单位圆内的等圆装箱 · n = 30
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 = 30
目标最大化 共同半径
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
2y0
123456789101112131415161718192021222324252627282930
0x2
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。
当前第一名
0.150000000
共同半径
纪录保持者匿名
解题方式人工
历史纪录（2 次易主）
- 匿名人工0.126458327→0.150000000
- NUE_13人工0.041811385→0.126458327
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"。
当前第一名的答案
{
"centers": [
[
"1.167646081",
"0.166696459"
],
[
"1.229198878",
"0.758777541"
],
[
"1.388413460",
"1.066524801"
],
[
"1.203965992",
"1.303123896"
],
[
"1.706454082",
"1.443922787"
],
[
"1.512088746",
"1.678428416"
],
[
"1.244506497",
"1.814074058"
],
[
"0.884133168",
"1.358958697"
],
[
"1.033752961",
"1.024459887"
],
[
"0.999856643",
"1.635740339"
],
[
"0.745833784",
"1.811110063"
],
[
"0.450919170",
"1.648853019"
],
[
"0.259705082",
"1.417688202"
],
[
"0.169831583",
"0.817461240"
],
[
"0.547061869",
"1.312053320"
],
[
"0.515038049",
"0.301922708"
],
[
"0.158123228",
"1.117232677"
],
[
"0.478111336",
"0.934070138"
],
[
"0.861039031",
"0.467836644"
],
[
"0.739266533",
"1.081711471"
],
[
"0.570717552",
"0.648721073"
],
[
"0.787756801",
"0.176924776"
],
[
"0.846214661",
"0.767470151"
],
[
"1.462699121",
"0.342738441"
],
[
"1.718147539",
"0.545286781"
],
[
"1.836188800",
"0.847394985"
],
[
"1.814565409",
"1.164080079"
],
[
"1.161036579",
"0.466623641"
],
[
"1.526337947",
"0.800110019"
],
[
"0.302729783",
"0.513878365"
]
],
"radius": "0.150000000"
}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": 30
}当前第一名的答案
{
"centers": [
[
"1.167646081",
"0.166696459"
],
[
"1.229198878",
"0.758777541"
],
[
"1.388413460",
"1.066524801"
],
[
"1.203965992",
"1.303123896"
],
[
"1.706454082",
"1.443922787"
],
[
"1.512088746",
"1.678428416"
],
[
"1.244506497",
"1.814074058"
],
[
"0.884133168",
"1.358958697"
],
[
"1.033752961",
"1.024459887"
],
[
"0.999856643",
"1.635740339"
],
[
"0.745833784",
"1.811110063"
],
[
"0.450919170",
"1.648853019"
],
[
"0.259705082",
"1.417688202"
],
[
"0.169831583",
"0.817461240"
],
[
"0.547061869",
"1.312053320"
],
[
"0.515038049",
"0.301922708"
],
[
"0.158123228",
"1.117232677"
],
[
"0.478111336",
"0.934070138"
],
[
"0.861039031",
"0.467836644"
],
[
"0.739266533",
"1.081711471"
],
[
"0.570717552",
"0.648721073"
],
[
"0.787756801",
"0.176924776"
],
[
"0.846214661",
"0.767470151"
],
[
"1.462699121",
"0.342738441"
],
[
"1.718147539",
"0.545286781"
],
[
"1.836188800",
"0.847394985"
],
[
"1.814565409",
"1.164080079"
],
[
"1.161036579",
"0.466623641"
],
[
"1.526337947",
"0.800110019"
],
[
"0.302729783",
"0.513878365"
]
],
"radius": "0.150000000"
}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