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": [
[
"10.003904230",
"15.056574842"
],
[
"8.886981509",
"13.392703456"
],
[
"10.878519520",
"13.208919553"
],
[
"9.723588986",
"11.576088994"
],
[
"7.732050974",
"11.392305091"
],
[
"11.684352136",
"11.181870731"
],
[
"6.732050953",
"9.660254246"
],
[
"8.851625356",
"9.726770584"
],
[
"11.250887941",
"9.229408448"
],
[
"12.906553448",
"8.107458404"
],
[
"5.732050931",
"7.928203401"
],
[
"7.732050974",
"7.928203401"
],
[
"9.732051018",
"7.928203401"
],
[
"10.802998665",
"6.239099666"
],
[
"4.732050910",
"6.196152556"
],
[
"8.732050996",
"6.196152556"
],
[
"6.732050953",
"6.196152556"
],
[
"12.871511437",
"6.107765370"
],
[
"14.269927879",
"4.677929146"
],
[
"5.732050931",
"4.464101712"
],
[
"9.732051018",
"4.464101712"
],
[
"3.732050888",
"4.464101712"
],
[
"7.732050974",
"4.464101712"
],
[
"11.732051061",
"4.464101712"
],
[
"2.732050867",
"2.732050867"
],
[
"4.732050910",
"2.732050867"
],
[
"6.732050953",
"2.732050867"
],
[
"8.732050996",
"2.732050867"
],
[
"10.732051039",
"2.732050867"
],
[
"12.732051082",
"2.732050867"
],
[
"14.732051126",
"2.732050867"
],
[
"1.732050845",
"1.000000022"
],
[
"3.732050888",
"1.000000022"
],
[
"5.732050931",
"1.000000022"
],
[
"7.732050974",
"1.000000022"
],
[
"9.732051018",
"1.000000022"
],
[
"11.732051061",
"1.000000022"
],
[
"13.732051104",
"1.000000022"
],
[
"15.732051147",
"1.000000022"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"17.205712692",
"0.000000000"
],
[
"10.189582397",
"17.648874420"
]
]
}{
"n": 39
}{
"centers": [
[
"10.003904230",
"15.056574842"
],
[
"8.886981509",
"13.392703456"
],
[
"10.878519520",
"13.208919553"
],
[
"9.723588986",
"11.576088994"
],
[
"7.732050974",
"11.392305091"
],
[
"11.684352136",
"11.181870731"
],
[
"6.732050953",
"9.660254246"
],
[
"8.851625356",
"9.726770584"
],
[
"11.250887941",
"9.229408448"
],
[
"12.906553448",
"8.107458404"
],
[
"5.732050931",
"7.928203401"
],
[
"7.732050974",
"7.928203401"
],
[
"9.732051018",
"7.928203401"
],
[
"10.802998665",
"6.239099666"
],
[
"4.732050910",
"6.196152556"
],
[
"8.732050996",
"6.196152556"
],
[
"6.732050953",
"6.196152556"
],
[
"12.871511437",
"6.107765370"
],
[
"14.269927879",
"4.677929146"
],
[
"5.732050931",
"4.464101712"
],
[
"9.732051018",
"4.464101712"
],
[
"3.732050888",
"4.464101712"
],
[
"7.732050974",
"4.464101712"
],
[
"11.732051061",
"4.464101712"
],
[
"2.732050867",
"2.732050867"
],
[
"4.732050910",
"2.732050867"
],
[
"6.732050953",
"2.732050867"
],
[
"8.732050996",
"2.732050867"
],
[
"10.732051039",
"2.732050867"
],
[
"12.732051082",
"2.732050867"
],
[
"14.732051126",
"2.732050867"
],
[
"1.732050845",
"1.000000022"
],
[
"3.732050888",
"1.000000022"
],
[
"5.732050931",
"1.000000022"
],
[
"7.732050974",
"1.000000022"
],
[
"9.732051018",
"1.000000022"
],
[
"11.732051061",
"1.000000022"
],
[
"13.732051104",
"1.000000022"
],
[
"15.732051147",
"1.000000022"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"17.205712692",
"0.000000000"
],
[
"10.189582397",
"17.648874420"
]
]
}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？