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": [
[
"8.766108866",
"14.971117785"
],
[
"9.845454227",
"13.274998620"
],
[
"7.848053267",
"13.173069543"
],
[
"8.935026917",
"11.494234109"
],
[
"6.937744435",
"11.390009254"
],
[
"10.932427877",
"11.392305032"
],
[
"9.861808768",
"9.699193629"
],
[
"11.932427893",
"9.660254196"
],
[
"7.851597005",
"9.611000089"
],
[
"5.874712542",
"9.307803865"
],
[
"8.932427844",
"7.928203360"
],
[
"10.932427877",
"7.928203360"
],
[
"12.932427909",
"7.928203360"
],
[
"6.964845429",
"7.569567649"
],
[
"4.965308803",
"7.526516418"
],
[
"9.932427860",
"6.196152524"
],
[
"11.932427893",
"6.196152524"
],
[
"13.932427926",
"6.196152524"
],
[
"5.192253537",
"5.539434079"
],
[
"7.282871543",
"5.595014656"
],
[
"3.449705476",
"4.557840280"
],
[
"8.932427844",
"4.464101688"
],
[
"10.932427877",
"4.464101688"
],
[
"12.932427909",
"4.464101688"
],
[
"14.932427942",
"4.464101688"
],
[
"6.282871526",
"3.862963820"
],
[
"2.633315192",
"2.732050852"
],
[
"7.932427827",
"2.732050852"
],
[
"9.932427860",
"2.732050852"
],
[
"11.932427893",
"2.732050852"
],
[
"13.932427926",
"2.732050852"
],
[
"15.932427958",
"2.732050852"
],
[
"5.282871510",
"2.130912984"
],
[
"1.633315176",
"1.000000016"
],
[
"3.633315209",
"1.000000016"
],
[
"10.932427877",
"1.000000016"
],
[
"12.932427909",
"1.000000016"
],
[
"14.932427942",
"1.000000016"
],
[
"16.932427975",
"1.000000016"
],
[
"6.932427811",
"1.000000016"
],
[
"8.932427844",
"1.000000016"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"18.664478811",
"0.000000000"
],
[
"8.759046053",
"17.156712807"
]
]
}{
"n": 41
}{
"centers": [
[
"8.766108866",
"14.971117785"
],
[
"9.845454227",
"13.274998620"
],
[
"7.848053267",
"13.173069543"
],
[
"8.935026917",
"11.494234109"
],
[
"6.937744435",
"11.390009254"
],
[
"10.932427877",
"11.392305032"
],
[
"9.861808768",
"9.699193629"
],
[
"11.932427893",
"9.660254196"
],
[
"7.851597005",
"9.611000089"
],
[
"5.874712542",
"9.307803865"
],
[
"8.932427844",
"7.928203360"
],
[
"10.932427877",
"7.928203360"
],
[
"12.932427909",
"7.928203360"
],
[
"6.964845429",
"7.569567649"
],
[
"4.965308803",
"7.526516418"
],
[
"9.932427860",
"6.196152524"
],
[
"11.932427893",
"6.196152524"
],
[
"13.932427926",
"6.196152524"
],
[
"5.192253537",
"5.539434079"
],
[
"7.282871543",
"5.595014656"
],
[
"3.449705476",
"4.557840280"
],
[
"8.932427844",
"4.464101688"
],
[
"10.932427877",
"4.464101688"
],
[
"12.932427909",
"4.464101688"
],
[
"14.932427942",
"4.464101688"
],
[
"6.282871526",
"3.862963820"
],
[
"2.633315192",
"2.732050852"
],
[
"7.932427827",
"2.732050852"
],
[
"9.932427860",
"2.732050852"
],
[
"11.932427893",
"2.732050852"
],
[
"13.932427926",
"2.732050852"
],
[
"15.932427958",
"2.732050852"
],
[
"5.282871510",
"2.130912984"
],
[
"1.633315176",
"1.000000016"
],
[
"3.633315209",
"1.000000016"
],
[
"10.932427877",
"1.000000016"
],
[
"12.932427909",
"1.000000016"
],
[
"14.932427942",
"1.000000016"
],
[
"16.932427975",
"1.000000016"
],
[
"6.932427811",
"1.000000016"
],
[
"8.932427844",
"1.000000016"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"18.664478811",
"0.000000000"
],
[
"8.759046053",
"17.156712807"
]
]
}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？