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": [
[
"8.249947922",
"16.739220815"
],
[
"9.417271245",
"15.019327398"
],
[
"7.420319152",
"14.908953739"
],
[
"8.514381591",
"13.234729326"
],
[
"10.511333685",
"13.124355666"
],
[
"6.549817723",
"12.859910947"
],
[
"9.443370478",
"11.433362427"
],
[
"11.511333686",
"11.392304857"
],
[
"6.940735450",
"10.898487143"
],
[
"5.257594622",
"9.818192295"
],
[
"8.511333683",
"9.660254048"
],
[
"10.511333685",
"9.660254048"
],
[
"12.511333687",
"9.660254048"
],
[
"7.377038860",
"8.013021440"
],
[
"9.511333684",
"7.928203238"
],
[
"11.511333686",
"7.928203238"
],
[
"13.511333688",
"7.928203238"
],
[
"5.343882680",
"7.820054567"
],
[
"3.845797018",
"6.495011414"
],
[
"6.511333681",
"6.196152425"
],
[
"8.511333683",
"6.196152429"
],
[
"10.511333685",
"6.196152429"
],
[
"12.511333687",
"6.196152429"
],
[
"14.511333689",
"6.196152429"
],
[
"5.083428795",
"4.795763464"
],
[
"3.063775794",
"4.654239073"
],
[
"13.511333688",
"4.464101620"
],
[
"7.511260651",
"4.464059453"
],
[
"9.511333684",
"4.464101620"
],
[
"11.511333686",
"4.464101620"
],
[
"15.511333690",
"4.464101620"
],
[
"4.505863572",
"2.879869962"
],
[
"6.500830608",
"2.738072450"
],
[
"10.511333685",
"2.732050810"
],
[
"14.511333689",
"2.732050810"
],
[
"2.511333677",
"2.732050810"
],
[
"8.511333683",
"2.732050810"
],
[
"12.511333687",
"2.732050810"
],
[
"16.511333691",
"2.732050810"
],
[
"1.511333676",
"1.000000001"
],
[
"3.511333678",
"1.000000001"
],
[
"5.511333680",
"1.000000001"
],
[
"7.511333682",
"1.000000001"
],
[
"9.511333684",
"1.000000001"
],
[
"11.511333686",
"1.000000001"
],
[
"13.511333688",
"1.000000001"
],
[
"15.511333690",
"1.000000001"
],
[
"17.511333692",
"1.000000001"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"19.243384501",
"0.000000000"
],
[
"8.157417267",
"19.201458500"
]
]
}{
"n": 48
}{
"centers": [
[
"8.249947922",
"16.739220815"
],
[
"9.417271245",
"15.019327398"
],
[
"7.420319152",
"14.908953739"
],
[
"8.514381591",
"13.234729326"
],
[
"10.511333685",
"13.124355666"
],
[
"6.549817723",
"12.859910947"
],
[
"9.443370478",
"11.433362427"
],
[
"11.511333686",
"11.392304857"
],
[
"6.940735450",
"10.898487143"
],
[
"5.257594622",
"9.818192295"
],
[
"8.511333683",
"9.660254048"
],
[
"10.511333685",
"9.660254048"
],
[
"12.511333687",
"9.660254048"
],
[
"7.377038860",
"8.013021440"
],
[
"9.511333684",
"7.928203238"
],
[
"11.511333686",
"7.928203238"
],
[
"13.511333688",
"7.928203238"
],
[
"5.343882680",
"7.820054567"
],
[
"3.845797018",
"6.495011414"
],
[
"6.511333681",
"6.196152425"
],
[
"8.511333683",
"6.196152429"
],
[
"10.511333685",
"6.196152429"
],
[
"12.511333687",
"6.196152429"
],
[
"14.511333689",
"6.196152429"
],
[
"5.083428795",
"4.795763464"
],
[
"3.063775794",
"4.654239073"
],
[
"13.511333688",
"4.464101620"
],
[
"7.511260651",
"4.464059453"
],
[
"9.511333684",
"4.464101620"
],
[
"11.511333686",
"4.464101620"
],
[
"15.511333690",
"4.464101620"
],
[
"4.505863572",
"2.879869962"
],
[
"6.500830608",
"2.738072450"
],
[
"10.511333685",
"2.732050810"
],
[
"14.511333689",
"2.732050810"
],
[
"2.511333677",
"2.732050810"
],
[
"8.511333683",
"2.732050810"
],
[
"12.511333687",
"2.732050810"
],
[
"16.511333691",
"2.732050810"
],
[
"1.511333676",
"1.000000001"
],
[
"3.511333678",
"1.000000001"
],
[
"5.511333680",
"1.000000001"
],
[
"7.511333682",
"1.000000001"
],
[
"9.511333684",
"1.000000001"
],
[
"11.511333686",
"1.000000001"
],
[
"13.511333688",
"1.000000001"
],
[
"15.511333690",
"1.000000001"
],
[
"17.511333692",
"1.000000001"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"19.243384501",
"0.000000000"
],
[
"8.157417267",
"19.201458500"
]
]
}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？