等圆装入扇形 · n = 16
在半径 1 的扇形（四分之一圆）内放置 n 个半径相同的圆，使共同半径尽可能大。
严格定义
- 容器容器是半径 1 的扇形（四分之一圆）：圆心在原点 (0, 0)，直角边沿 x 轴和 y 轴延伸到 1，弧在第一象限。
- 提交恰好 n 个圆：一个共同半径与 n 个圆心；所有圆共用同一个半径
- 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
12345678910111213141516
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
0.107771974
共同半径
已追平已知最好
纪录保持者创始基准
解题方式人工
ANSWER FORMAT
答案怎么写
容器是半径 1 的扇形（四分之一圆）：圆心在原点 (0, 0)，直角边沿 x 轴和 y 轴延伸到 1，弧在第一象限。坐标和半径用同一个单位，直接写成小数，例如 "0.25"，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"。所有圆共用同一个半径。
当前第一名的答案
{
"centers": [
[
"0.885695236",
"0.107771975"
],
[
"0.670151287",
"0.107771975"
],
[
"0.260045208",
"0.107771975"
],
[
"0.465098247",
"0.174198212"
],
[
"0.107771975",
"0.26032379"
],
[
"0.834005506",
"0.317026284"
],
[
"0.618627627",
"0.325485766"
],
[
"0.365677126",
"0.365443172"
],
[
"0.174626665",
"0.465237538"
],
[
"0.733642693",
"0.50777874"
],
[
"0.518323595",
"0.517621519"
],
[
"0.326032964",
"0.618649815"
],
[
"0.107771975",
"0.670151287"
],
[
"0.508772676",
"0.73295376"
],
[
"0.317026284",
"0.834005506"
],
[
"0.107771975",
"0.885695236"
]
],
"radius": "0.107771974"
}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": 16
}当前第一名的答案
{
"centers": [
[
"0.885695236",
"0.107771975"
],
[
"0.670151287",
"0.107771975"
],
[
"0.260045208",
"0.107771975"
],
[
"0.465098247",
"0.174198212"
],
[
"0.107771975",
"0.26032379"
],
[
"0.834005506",
"0.317026284"
],
[
"0.618627627",
"0.325485766"
],
[
"0.365677126",
"0.365443172"
],
[
"0.174626665",
"0.465237538"
],
[
"0.733642693",
"0.50777874"
],
[
"0.518323595",
"0.517621519"
],
[
"0.326032964",
"0.618649815"
],
[
"0.107771975",
"0.670151287"
],
[
"0.508772676",
"0.73295376"
],
[
"0.317026284",
"0.834005506"
],
[
"0.107771975",
"0.885695236"
]
],
"radius": "0.107771974"
}提交 radius 与 centers。每个数写成十进制字符串，例如 "0.25"。所有圆共用同一个半径。 · 验证器 v1.0.0