384"
    ],
    [
      "1.048575227",
      "0.421691672"
    ],
    [
      "0.937122217",
      "0.431954135"
    ],
    [
      "1.761582067",
      "0.438951968"
    ],
    [
      "0.829659924",
      "0.444055423"
    ],
    [
      "1.654006238",
      "0.449998543"
    ],
    [
      "0.72219763",
      "0.456156711"
    ],
    [
      "1.543694117",
      "0.459526859"
    ],
    [
      "0.614735336",
      "0.468257999"
    ],
    [
      "1.435173278",
      "0.47240224"
    ],
    [
      "0.507273043",
      "0.480359287"
    ],
    [
      "0.292094031",
      "0.48288485"
    ],
    [
      "1.327710984",
      "0.484503528"
    ],
    [
      "0.399810749",
      "0.492460575"
    ],
    [
      "1.22024869",
      "0.496604816"
    ],
    [
      "1.112786396",
      "0.508706104"
    ],
    [
      "0.18850593",
      "0.513934663"
    ],
    [
      "1.001333387",
      "0.518968567"
    ],
    [
      "0.893871093",
      "0.531069855"
    ],
    [
      "1.717360767",
      "0.537638656"
    ],
    [
      "1.825501188",
      "0.538123472"
    ],
    [
      "0.7864088",
      "0.543171143"
    ],
    [
      "1.606846741",
      "0.547315384"
    ],
    [
      "0.678946506",
      "0.555272431"
    ],
    [
      "1.499384447",
      "0.559416672"
    ],
    [
      "0.571484212",
      "0.56737372"
    ],
    [
      "1.391922154",
      "0.57151796"
    ],
    [
      "0.464021919",
      "0.579475008"
    ],
    [
      "1.28445986",
      "0.583619248"
    ],
    [
      "0.356559625",
      "0.591576296"
    ],
    [
      "1.176997566",
      "0.595720537"
    ],
    [
      "0.249079628",
      "0.603519331"
    ],
    [
      "1.065544557",
      "0.605982999"
    ],
    [
      "0.13823731",
      "0.613612324"
    ],
    [
      "0.958082263",
      "0.618084287"
    ],
    [
      "0.850619969",
      "0.630185576"
    ],
    [
      "1.671175235",
      "0.635421489"
    ],
    [
      "1.779315656",
      "0.635906305"
    ],
    [
      "0.743157676",
      "0.642286864"
    ],
    [
      "1.563595617",
      "0.646431105"
    ],
    [
      "0.635695382",
      "0.654388152"
    ],
    [
      "1.456133323",
      "0.658532393"
    ],
    [
      "1.883949139",
      "0.663226992"
    ],
    [
      "0.528233088",
      "0.66648944"
    ],
    [
      "1.34867103",
      "0.670633681"
    ],
    [
      "0.420770795",
      "0.678590728"
    ],
    [
      "1.241208736",
      "0.682734969"
    ],
    [
      "0.313308501",
      "0.690692016"
    ],
    [
      "1.129755727",
      "0.692997432"
    ],
    [
      "0.205828504",
      "0.702635051"
    ],
    [
      "1.022293433",
      "0.70509872"
    ],
    [
      "0.098300084",
      "0.714133947"
    ],
    [
      "0.914831139",
      "0.717200008"
    ],
    [
      "0.807368846",
      "0.729301296"
    ],
    [
      "1.637149153",
      "0.738070461"
    ],
    [
      "0.699906552",
      "0.741402584"
    ],
    [
      "1.785274764",
      "0.7438835"
    ],
    [
      "1.520344493",
      "0.745546825"
    ],
    [
      "0.592444258",
      "0.753503872"
    ],
    [
      "1.412882199",
      "0.757648113"
    ],
    [
      "0.484981964",
      "0.76560516"
    ],
    [
      "1.916610601",
      "0.766318285"
    ],
    [
      "1.305419906",
      "0.769749401"
    ],
    [
      "0.377519671",
      "0.777706448"
    ],
    [
      "1.193966896",
      "0.780011864"
    ],
    [
      "0.269765341",
      "0.789937013"
    ],
    [
      "1.086504603",
      "0.792113152"
    ],
    [
      "0.16202263",
      "0.801506842"
    ],
    [
      "0.979042309",
      "0.80421444"
    ],
    [
      "0.871580015",
      "0.816315728"
    ],
    [
      "1.708124052",
      "0.819661818"
    ],
    [
      "0.764117722",
      "0.828417016"
    ],
    [
      "1.584555663",
      "0.832561257"
    ],
    [
      "1.834006384",
      "0.840422689"
    ],
    [
      "0.656655428",
      "0.840518304"
    ],
    [
      "1.477093369",
      "0.844662545"
    ],
    [
      "0.065906482",
      "0.852075667"
    ],
    [
      "0.549193134",
      "0.852619592"
    ],
    [
      "1.369631075",
      "0.856763833"
    ],
    [
      "0.44173084",
      "0.864720881"
    ],
    [
      "1.258178066",
      "0.867026296"
    ],
    [
      "1.937292186",
      "0.872463741"
    ],
    [
      "0.334268547",
      "0.876822169"
    ],
    [
      "1.150715772",
      "0.879127584"
    ],
    [
      "1.043253479",
      "0.891228872"
    ],
    [
      "0.935791185",
      "0.90333016"
    ],
    [
      "0.158407919",
      "0.909587921"
    ],
    [
      "0.828328891",
      "0.915431448"
    ],
    [
      "1.756855672",
      "0.916201006"
    ],
    [
      "1.648766833",
      "0.919575689"
    ],
    [
      "0.720866598",
      "0.927532737"
    ],
    [
      "1.541304539",
      "0.931676977"
    ],
    [
      "0.613404304",
      "0.939634025"
    ],
    [
      "1.433842245",
      "0.943778265"
    ],
    [
      "1.860141473",
      "0.948242058"
    ],
    [
      "0.50594201",
      "0.951735313"
    ],
    [
      "0.257471333",
      "0.952958715"
    ],
    [
      "1.322389236",
      "0.954040728"
    ],
    [
      "0.05485302",
      "0.961923038"
    ],
    [
      "0.398479717",
      "0.963836601"
    ],
    [
      "1.214926942",
      "0.966142016"
    ],
    [
      "1.107464648",
      "0.978243305"
    ],
    [
      "1.000002355",
      "0.990344593"
    ],
    [
      "0.892540061",
      "1.002445881"
    ],
    [
      "1.945822324",
      "1.014222189"
    ],
    [
      "0.785077767",
      "1.014547169"
    ],
    [
      "0.148049194",
      "1.017232162"
    ],
    [
      "1.605515709",
      "1.01869141"
    ],
    [
      "1.739288247",
      "1.022906073"
    ],
    [
      "0.677615474",
      "1.026648457"
    ],
    [
      "1.498053415",
      "1.030792698"
    ],
    [
      "0.57015318",
      "1.038749745"
    ],
    [
      "1.386600406",
      "1.041055161"
    ],
    [
      "0.462690886",
      "1.050851033"
    ],
    [
      "1.279138112",
      "1.053156449"
    ],
    [
      "1.842574048",
      "1.054947125"
    ],
    [
      "0.247112608",
      "1.060602956"
    ],
    [
      "0.355228593",
      "1.062952321"
    ],
    [
      "1.171675818",
      "1.065257737"
    ],
    [
      "0.057108715",
      "1.075750664"
    ],
    [
      "1.064213524",
      "1.077359025"
    ],
    [
      "0.956751231",
      "1.089460313"
    ],
    [
      "0.849288937",
      "1.101561601"
    ],
    [
      "1.669726878",
      "1.105705842"
    ],
    [
      "0.741826643",
      "1.113662889"
    ],
    [
      "1.562264585",
      "1.11780713"
    ],
    [
      "1.938018224",
      "1.122081735"
    ],
    [
      "0.63436435",
      "1.125764177"
    ],
    [
      "1.450811575",
      "1.128069593"
    ],
    [
      "0.16915273",
      "1.135548558"
    ],
    [
      "0.526902056",
      "1.137865465"
    ],
    [
      "1.343349282",
      "1.140170881"
    ],
    [
      "0.419439762",
      "1.149966753"
    ],
    [
      "1.235886988",
      "1.152272169"
    ],
    [
      "0.29913599",
      "1.155408828"
    ],
    [
      "1.837912003",
      "1.162988094"
    ],
    [
      "1.128424694",
      "1.164373457"
    ],
    [
      "1.020962401",
      "1.176474745"
    ],
    [
      "0.071916282",
      "1.182873592"
    ],
    [
      "0.913500107",
      "1.188576033"
    ],
    [
      "1.733938048",
      "1.192720274"
    ],
    [
      "0.806037813",
      "1.200677321"
    ],
    [
      "1.626475754",
      "1.204821562"
    ],
    [
      "0.698575519",
      "1.212778609"
    ],
    [
      "1.515022745",
      "1.215084025"
    ],
    [
      "0.591113226",
      "1.224879898"
    ],
    [
      "1.407560451",
      "1.227185313"
    ],
    [
      "0.483650932",
      "1.236981186"
    ],
    [
      "1.915385217",
      "1.238436665"
    ],
    [
      "1.300098158",
      "1.239286601"
    ],
    [
      "0.161519188",
      "1.243420309"
    ],
    [
      "0.376188638",
      "1.249082474"
    ],
    [
      "1.192635864",
      "1.251387889"
    ],
    [
      "0.268514374",
      "1.259124316"
    ],
    [
      "1.08517357",
      "1.263489177"
    ],
    [
      "1.811411262",
      "1.268168845"
    ],
    [
      "0.977711277",
      "1.275590466"
    ],
    [
      "0.870248983",
      "1.287691754"
    ],
    [
      "1.690686924",
      "1.291835994"
    ],
    [
      "0.762786689",
      "1.299793042"
    ],
    [
      "1.579233915",
      "1.302098457"
    ],
    [
      "0.655324396",
      "1.31189433"
    ],
    [
      "1.471771621",
      "1.314199745"
    ],
    [
      "0.547862102",
      "1.323995618"
    ],
    [
      "1.364309327",
      "1.326301034"
    ],
    [
      "0.440399808",
      "1.336096906"
    ],
    [
      "1.256847034",
      "1.338402322"
    ],
    [
      "0.118268064",
      "1.342536029"
    ],
    [
      "0.332937514",
      "1.348198194"
    ],
    [
      "1.14938474",
      "1.35050361"
    ],
    [
      "1.87707276",
      "1.354213434"
    ],
    [
      "0.22526325",
      "1.358240036"
    ],
    [
      "1.041922446",
      "1.362604898"
    ],
    [
      "1.768160138",
      "1.367284565"
    ],
    [
      "0.934460153",
      "1.374706186"
    ],
    [
      "0.826997859",
      "1.386807474"
    ],
    [
      "1.643445085",
      "1.38911289"
    ],
    [
      "0.719535565",
      "1.398908762"
    ],
    [
      "1.535982791",
      "1.401214178"
    ],
    [
      "0.612073272",
      "1.41101005"
    ],
    [
      "1.428520497",
      "1.413315466"
    ],
    [
      "0.504610978",
      "1.423111338"
    ],
    [
      "1.321058203",
      "1.425416754"
    ],
    [
      "0.396208796",
      "1.435903904"
    ],
    [
      "1.21359591",
      "1.437518042"
    ],
    [
      "0.287796873",
      "1.446467763"
    ],
    [
      "1.106133616",
      "1.44961933"
    ],
    [
      "0.169663494",
      "1.452794509"
    ],
    [
      "1.828018117",
      "1.457349032"
    ],
    [
      "0.998671322",
      "1.461720618"
    ],
    [
      "1.720170878",
      "1.465321409"
    ],
    [
      "0.891209029",
      "1.473821906"
    ],
    [
      "0.783746735",
      "1.485923194"
    ],
    [
      "1.615071764",
      "1.493559743"
    ],
    [
      "0.676284441",
      "1.498024482"
    ],
    [
      "1.492731667",
      "1.500329898"
    ],
    [
      "0.568822148",
      "1.51012577"
    ],
    [
      "1.385269373",
      "1.512431186"
    ],
    [
      "0.461359854",
      "1.522227059"
    ],
    [
      "1.27780708",
      "1.524532474"
    ],
    [
      "1.170344786",
      "1.536633762"
    ],
    [
      "0.338392926",
      "1.542042996"
    ],
    [
      "0.22784085",
      "1.54494764"
    ],
    [
      "1.062882492",
      "1.54873505"
    ],
    [
      "0.955420198",
      "1.560836338"
    ],
    [
      "1.757223215",
      "1.566917226"
    ],
    [
      "0.847957905",
      "1.572937627"
    ],
    [
      "0.740495611",
      "1.585038915"
    ],
    [
      "1.557441487",
      "1.586974142"
    ],
    [
      "0.633033317",
      "1.597140203"
    ],
    [
      "1.449480543",
      "1.599445618"
    ],
    [
      "0.525100078",
      "1.609589476"
    ],
    [
      "1.342018249",
      "1.611546906"
    ],
    [
      "1.66134775",
      "1.616942029"
    ],
    [
      "0.413941952",
      "1.619418253"
    ],
    [
      "1.234555956",
      "1.623648195"
    ],
    [
      "1.127093662",
      "1.635749483"
    ],
    [
      "0.309158501",
      "1.646158"
    ],
    [
      "1.019631368",
      "1.647850771"
    ],
    [
      "0.912169075",
      "1.659952059"
    ],
    [
      "0.804706781",
      "1.672053347"
    ],
    [
      "0.697244487",
      "1.684154635"
    ],
    [
      "1.514190363",
      "1.686089862"
    ],
    [
      "0.589782193",
      "1.696255923"
    ],
    [
      "1.406229419",
      "1.698561339"
    ],
    [
      "1.298816586",
      "1.71109406"
    ],
    [
      "1.618096626",
      "1.716057749"
    ],
    [
      "1.191304832",
      "1.722763915"
    ],
    [
      "0.393038221",
      "1.725520184"
    ],
    [
      "0.979101932",
      "1.748110187"
    ],
    [
      "1.087175362",
      "1.751946774"
    ],
    [
      "0.49765812",
      "1.752892844"
    ],
    [
      "0.871304785",
      "1.760075461"
    ],
    [
      "0.763842492",
      "1.772176749"
    ],
    [
      "0.656380198",
      "1.784278037"
    ],
    [
      "1.513789693",
      "1.794230628"
    ],
    [
      "1.406369807",
      "1.806702756"
    ],
    [
      "1.254765167",
      "1.810327443"
    ],
    [
      "0.563098208",
      "1.838986867"
    ],
    [
      "1.151514086",
      "1.842480202"
    ],
    [
      "0.93563268",
      "1.847130437"
    ],
    [
      "1.04370611",
      "1.850967024"
    ],
    [
      "0.786859681",
      "1.877840341"
    ],
    [
      "1.33241047",
      "1.885598903"
    ],
    [
      "0.679397387",
      "1.889941629"
    ],
    [
      "1.229159388",
      "1.917751662"
    ],
    [
      "0.876807789",
      "1.937873029"
    ],
    [
      "1.104959901",
      "1.940088058"
    ],
    [
      "0.987244568",
      "1.943283316"
    ]
  ],
  "radius": "0.054070753"
}
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": 288
}

起步布局答案

{
  "centers": [
    [
      "1.012375484",
      "0.054151711"
    ],
    [
      "0.894565146",
      "0.060047413"
    ],
    [
      "1.192676593",
      "0.073901804"
    ],
    [
      "0.785067297",
      "0.078812684"
    ],
    [
      "1.297118727",
      "0.101945101"
    ],
    [
      "1.096111844",
      "0.122582754"
    ],
    [
      "0.608079113",
      "0.139081794"
    ],
    [
      "0.9618124",
      "0.14974439"
    ],
    [
      "0.714096938",
      "0.160407989"
    ],
    [
      "0.854350106",
      "0.161845678"
    ],
    [
      "1.450928732",
      "0.16846803"
    ],
    [
      "0.512378408",
      "0.189440118"
    ],
    [
      "1.238854817",
      "0.193048903"
    ],
    [
      "1.346884978",
      "0.197955028"
    ],
    [
      "1.135077475",
      "0.223460231"
    ],
    [
      "1.542889797",
      "0.225369245"
    ],
    [
      "1.027615181",
      "0.235561519"
    ],
    [
      "0.918561276",
      "0.24886011"
    ],
    [
      "0.797242749",
      "0.253678872"
    ],
    [
      "0.689780455",
      "0.26578016"
    ],
    [
      "0.581736752",
      "0.272427659"
    ],
    [
      "1.422524109",
      "0.275453879"
    ],
    [
      "0.474069267",
      "0.290568727"
    ],
    [
      "0.36617176",
      "0.297829151"
    ],
    [
      "1.306750938",
      "0.298373376"
    ],
    [
      "1.199288644",
      "0.310474664"
    ],
    [
      "1.091826351",
      "0.322575952"
    ],
    [
      "1.576672263",
      "0.32809865"
    ],
    [
      "0.984364057",
      "0.33467724"
    ],
    [
      "0.861453918",
      "0.340693304"
    ],
    [
      "1.683336788",
      "0.345910577"
    ],
    [
      "0.753991625",
      "0.352794592"
    ],
    [
      "0.646529331",
      "0.36489588"
    ],
    [
      "1.478424401",
      "0.37328652"
    ],
    [
      "0.290170697",
      "0.374760447"
    ],
    [
      "0.539067037",
      "0.376997168"
    ],
    [
      "1.370962108",
      "0.385387808"
    ],
    [
      "0.426408226",
      "0.387640921"
    ],
    [
      "1.263499814",
      "0.397489096"
    ],
    [
      "1.15603752",
      "0.409590384"
    ],
    [
      "1.048575227",
      "0.421691672"
    ],
    [
      "0.937122217",
      "0.431954135"
    ],
    [
      "1.761582067",
      "0.438951968"
    ],
    [
      "0.829659924",
      "0.444055423"
    ],
    [
      "1.654006238",
      "0.449998543"
    ],
    [
      "0.72219763",
      "0.456156711"
    ],
    [
      "1.543694117",
      "0.459526859"
    ],
    [
      "0.614735336",
      "0.468257999"
    ],
    [
      "1.435173278",
      "0.47240224"
    ],
    [
      "0.507273043",
      "0.480359287"
    ],
    [
      "0.292094031",
      "0.48288485"
    ],
    [
      "1.327710984",
      "0.484503528"
    ],
    [
      "0.399810749",
      "0.492460575"
    ],
    [
      "1.22024869",
      "0.496604816"
    ],
    [
      "1.112786396",
      "0.508706104"
    ],
    [
      "0.18850593",
      "0.513934663"
    ],
    [
      "1.001333387",
      "0.518968567"
    ],
    [
      "0.893871093",
      "0.531069855"
    ],
    [
      "1.717360767",
      "0.537638656"
    ],
    [
      "1.825501188",
      "0.538123472"
    ],
    [
      "0.7864088",
      "0.543171143"
    ],
    [
      "1.606846741",
      "0.547315384"
    ],
    [
      "0.678946506",
      "0.555272431"
    ],
    [
      "1.499384447",
      "0.559416672"
    ],
    [
      "0.571484212",
      "0.56737372"
    ],
    [
      "1.391922154",
      "0.57151796"
    ],
    [
      "0.464021919",
      "0.579475008"
    ],
    [
      "1.28445986",
      "0.583619248"
    ],
    [
      "0.356559625",
      "0.591576296"
    ],
    [
      "1.176997566",
      "0.595720537"
    ],
    [
      "0.249079628",
      "0.603519331"
    ],
    [
      "1.065544557",
      "0.605982999"
    ],
    [
      "0.13823731",
      "0.613612324"
    ],
    [
      "0.958082263",
      "0.618084287"
    ],
    [
      "0.850619969",
      "0.630185576"
    ],
    [
      "1.671175235",
      "0.635421489"
    ],
    [
      "1.779315656",
      "0.635906305"
    ],
    [
      "0.743157676",
      "0.642286864"
    ],
    [
      "1.563595617",
      "0.646431105"
    ],
    [
      "0.635695382",
      "0.654388152"
    ],
    [
      "1.456133323",
      "0.658532393"
    ],
    [
      "1.883949139",
      "0.663226992"
    ],
    [
      "0.528233088",
      "0.66648944"
    ],
    [
      "1.34867103",
      "0.670633681"
    ],
    [
      "0.420770795",
      "0.678590728"
    ],
    [
      "1.241208736",
      "0.682734969"
    ],
    [
      "0.313308501",
      "0.690692016"
    ],
    [
      "1.129755727",
      "0.692997432"
    ],
    [
      "0.205828504",
      "0.702635051"
    ],
    [
      "1.022293433",
      "0.70509872"
    ],
    [
      "0.098300084",
      "0.714133947"
    ],
    [
      "0.914831139",
      "0.717200008"
    ],
    [
      "0.807368846",
      "0.729301296"
    ],
    [
      "1.637149153",
      "0.738070461"
    ],
    [
      "0.699906552",
      "0.741402584"
    ],
    [
      "1.785274764",
      "0.7438835"
    ],
    [
      "1.520344493",
      "0.745546825"
    ],
    [
      "0.592444258",
      "0.753503872"
    ],
    [
      "1.412882199",
      "0.757648113"
    ],
    [
      "0.484981964",
      "0.76560516"
    ],
    [
      "1.916610601",
      "0.766318285"
    ],
    [
      "1.305419906",
      "0.769749401"
    ],
    [
      "0.377519671",
      "0.777706448"
    ],
    [
      "1.193966896",
      "0.780011864"
    ],
    [
      "0.269765341",
      "0.789937013"
    ],
    [
      "1.086504603",
      "0.792113152"
    ],
    [
      "0.16202263",
      "0.801506842"
    ],
    [
      "0.979042309",
      "0.80421444"
    ],
    [
      "0.871580015",
      "0.816315728"
    ],
    [
      "1.708124052",
      "0.819661818"
    ],
    [
      "0.764117722",
      "0.828417016"
    ],
    [
      "1.584555663",
      "0.832561257"
    ],
    [
      "1.834006384",
      "0.840422689"
    ],
    [
      "0.656655428",
      "0.840518304"
    ],
    [
      "1.477093369",
      "0.844662545"
    ],
    [
      "0.065906482",
      "0.852075667"
    ],
    [
      "0.549193134",
      "0.852619592"
    ],
    [
      "1.369631075",
      "0.856763833"
    ],
    [
      "0.44173084",
      "0.864720881"
    ],
    [
      "1.258178066",
      "0.867026296"
    ],
    [
      "1.937292186",
      "0.872463741"
    ],
    [
      "0.334268547",
      "0.876822169"
    ],
    [
      "1.150715772",
      "0.879127584"
    ],
    [
      "1.043253479",
      "0.891228872"
    ],
    [
      "0.935791185",
      "0.90333016"
    ],
    [
      "0.158407919",
      "0.909587921"
    ],
    [
      "0.828328891",
      "0.915431448"
    ],
    [
      "1.756855672",
      "0.916201006"
    ],
    [
      "1.648766833",
      "0.919575689"
    ],
    [
      "0.720866598",
      "0.927532737"
    ],
    [
      "1.541304539",
      "0.931676977"
    ],
    [
      "0.613404304",
      "0.939634025"
    ],
    [
      "1.433842245",
      "0.943778265"
    ],
    [
      "1.860141473",
      "0.948242058"
    ],
    [
      "0.50594201",
      "0.951735313"
    ],
    [
      "0.257471333",
      "0.952958715"
    ],
    [
      "1.322389236",
      "0.954040728"
    ],
    [
      "0.05485302",
      "0.961923038"
    ],
    [
      "0.398479717",
      "0.963836601"
    ],
    [
      "1.214926942",
      "0.966142016"
    ],
    [
      "1.107464648",
      "0.978243305"
    ],
    [
      "1.000002355",
      "0.990344593"
    ],
    [
      "0.892540061",
      "1.002445881"
    ],
    [
      "1.945822324",
      "1.014222189"
    ],
    [
      "0.785077767",
      "1.014547169"
    ],
    [
      "0.148049194",
      "1.017232162"
    ],
    [
      "1.605515709",
      "1.01869141"
    ],
    [
      "1.739288247",
      "1.022906073"
    ],
    [
      "0.677615474",
      "1.026648457"
    ],
    [
      "1.498053415",
      "1.030792698"
    ],
    [
      "0.57015318",
      "1.038749745"
    ],
    [
      "1.386600406",
      "1.041055161"
    ],
    [
      "0.462690886",
      "1.050851033"
    ],
    [
      "1.279138112",
      "1.053156449"
    ],
    [
      "1.842574048",
      "1.054947125"
    ],
    [
      "0.247112608",
      "1.060602956"
    ],
    [
      "0.355228593",
      "1.062952321"
    ],
    [
      "1.171675818",
      "1.065257737"
    ],
    [
      "0.057108715",
      "1.075750664"
    ],
    [
      "1.064213524",
      "1.077359025"
    ],
    [
      "0.956751231",
      "1.089460313"
    ],
    [
      "0.849288937",
      "1.101561601"
    ],
    [
      "1.669726878",
      "1.105705842"
    ],
    [
      "0.741826643",
      "1.113662889"
    ],
    [
      "1.562264585",
      "1.11780713"
    ],
    [
      "1.938018224",
      "1.122081735"
    ],
    [
      "0.63436435",
      "1.125764177"
    ],
    [
      "1.450811575",
      "1.128069593"
    ],
    [
      "0.16915273",
      "1.135548558"
    ],
    [
      "0.526902056",
      "1.137865465"
    ],
    [
      "1.343349282",
      "1.140170881"
    ],
    [
      "0.419439762",
      "1.149966753"
    ],
    [
      "1.235886988",
      "1.152272169"
    ],
    [
      "0.29913599",
      "1.155408828"
    ],
    [
      "1.837912003",
      "1.162988094"
    ],
    [
      "1.128424694",
      "1.164373457"
    ],
    [
      "1.020962401",
      "1.176474745"
    ],
    [
      "0.071916282",
      "1.182873592"
    ],
    [
      "0.913500107",
      "1.188576033"
    ],
    [
      "1.733938048",
      "1.192720274"
    ],
    [
      "0.806037813",
      "1.200677321"
    ],
    [
      "1.626475754",
      "1.204821562"
    ],
    [
      "0.698575519",
      "1.212778609"
    ],
    [
      "1.515022745",
      "1.215084025"
    ],
    [
      "0.591113226",
      "1.224879898"
    ],
    [
      "1.407560451",
      "1.227185313"
    ],
    [
      "0.483650932",
      "1.236981186"
    ],
    [
      "1.915385217",
      "1.238436665"
    ],
    [
      "1.300098158",
      "1.239286601"
    ],
    [
      "0.161519188",
      "1.243420309"
    ],
    [
      "0.376188638",
      "1.249082474"
    ],
    [
      "1.192635864",
      "1.251387889"
    ],
    [
      "0.268514374",
      "1.259124316"
    ],
    [
      "1.08517357",
      "1.263489177"
    ],
    [
      "1.811411262",
      "1.268168845"
    ],
    [
      "0.977711277",
      "1.275590466"
    ],
    [
      "0.870248983",
      "1.287691754"
    ],
    [
      "1.690686924",
      "1.291835994"
    ],
    [
      "0.762786689",
      "1.299793042"
    ],
    [
      "1.579233915",
      "1.302098457"
    ],
    [
      "0.655324396",
      "1.31189433"
    ],
    [
      "1.471771621",
      "1.314199745"
    ],
    [
      "0.547862102",
      "1.323995618"
    ],
    [
      "1.364309327",
      "1.326301034"
    ],
    [
      "0.440399808",
      "1.336096906"
    ],
    [
      "1.256847034",
      "1.338402322"
    ],
    [
      "0.118268064",
      "1.342536029"
    ],
    [
      "0.332937514",
      "1.348198194"
    ],
    [
      "1.14938474",
      "1.35050361"
    ],
    [
      "1.87707276",
      "1.354213434"
    ],
    [
      "0.22526325",
      "1.358240036"
    ],
    [
      "1.041922446",
      "1.362604898"
    ],
    [
      "1.768160138",
      "1.367284565"
    ],
    [
      "0.934460153",
      "1.374706186"
    ],
    [
      "0.826997859",
      "1.386807474"
    ],
    [
      "1.643445085",
      "1.38911289"
    ],
    [
      "0.719535565",
      "1.398908762"
    ],
    [
      "1.535982791",
      "1.401214178"
    ],
    [
      "0.612073272",
      "1.41101005"
    ],
    [
      "1.428520497",
      "1.413315466"
    ],
    [
      "0.504610978",
      "1.423111338"
    ],
    [
      "1.321058203",
      "1.425416754"
    ],
    [
      "0.396208796",
      "1.435903904"
    ],
    [
      "1.21359591",
      "1.437518042"
    ],
    [
      "0.287796873",
      "1.446467763"
    ],
    [
      "1.106133616",
      "1.44961933"
    ],
    [
      "0.169663494",
      "1.452794509"
    ],
    [
      "1.828018117",
      "1.457349032"
    ],
    [
      "0.998671322",
      "1.461720618"
    ],
    [
      "1.720170878",
      "1.465321409"
    ],
    [
      "0.891209029",
      "1.473821906"
    ],
    [
      "0.783746735",
      "1.485923194"
    ],
    [
      "1.615071764",
      "1.493559743"
    ],
    [
      "0.676284441",
      "1.498024482"
    ],
    [
      "1.492731667",
      "1.500329898"
    ],
    [
      "0.568822148",
      "1.51012577"
    ],
    [
      "1.385269373",
      "1.512431186"
    ],
    [
      "0.461359854",
      "1.522227059"
    ],
    [
      "1.27780708",
      "1.524532474"
    ],
    [
      "1.170344786",
      "1.536633762"
    ],
    [
      "0.338392926",
      "1.542042996"
    ],
    [
      "0.22784085",
      "1.54494764"
    ],
    [
      "1.062882492",
      "1.54873505"
    ],
    [
      "0.955420198",
      "1.560836338"
    ],
    [
      "1.757223215",
      "1.566917226"
    ],
    [
      "0.847957905",
      "1.572937627"
    ],
    [
      "0.740495611",
      "1.585038915"
    ],
    [
      "1.557441487",
      "1.586974142"
    ],
    [
      "0.633033317",
      "1.597140203"
    ],
    [
      "1.449480543",
      "1.599445618"
    ],
    [
      "0.525100078",
      "1.609589476"
    ],
    [
      "1.342018249",
      "1.611546906"
    ],
    [
      "1.66134775",
      "1.616942029"
    ],
    [
      "0.413941952",
      "1.619418253"
    ],
    [
      "1.234555956",
      "1.623648195"
    ],
    [
      "1.127093662",
      "1.635749483"
    ],
    [
      "0.309158501",
      "1.646158"
    ],
    [
      "1.019631368",
      "1.647850771"
    ],
    [
      "0.912169075",
      "1.659952059"
    ],
    [
      "0.804706781",
      "1.672053347"
    ],
    [
      "0.697244487",
      "1.684154635"
    ],
    [
      "1.514190363",
      "1.686089862"
    ],
    [
      "0.589782193",
      "1.696255923"
    ],
    [
      "1.406229419",
      "1.698561339"
    ],
    [
      "1.298816586",
      "1.71109406"
    ],
    [
      "1.618096626",
      "1.716057749"
    ],
    [
      "1.191304832",
      "1.722763915"
    ],
    [
      "0.393038221",
      "1.725520184"
    ],
    [
      "0.979101932",
      "1.748110187"
    ],
    [
      "1.087175362",
      "1.751946774"
    ],
    [
      "0.49765812",
      "1.752892844"
    ],
    [
      "0.871304785",
      "1.760075461"
    ],
    [
      "0.763842492",
      "1.772176749"
    ],
    [
      "0.656380198",
      "1.784278037"
    ],
    [
      "1.513789693",
      "1.794230628"
    ],
    [
      "1.406369807",
      "1.806702756"
    ],
    [
      "1.254765167",
      "1.810327443"
    ],
    [
      "0.563098208",
      "1.838986867"
    ],
    [
      "1.151514086",
      "1.842480202"
    ],
    [
      "0.93563268",
      "1.847130437"
    ],
    [
      "1.04370611",
      "1.850967024"
    ],
    [
      "0.786859681",
      "1.877840341"
    ],
    [
      "1.33241047",
      "1.885598903"
    ],
    [
      "0.679397387",
      "1.889941629"
    ],
    [
      "1.229159388",
      "1.917751662"
    ],
    [
      "0.876807789",
      "1.937873029"
    ],
    [
      "1.104959901",
      "1.940088058"
    ],
    [
      "0.987244568",
      "1.943283316"
    ]
  ],
  "radius": "0.054070753"
}

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?