文献中也称circles in arbitrary trianglesunit circles in a minimum-area trianglecircle packing in a triangle of variable shape
在任意三角形中放置 n 个半径为 1、内部互不重叠的圆；三角形的三个顶点也是答案的一部分。让这个三角形的面积尽可能小。
普通装箱只移动圆；这里连三条边的方向都能改变。一条边转动一点，可能同时释放多个接触，也可能让整套构形失稳。
候选最优解通常由圆—圆、圆—边相切关系卡死。真正的搜索不是把圆平均铺开，而是在大量可能的接触图之间找到对的那一张。
Friedman 的公开表给出了 n≤50 的当前最好已知构形。n=1、2 已证明，n=3 仍是简单的等边三角形排布，因此本站从 n=4 开放；匹配公开构形只是到达前沿，打破它们才是新纪录。
查看来源
三角形面积
坐标单位就是圆的半径：每个圆半径固定为 1。三个顶点和所有圆心都写在 0≤x,y≤200 的坐标框内，顶点必须逆时针排列。
提交按逆时针排列的三个顶点 triangle，以及恰好 n 个圆心 centers。圆的半径固定为 1；所有数写成最多九位小数的字符串。
{
"centers": [
[
"7.502178606",
"14.851773021"
],
[
"8.511018145",
"13.124355726"
],
[
"6.533139748",
"12.827712687"
],
[
"9.511018150",
"11.392304909"
],
[
"6.914080813",
"10.864326849"
],
[
"5.236872497",
"9.774844260"
],
[
"8.511018145",
"9.660254092"
],
[
"10.511018156",
"9.660254092"
],
[
"7.426058473",
"7.980116432"
],
[
"9.511018150",
"7.928203275"
],
[
"11.511018161",
"7.928203275"
],
[
"5.283829790",
"7.775395572"
],
[
"3.812625525",
"6.420567886"
],
[
"8.511018145",
"6.196152457"
],
[
"12.511018167",
"6.196152457"
],
[
"6.511018133",
"6.196152457"
],
[
"10.511018156",
"6.196152457"
],
[
"3.483388719",
"4.447853216"
],
[
"5.498784259",
"4.471222697"
],
[
"7.511018139",
"4.464101640"
],
[
"9.511018150",
"4.464101640"
],
[
"11.511018161",
"4.464101640"
],
[
"13.511018173",
"4.464101640"
],
[
"2.292685502",
"2.840922635"
],
[
"4.511018122",
"2.732050823"
],
[
"6.511018133",
"2.732050823"
],
[
"8.511018145",
"2.732050823"
],
[
"10.511018156",
"2.732050823"
],
[
"12.511018167",
"2.732050823"
],
[
"14.511018178",
"2.732050823"
],
[
"1.511018105",
"1.000000006"
],
[
"7.511018139",
"1.000000006"
],
[
"9.511018150",
"1.000000006"
],
[
"11.511018161",
"1.000000006"
],
[
"13.511018173",
"1.000000006"
],
[
"3.511018117",
"1.000000006"
],
[
"5.511018128",
"1.000000006"
],
[
"15.511018184",
"1.000000006"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"17.243069001",
"0.000000000"
],
[
"7.307218921",
"17.209397154"
]
]
}{
"n": 38
}{
"centers": [
[
"7.502178606",
"14.851773021"
],
[
"8.511018145",
"13.124355726"
],
[
"6.533139748",
"12.827712687"
],
[
"9.511018150",
"11.392304909"
],
[
"6.914080813",
"10.864326849"
],
[
"5.236872497",
"9.774844260"
],
[
"8.511018145",
"9.660254092"
],
[
"10.511018156",
"9.660254092"
],
[
"7.426058473",
"7.980116432"
],
[
"9.511018150",
"7.928203275"
],
[
"11.511018161",
"7.928203275"
],
[
"5.283829790",
"7.775395572"
],
[
"3.812625525",
"6.420567886"
],
[
"8.511018145",
"6.196152457"
],
[
"12.511018167",
"6.196152457"
],
[
"6.511018133",
"6.196152457"
],
[
"10.511018156",
"6.196152457"
],
[
"3.483388719",
"4.447853216"
],
[
"5.498784259",
"4.471222697"
],
[
"7.511018139",
"4.464101640"
],
[
"9.511018150",
"4.464101640"
],
[
"11.511018161",
"4.464101640"
],
[
"13.511018173",
"4.464101640"
],
[
"2.292685502",
"2.840922635"
],
[
"4.511018122",
"2.732050823"
],
[
"6.511018133",
"2.732050823"
],
[
"8.511018145",
"2.732050823"
],
[
"10.511018156",
"2.732050823"
],
[
"12.511018167",
"2.732050823"
],
[
"14.511018178",
"2.732050823"
],
[
"1.511018105",
"1.000000006"
],
[
"7.511018139",
"1.000000006"
],
[
"9.511018150",
"1.000000006"
],
[
"11.511018161",
"1.000000006"
],
[
"13.511018173",
"1.000000006"
],
[
"3.511018117",
"1.000000006"
],
[
"5.511018128",
"1.000000006"
],
[
"15.511018184",
"1.000000006"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"17.243069001",
"0.000000000"
],
[
"7.307218921",
"17.209397154"
]
]
}提交按逆时针排列的三个顶点 triangle，以及恰好 n 个圆心 centers。圆的半径固定为 1；所有数写成最多九位小数的字符串。 · 验证器 v1.0.0
聊思路、贴方法、问为什么卡住。发帖即公开署名，与纪录同一个名字；署名后的 #编号是账号的注册序号，冒不了名。发言资格与实绩绑定：破过一次纪录，就永久拥有发言权。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？