单位正方形内的等圆装箱 · n = 14
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。
已完成已经有达到上限的答案，这道子题没有可争的了
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
1y0
1234567891011121314
0x1
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
0.129331793
共同半径
已达最优最优值已证明，无法再提升
纪录保持者参考答案
解题方式—
历史纪录（2 次易主）
- 匿名人工0.127279379→0.129331793
- NUE_13人工0.125000000→0.127279379
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"。
当前第一名的答案
{
"centers": [
[
"0.129331794",
"0.129331794"
],
[
"0.387995381",
"0.129331794"
],
[
"0.646658969",
"0.129331794"
],
[
"0.870668206",
"0.258663587"
],
[
"0.129331794",
"0.387995381"
],
[
"0.387995381",
"0.387995381"
],
[
"0.646658969",
"0.387995381"
],
[
"0.870668206",
"0.517327175"
],
[
"0.129331794",
"0.646658969"
],
[
"0.387995381",
"0.646658969"
],
[
"0.646658969",
"0.646658969"
],
[
"0.855841478",
"0.855841478"
],
[
"0.258663587",
"0.870668206"
],
[
"0.517327175",
"0.870668206"
]
],
"radius": "0.129331793"
}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": 14
}当前第一名的答案
{
"centers": [
[
"0.129331794",
"0.129331794"
],
[
"0.387995381",
"0.129331794"
],
[
"0.646658969",
"0.129331794"
],
[
"0.870668206",
"0.258663587"
],
[
"0.129331794",
"0.387995381"
],
[
"0.387995381",
"0.387995381"
],
[
"0.646658969",
"0.387995381"
],
[
"0.870668206",
"0.517327175"
],
[
"0.129331794",
"0.646658969"
],
[
"0.387995381",
"0.646658969"
],
[
"0.646658969",
"0.646658969"
],
[
"0.855841478",
"0.855841478"
],
[
"0.258663587",
"0.870668206"
],
[
"0.517327175",
"0.870668206"
]
],
"radius": "0.129331793"
}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