P01 · 装箱与覆盖 · 经典问题 · 难

单位正方形内的等圆装箱 · n = 212

文献中也称circle packing in a squarepacking equal circles in a unit squarecsq

在边长 1 的正方形内放置 n 个半径相同、互不重叠的圆,使共同半径尽可能大。

子题n = 212
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[0.0357866596605, 0.0357866596615]见来源署名packomania.com ↗
本站纪录暂无选手纪录——

严格定义

  • 容器单位正方形:左下角是原点 (0, 0),右上角是 (1, 1)
  • 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
放大来摆,然后提交 ↗

当前展示:起步布局

1y0
0x1
已验证构造r = 0.035786659

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 = 1–30 已证明最优,适合观察经典接触结构;n = 31–300 接入 Packomania 的公开前沿,除 n = 36 外最优性仍未知。大规模部分集中成一张表,供算法批量挑战。

查看来源
单位正方形内的等圆装箱 n = 212 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

容器是边长 1 的正方形,左下角是原点 (0, 0),右上角是 (1, 1)。坐标和长度用同一个单位,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 "0.25"。

起步布局答案

{
  "centers": [
    [
      "0.03578666",
      "0.03578666"
    ],
    [
      "0.159199641",
      "0.03578666"
    ],
    [
      "0.2823859",
      "0.03578666"
    ],
    [
      "0.406354525",
      "0.03578666"
    ],
    [
      "0.530323151",
      "0.03578666"
    ],
    [
      "0.654291777",
      "0.03578666"
    ],
    [
      "0.778260402",
      "0.03578666"
    ],
    [
      "0.902229028",
      "0.03578666"
    ],
    [
      "0.344370213",
      "0.071573319"
    ],
    [
      "0.468338838",
      "0.071573319"
    ],
    [
      "0.592307464",
      "0.071573319"
    ],
    [
      "0.716276089",
      "0.071573319"
    ],
    [
      "0.840244715",
      "0.071573319"
    ],
    [
      "0.96421334",
      "0.071573319"
    ],
    [
      "0.09749315",
      "0.072050265"
    ],
    [
      "0.22079277",
      "0.072242474"
    ],
    [
      "0.406354525",
      "0.107359979"
    ],
    [
      "0.530323151",
      "0.107359979"
    ],
    [
      "0.654291777",
      "0.107359979"
    ],
    [
      "0.778260402",
      "0.107359979"
    ],
    [
      "0.902229028",
      "0.107359979"
    ],
    [
      "0.282777083",
      "0.108029134"
    ],
    [
      "0.03578666",
      "0.10831387"
    ],
    [
      "0.15908628",
      "0.10850608"
    ],
    [
      "0.468338838",
      "0.143146639"
    ],
    [
      "0.592307464",
      "0.143146639"
    ],
    [
      "0.716276089",
      "0.143146639"
    ],
    [
      "0.840244715",
      "0.143146639"
    ],
    [
      "0.96421334",
      "0.143146639"
    ],
    [
      "0.344761396",
      "0.143815794"
    ],
    [
      "0.221070593",
      "0.144292739"
    ],
    [
      "0.097379789",
      "0.144769685"
    ],
    [
      "0.530323151",
      "0.178933298"
    ],
    [
      "0.654291777",
      "0.178933298"
    ],
    [
      "0.778260402",
      "0.178933298"
    ],
    [
      "0.902229028",
      "0.178933298"
    ],
    [
      "0.406745709",
      "0.179602453"
    ],
    [
      "0.283054905",
      "0.180079399"
    ],
    [
      "0.159364102",
      "0.180556345"
    ],
    [
      "0.03578666",
      "0.1812255"
    ],
    [
      "0.592307464",
      "0.214719958"
    ],
    [
      "0.716276089",
      "0.214719958"
    ],
    [
      "0.840244715",
      "0.214719958"
    ],
    [
      "0.96421334",
      "0.214719958"
    ],
    [
      "0.468730021",
      "0.215389113"
    ],
    [
      "0.345039218",
      "0.215866059"
    ],
    [
      "0.221348415",
      "0.216343004"
    ],
    [
      "0.097770972",
      "0.217012159"
    ],
    [
      "0.654291777",
      "0.250506618"
    ],
    [
      "0.778260402",
      "0.250506618"
    ],
    [
      "0.902229028",
      "0.250506618"
    ],
    [
      "0.530714334",
      "0.251175773"
    ],
    [
      "0.407023531",
      "0.251652718"
    ],
    [
      "0.283332728",
      "0.252129664"
    ],
    [
      "0.03578666",
      "0.252798819"
    ],
    [
      "0.159755285",
      "0.252798819"
    ],
    [
      "0.716276089",
      "0.286293277"
    ],
    [
      "0.840244715",
      "0.286293277"
    ],
    [
      "0.96421334",
      "0.286293277"
    ],
    [
      "0.592698647",
      "0.286962432"
    ],
    [
      "0.469007844",
      "0.287439378"
    ],
    [
      "0.34531704",
      "0.287916324"
    ],
    [
      "0.097770972",
      "0.288585479"
    ],
    [
      "0.221739598",
      "0.288585479"
    ],
    [
      "0.778260402",
      "0.322079937"
    ],
    [
      "0.902229028",
      "0.322079937"
    ],
    [
      "0.65468296",
      "0.322749092"
    ],
    [
      "0.530992156",
      "0.323226038"
    ],
    [
      "0.407301353",
      "0.323702983"
    ],
    [
      "0.03578666",
      "0.324372138"
    ],
    [
      "0.159755285",
      "0.324372138"
    ],
    [
      "0.283723911",
      "0.324372138"
    ],
    [
      "0.840244715",
      "0.357866597"
    ],
    [
      "0.96421334",
      "0.357866597"
    ],
    [
      "0.716667272",
      "0.358535752"
    ],
    [
      "0.592976469",
      "0.359012697"
    ],
    [
      "0.469285666",
      "0.359489643"
    ],
    [
      "0.097770972",
      "0.360158798"
    ],
    [
      "0.221739598",
      "0.360158798"
    ],
    [
      "0.345708223",
      "0.360158798"
    ],
    [
      "0.902229028",
      "0.393653256"
    ],
    [
      "0.778651585",
      "0.394322411"
    ],
    [
      "0.654960782",
      "0.394799357"
    ],
    [
      "0.531269979",
      "0.395276303"
    ],
    [
      "0.03578666",
      "0.395945457"
    ],
    [
      "0.159755285",
      "0.395945457"
    ],
    [
      "0.283723911",
      "0.395945457"
    ],
    [
      "0.407692536",
      "0.395945457"
    ],
    [
      "0.96421334",
      "0.429439916"
    ],
    [
      "0.840635898",
      "0.430109071"
    ],
    [
      "0.716945095",
      "0.430586017"
    ],
    [
      "0.593254291",
      "0.431062962"
    ],
    [
      "0.097770972",
      "0.431732117"
    ],
    [
      "0.221739598",
      "0.431732117"
    ],
    [
      "0.345708223",
      "0.431732117"
    ],
    [
      "0.469676849",
      "0.431732117"
    ],
    [
      "0.902620211",
      "0.465895731"
    ],
    [
      "0.778929407",
      "0.466372676"
    ],
    [
      "0.655238604",
      "0.466849622"
    ],
    [
      "0.03578666",
      "0.467518777"
    ],
    [
      "0.159755285",
      "0.467518777"
    ],
    [
      "0.283723911",
      "0.467518777"
    ],
    [
      "0.407692536",
      "0.467518777"
    ],
    [
      "0.531661162",
      "0.467518777"
    ],
    [
      "0.84091372",
      "0.502159336"
    ],
    [
      "0.96421334",
      "0.502351545"
    ],
    [
      "0.717222917",
      "0.502636282"
    ],
    [
      "0.097770972",
      "0.503305436"
    ],
    [
      "0.221739598",
      "0.503305436"
    ],
    [
      "0.345708223",
      "0.503305436"
    ],
    [
      "0.469676849",
      "0.503305436"
    ],
    [
      "0.593645475",
      "0.503305436"
    ],
    [
      "0.77920723",
      "0.538422941"
    ],
    [
      "0.90250685",
      "0.53861515"
    ],
    [
      "0.03578666",
      "0.539092096"
    ],
    [
      "0.159755285",
      "0.539092096"
    ],
    [
      "0.283723911",
      "0.539092096"
    ],
    [
      "0.407692536",
      "0.539092096"
    ],
    [
      "0.531661162",
      "0.539092096"
    ],
    [
      "0.655629787",
      "0.539092096"
    ],
    [
      "0.097770972",
      "0.574878756"
    ],
    [
      "0.221739598",
      "0.574878756"
    ],
    [
      "0.345708223",
      "0.574878756"
    ],
    [
      "0.469676849",
      "0.574878756"
    ],
    [
      "0.593645475",
      "0.574878756"
    ],
    [
      "0.7176141",
      "0.574878756"
    ],
    [
      "0.840800359",
      "0.574878756"
    ],
    [
      "0.96421334",
      "0.574878756"
    ],
    [
      "0.03578666",
      "0.610665415"
    ],
    [
      "0.159755285",
      "0.610665415"
    ],
    [
      "0.283723911",
      "0.610665415"
    ],
    [
      "0.407692536",
      "0.610665415"
    ],
    [
      "0.531661162",
      "0.610665415"
    ],
    [
      "0.655629787",
      "0.610665415"
    ],
    [
      "0.90250685",
      "0.611142361"
    ],
    [
      "0.77920723",
      "0.61133457"
    ],
    [
      "0.097770972",
      "0.646452075"
    ],
    [
      "0.221739598",
      "0.646452075"
    ],
    [
      "0.345708223",
      "0.646452075"
    ],
    [
      "0.469676849",
      "0.646452075"
    ],
    [
      "0.593645475",
      "0.646452075"
    ],
    [
      "0.717222917",
      "0.64712123"
    ],
    [
      "0.96421334",
      "0.647405966"
    ],
    [
      "0.84091372",
      "0.647598176"
    ],
    [
      "0.03578666",
      "0.682238735"
    ],
    [
      "0.159755285",
      "0.682238735"
    ],
    [
      "0.283723911",
      "0.682238735"
    ],
    [
      "0.407692536",
      "0.682238735"
    ],
    [
      "0.531663228",
      "0.682242313"
    ],
    [
      "0.655238604",
      "0.68290789"
    ],
    [
      "0.778929407",
      "0.683384835"
    ],
    [
      "0.902620211",
      "0.683861781"
    ],
    [
      "0.097770972",
      "0.718025394"
    ],
    [
      "0.221739598",
      "0.718025394"
    ],
    [
      "0.345708223",
      "0.718025394"
    ],
    [
      "0.469676849",
      "0.718025394"
    ],
    [
      "0.593513003",
      "0.719138956"
    ],
    [
      "0.716945095",
      "0.719171495"
    ],
    [
      "0.840635898",
      "0.719648441"
    ],
    [
      "0.96421334",
      "0.720317596"
    ],
    [
      "0.03578666",
      "0.753812054"
    ],
    [
      "0.159755285",
      "0.753812054"
    ],
    [
      "0.283723911",
      "0.753812054"
    ],
    [
      "0.407692536",
      "0.753812054"
    ],
    [
      "0.531272147",
      "0.754477545"
    ],
    [
      "0.655219493",
      "0.755402562"
    ],
    [
      "0.778651585",
      "0.7554351"
    ],
    [
      "0.902229028",
      "0.756104255"
    ],
    [
      "0.097770972",
      "0.789598714"
    ],
    [
      "0.221739598",
      "0.789598714"
    ],
    [
      "0.345708223",
      "0.789598714"
    ],
    [
      "0.469287834",
      "0.790264205"
    ],
    [
      "0.592978637",
      "0.790741151"
    ],
    [
      "0.840244715",
      "0.791890915"
    ],
    [
      "0.96421334",
      "0.791890915"
    ],
    [
      "0.717465252",
      "0.792569622"
    ],
    [
      "0.03578666",
      "0.825385373"
    ],
    [
      "0.159755285",
      "0.825385373"
    ],
    [
      "0.283723911",
      "0.825385373"
    ],
    [
      "0.407303521",
      "0.826050865"
    ],
    [
      "0.530994325",
      "0.82652781"
    ],
    [
      "0.654703181",
      "0.826974019"
    ],
    [
      "0.902229028",
      "0.827677575"
    ],
    [
      "0.779058382",
      "0.829025437"
    ],
    [
      "0.097770972",
      "0.861172033"
    ],
    [
      "0.345319209",
      "0.861837524"
    ],
    [
      "0.96421334",
      "0.863464234"
    ],
    [
      "0.835571055",
      "0.873112969"
    ],
    [
      "0.476396964",
      "0.873639489"
    ],
    [
      "0.699724622",
      "0.882614022"
    ],
    [
      "0.615763849",
      "0.887027898"
    ],
    [
      "0.255801583",
      "0.891287449"
    ],
    [
      "0.184241045",
      "0.892640021"
    ],
    [
      "0.544853422",
      "0.896746508"
    ],
    [
      "0.03578666",
      "0.896958693"
    ],
    [
      "0.407303521",
      "0.897624184"
    ],
    [
      "0.902229028",
      "0.899250894"
    ],
    [
      "0.769175886",
      "0.89991321"
    ],
    [
      "0.31739688",
      "0.9277396"
    ],
    [
      "0.122256732",
      "0.928426681"
    ],
    [
      "0.660785289",
      "0.942667901"
    ],
    [
      "0.449968956",
      "0.955090702"
    ],
    [
      "0.95910096",
      "0.95910096"
    ],
    [
      "0.060272419",
      "0.96421334"
    ],
    [
      "0.184241045",
      "0.96421334"
    ],
    [
      "0.255814364",
      "0.96421334"
    ],
    [
      "0.378979397",
      "0.96421334"
    ],
    [
      "0.520958515",
      "0.96421334"
    ],
    [
      "0.592531835",
      "0.96421334"
    ],
    [
      "0.729038744",
      "0.96421334"
    ],
    [
      "0.800612063",
      "0.96421334"
    ],
    [
      "0.872185383",
      "0.96421334"
    ]
  ],
  "radius": "0.035786659"
}
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": 212
}

起步布局答案

{
  "centers": [
    [
      "0.03578666",
      "0.03578666"
    ],
    [
      "0.159199641",
      "0.03578666"
    ],
    [
      "0.2823859",
      "0.03578666"
    ],
    [
      "0.406354525",
      "0.03578666"
    ],
    [
      "0.530323151",
      "0.03578666"
    ],
    [
      "0.654291777",
      "0.03578666"
    ],
    [
      "0.778260402",
      "0.03578666"
    ],
    [
      "0.902229028",
      "0.03578666"
    ],
    [
      "0.344370213",
      "0.071573319"
    ],
    [
      "0.468338838",
      "0.071573319"
    ],
    [
      "0.592307464",
      "0.071573319"
    ],
    [
      "0.716276089",
      "0.071573319"
    ],
    [
      "0.840244715",
      "0.071573319"
    ],
    [
      "0.96421334",
      "0.071573319"
    ],
    [
      "0.09749315",
      "0.072050265"
    ],
    [
      "0.22079277",
      "0.072242474"
    ],
    [
      "0.406354525",
      "0.107359979"
    ],
    [
      "0.530323151",
      "0.107359979"
    ],
    [
      "0.654291777",
      "0.107359979"
    ],
    [
      "0.778260402",
      "0.107359979"
    ],
    [
      "0.902229028",
      "0.107359979"
    ],
    [
      "0.282777083",
      "0.108029134"
    ],
    [
      "0.03578666",
      "0.10831387"
    ],
    [
      "0.15908628",
      "0.10850608"
    ],
    [
      "0.468338838",
      "0.143146639"
    ],
    [
      "0.592307464",
      "0.143146639"
    ],
    [
      "0.716276089",
      "0.143146639"
    ],
    [
      "0.840244715",
      "0.143146639"
    ],
    [
      "0.96421334",
      "0.143146639"
    ],
    [
      "0.344761396",
      "0.143815794"
    ],
    [
      "0.221070593",
      "0.144292739"
    ],
    [
      "0.097379789",
      "0.144769685"
    ],
    [
      "0.530323151",
      "0.178933298"
    ],
    [
      "0.654291777",
      "0.178933298"
    ],
    [
      "0.778260402",
      "0.178933298"
    ],
    [
      "0.902229028",
      "0.178933298"
    ],
    [
      "0.406745709",
      "0.179602453"
    ],
    [
      "0.283054905",
      "0.180079399"
    ],
    [
      "0.159364102",
      "0.180556345"
    ],
    [
      "0.03578666",
      "0.1812255"
    ],
    [
      "0.592307464",
      "0.214719958"
    ],
    [
      "0.716276089",
      "0.214719958"
    ],
    [
      "0.840244715",
      "0.214719958"
    ],
    [
      "0.96421334",
      "0.214719958"
    ],
    [
      "0.468730021",
      "0.215389113"
    ],
    [
      "0.345039218",
      "0.215866059"
    ],
    [
      "0.221348415",
      "0.216343004"
    ],
    [
      "0.097770972",
      "0.217012159"
    ],
    [
      "0.654291777",
      "0.250506618"
    ],
    [
      "0.778260402",
      "0.250506618"
    ],
    [
      "0.902229028",
      "0.250506618"
    ],
    [
      "0.530714334",
      "0.251175773"
    ],
    [
      "0.407023531",
      "0.251652718"
    ],
    [
      "0.283332728",
      "0.252129664"
    ],
    [
      "0.03578666",
      "0.252798819"
    ],
    [
      "0.159755285",
      "0.252798819"
    ],
    [
      "0.716276089",
      "0.286293277"
    ],
    [
      "0.840244715",
      "0.286293277"
    ],
    [
      "0.96421334",
      "0.286293277"
    ],
    [
      "0.592698647",
      "0.286962432"
    ],
    [
      "0.469007844",
      "0.287439378"
    ],
    [
      "0.34531704",
      "0.287916324"
    ],
    [
      "0.097770972",
      "0.288585479"
    ],
    [
      "0.221739598",
      "0.288585479"
    ],
    [
      "0.778260402",
      "0.322079937"
    ],
    [
      "0.902229028",
      "0.322079937"
    ],
    [
      "0.65468296",
      "0.322749092"
    ],
    [
      "0.530992156",
      "0.323226038"
    ],
    [
      "0.407301353",
      "0.323702983"
    ],
    [
      "0.03578666",
      "0.324372138"
    ],
    [
      "0.159755285",
      "0.324372138"
    ],
    [
      "0.283723911",
      "0.324372138"
    ],
    [
      "0.840244715",
      "0.357866597"
    ],
    [
      "0.96421334",
      "0.357866597"
    ],
    [
      "0.716667272",
      "0.358535752"
    ],
    [
      "0.592976469",
      "0.359012697"
    ],
    [
      "0.469285666",
      "0.359489643"
    ],
    [
      "0.097770972",
      "0.360158798"
    ],
    [
      "0.221739598",
      "0.360158798"
    ],
    [
      "0.345708223",
      "0.360158798"
    ],
    [
      "0.902229028",
      "0.393653256"
    ],
    [
      "0.778651585",
      "0.394322411"
    ],
    [
      "0.654960782",
      "0.394799357"
    ],
    [
      "0.531269979",
      "0.395276303"
    ],
    [
      "0.03578666",
      "0.395945457"
    ],
    [
      "0.159755285",
      "0.395945457"
    ],
    [
      "0.283723911",
      "0.395945457"
    ],
    [
      "0.407692536",
      "0.395945457"
    ],
    [
      "0.96421334",
      "0.429439916"
    ],
    [
      "0.840635898",
      "0.430109071"
    ],
    [
      "0.716945095",
      "0.430586017"
    ],
    [
      "0.593254291",
      "0.431062962"
    ],
    [
      "0.097770972",
      "0.431732117"
    ],
    [
      "0.221739598",
      "0.431732117"
    ],
    [
      "0.345708223",
      "0.431732117"
    ],
    [
      "0.469676849",
      "0.431732117"
    ],
    [
      "0.902620211",
      "0.465895731"
    ],
    [
      "0.778929407",
      "0.466372676"
    ],
    [
      "0.655238604",
      "0.466849622"
    ],
    [
      "0.03578666",
      "0.467518777"
    ],
    [
      "0.159755285",
      "0.467518777"
    ],
    [
      "0.283723911",
      "0.467518777"
    ],
    [
      "0.407692536",
      "0.467518777"
    ],
    [
      "0.531661162",
      "0.467518777"
    ],
    [
      "0.84091372",
      "0.502159336"
    ],
    [
      "0.96421334",
      "0.502351545"
    ],
    [
      "0.717222917",
      "0.502636282"
    ],
    [
      "0.097770972",
      "0.503305436"
    ],
    [
      "0.221739598",
      "0.503305436"
    ],
    [
      "0.345708223",
      "0.503305436"
    ],
    [
      "0.469676849",
      "0.503305436"
    ],
    [
      "0.593645475",
      "0.503305436"
    ],
    [
      "0.77920723",
      "0.538422941"
    ],
    [
      "0.90250685",
      "0.53861515"
    ],
    [
      "0.03578666",
      "0.539092096"
    ],
    [
      "0.159755285",
      "0.539092096"
    ],
    [
      "0.283723911",
      "0.539092096"
    ],
    [
      "0.407692536",
      "0.539092096"
    ],
    [
      "0.531661162",
      "0.539092096"
    ],
    [
      "0.655629787",
      "0.539092096"
    ],
    [
      "0.097770972",
      "0.574878756"
    ],
    [
      "0.221739598",
      "0.574878756"
    ],
    [
      "0.345708223",
      "0.574878756"
    ],
    [
      "0.469676849",
      "0.574878756"
    ],
    [
      "0.593645475",
      "0.574878756"
    ],
    [
      "0.7176141",
      "0.574878756"
    ],
    [
      "0.840800359",
      "0.574878756"
    ],
    [
      "0.96421334",
      "0.574878756"
    ],
    [
      "0.03578666",
      "0.610665415"
    ],
    [
      "0.159755285",
      "0.610665415"
    ],
    [
      "0.283723911",
      "0.610665415"
    ],
    [
      "0.407692536",
      "0.610665415"
    ],
    [
      "0.531661162",
      "0.610665415"
    ],
    [
      "0.655629787",
      "0.610665415"
    ],
    [
      "0.90250685",
      "0.611142361"
    ],
    [
      "0.77920723",
      "0.61133457"
    ],
    [
      "0.097770972",
      "0.646452075"
    ],
    [
      "0.221739598",
      "0.646452075"
    ],
    [
      "0.345708223",
      "0.646452075"
    ],
    [
      "0.469676849",
      "0.646452075"
    ],
    [
      "0.593645475",
      "0.646452075"
    ],
    [
      "0.717222917",
      "0.64712123"
    ],
    [
      "0.96421334",
      "0.647405966"
    ],
    [
      "0.84091372",
      "0.647598176"
    ],
    [
      "0.03578666",
      "0.682238735"
    ],
    [
      "0.159755285",
      "0.682238735"
    ],
    [
      "0.283723911",
      "0.682238735"
    ],
    [
      "0.407692536",
      "0.682238735"
    ],
    [
      "0.531663228",
      "0.682242313"
    ],
    [
      "0.655238604",
      "0.68290789"
    ],
    [
      "0.778929407",
      "0.683384835"
    ],
    [
      "0.902620211",
      "0.683861781"
    ],
    [
      "0.097770972",
      "0.718025394"
    ],
    [
      "0.221739598",
      "0.718025394"
    ],
    [
      "0.345708223",
      "0.718025394"
    ],
    [
      "0.469676849",
      "0.718025394"
    ],
    [
      "0.593513003",
      "0.719138956"
    ],
    [
      "0.716945095",
      "0.719171495"
    ],
    [
      "0.840635898",
      "0.719648441"
    ],
    [
      "0.96421334",
      "0.720317596"
    ],
    [
      "0.03578666",
      "0.753812054"
    ],
    [
      "0.159755285",
      "0.753812054"
    ],
    [
      "0.283723911",
      "0.753812054"
    ],
    [
      "0.407692536",
      "0.753812054"
    ],
    [
      "0.531272147",
      "0.754477545"
    ],
    [
      "0.655219493",
      "0.755402562"
    ],
    [
      "0.778651585",
      "0.7554351"
    ],
    [
      "0.902229028",
      "0.756104255"
    ],
    [
      "0.097770972",
      "0.789598714"
    ],
    [
      "0.221739598",
      "0.789598714"
    ],
    [
      "0.345708223",
      "0.789598714"
    ],
    [
      "0.469287834",
      "0.790264205"
    ],
    [
      "0.592978637",
      "0.790741151"
    ],
    [
      "0.840244715",
      "0.791890915"
    ],
    [
      "0.96421334",
      "0.791890915"
    ],
    [
      "0.717465252",
      "0.792569622"
    ],
    [
      "0.03578666",
      "0.825385373"
    ],
    [
      "0.159755285",
      "0.825385373"
    ],
    [
      "0.283723911",
      "0.825385373"
    ],
    [
      "0.407303521",
      "0.826050865"
    ],
    [
      "0.530994325",
      "0.82652781"
    ],
    [
      "0.654703181",
      "0.826974019"
    ],
    [
      "0.902229028",
      "0.827677575"
    ],
    [
      "0.779058382",
      "0.829025437"
    ],
    [
      "0.097770972",
      "0.861172033"
    ],
    [
      "0.345319209",
      "0.861837524"
    ],
    [
      "0.96421334",
      "0.863464234"
    ],
    [
      "0.835571055",
      "0.873112969"
    ],
    [
      "0.476396964",
      "0.873639489"
    ],
    [
      "0.699724622",
      "0.882614022"
    ],
    [
      "0.615763849",
      "0.887027898"
    ],
    [
      "0.255801583",
      "0.891287449"
    ],
    [
      "0.184241045",
      "0.892640021"
    ],
    [
      "0.544853422",
      "0.896746508"
    ],
    [
      "0.03578666",
      "0.896958693"
    ],
    [
      "0.407303521",
      "0.897624184"
    ],
    [
      "0.902229028",
      "0.899250894"
    ],
    [
      "0.769175886",
      "0.89991321"
    ],
    [
      "0.31739688",
      "0.9277396"
    ],
    [
      "0.122256732",
      "0.928426681"
    ],
    [
      "0.660785289",
      "0.942667901"
    ],
    [
      "0.449968956",
      "0.955090702"
    ],
    [
      "0.95910096",
      "0.95910096"
    ],
    [
      "0.060272419",
      "0.96421334"
    ],
    [
      "0.184241045",
      "0.96421334"
    ],
    [
      "0.255814364",
      "0.96421334"
    ],
    [
      "0.378979397",
      "0.96421334"
    ],
    [
      "0.520958515",
      "0.96421334"
    ],
    [
      "0.592531835",
      "0.96421334"
    ],
    [
      "0.729038744",
      "0.96421334"
    ],
    [
      "0.800612063",
      "0.96421334"
    ],
    [
      "0.872185383",
      "0.96421334"
    ]
  ],
  "radius": "0.035786659"
}

提交 radius 与 centers。每个数写成十进制字符串,例如 "0.25"。 · 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。