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": [
[
"10.542349166",
"14.312012839"
],
[
"11.542349167",
"12.579962030"
],
[
"9.448663025",
"12.637542585"
],
[
"9.453860554",
"10.637549336"
],
[
"11.453087722",
"10.581954922"
],
[
"7.620432811",
"9.838460656"
],
[
"13.228043356",
"9.660254048"
],
[
"10.453087721",
"8.849904113"
],
[
"6.526746670",
"8.163990401"
],
[
"8.600913000",
"8.095285791"
],
[
"12.228043355",
"7.928203238"
],
[
"14.228043357",
"7.928203238"
],
[
"5.233263033",
"6.183623462"
],
[
"7.230333453",
"6.291835053"
],
[
"9.228043352",
"6.196152429"
],
[
"11.228043354",
"6.196152429"
],
[
"13.228043356",
"6.196152429"
],
[
"15.228043358",
"6.196152429"
],
[
"8.141371676",
"4.511345824"
],
[
"4.089521998",
"4.432517481"
],
[
"10.228043353",
"4.464101620"
],
[
"12.228043355",
"4.464101620"
],
[
"14.228043357",
"4.464101620"
],
[
"16.228043359",
"4.464101620"
],
[
"6.088717845",
"4.375807909"
],
[
"2.995835857",
"2.758047226"
],
[
"11.228043354",
"2.732050810"
],
[
"15.228043358",
"2.732050810"
],
[
"17.228043360",
"2.732050810"
],
[
"7.228043350",
"2.732050810"
],
[
"9.228043352",
"2.732050810"
],
[
"13.228043356",
"2.732050810"
],
[
"5.088717844",
"2.643757100"
],
[
"1.898938180",
"1.055415442"
],
[
"3.949392338",
"1.000000001"
],
[
"6.228043349",
"1.000000001"
],
[
"8.228043351",
"1.000000001"
],
[
"10.228043353",
"1.000000001"
],
[
"12.228043355",
"1.000000001"
],
[
"14.228043357",
"1.000000001"
],
[
"16.228043359",
"1.000000001"
],
[
"18.228043361",
"1.000000001"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"19.960094171",
"0.000000000"
],
[
"10.594852190",
"16.221074936"
]
]
}{
"n": 42
}{
"centers": [
[
"10.542349166",
"14.312012839"
],
[
"11.542349167",
"12.579962030"
],
[
"9.448663025",
"12.637542585"
],
[
"9.453860554",
"10.637549336"
],
[
"11.453087722",
"10.581954922"
],
[
"7.620432811",
"9.838460656"
],
[
"13.228043356",
"9.660254048"
],
[
"10.453087721",
"8.849904113"
],
[
"6.526746670",
"8.163990401"
],
[
"8.600913000",
"8.095285791"
],
[
"12.228043355",
"7.928203238"
],
[
"14.228043357",
"7.928203238"
],
[
"5.233263033",
"6.183623462"
],
[
"7.230333453",
"6.291835053"
],
[
"9.228043352",
"6.196152429"
],
[
"11.228043354",
"6.196152429"
],
[
"13.228043356",
"6.196152429"
],
[
"15.228043358",
"6.196152429"
],
[
"8.141371676",
"4.511345824"
],
[
"4.089521998",
"4.432517481"
],
[
"10.228043353",
"4.464101620"
],
[
"12.228043355",
"4.464101620"
],
[
"14.228043357",
"4.464101620"
],
[
"16.228043359",
"4.464101620"
],
[
"6.088717845",
"4.375807909"
],
[
"2.995835857",
"2.758047226"
],
[
"11.228043354",
"2.732050810"
],
[
"15.228043358",
"2.732050810"
],
[
"17.228043360",
"2.732050810"
],
[
"7.228043350",
"2.732050810"
],
[
"9.228043352",
"2.732050810"
],
[
"13.228043356",
"2.732050810"
],
[
"5.088717844",
"2.643757100"
],
[
"1.898938180",
"1.055415442"
],
[
"3.949392338",
"1.000000001"
],
[
"6.228043349",
"1.000000001"
],
[
"8.228043351",
"1.000000001"
],
[
"10.228043353",
"1.000000001"
],
[
"12.228043355",
"1.000000001"
],
[
"14.228043357",
"1.000000001"
],
[
"16.228043359",
"1.000000001"
],
[
"18.228043361",
"1.000000001"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"19.960094171",
"0.000000000"
],
[
"10.594852190",
"16.221074936"
]
]
}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？