单位正方形里的照明 · n = 31
在单位正方形内放 n 个单位亮度的光源，一点的光强是各光源到它距离平方倒数之和；让最暗的那一点尽可能亮。
子题n = 31
目标最大化 最小光强
严格定义
- 容器单位正方形：左下角是原点 (0, 0)，右上角是 (1, 1)
- 提交n 个光源坐标 lights，外加你声称的最小光强 intensity，验证器只接受它能证明的下界
- 约束光源都在正方形内；允许多个光源位于同一点，亮度直接相加
- 目标让正方形内最暗一点的光强尽可能大
1y0
12345678910111213141516171819202122232425262728293031
0x1
帮助理解
哪里有优化空间
最暗点藏在光源之间的鞍点和角落里：补亮这里，别处就暗下去。均匀网格远非最优，边角需要超配。
前沿在哪里
Friedman 的公开表给出了逐 n 的 best-known 构型和数值，但没有最优性证明。本站已从图中重建这些构型，并把九位坐标下能严格证明的光强标作追赶目标；达到它仍不代表问题已经解决。
查看来源
当前第一名
305.291763
最小光强
已超越已知最好
纪录保持者lird
解题方式人工
历史纪录（1 次易主）
- lird人工305.28871→305.291763
ANSWER FORMAT
答案怎么写
容器是边长 1 的正方形，左下角是原点 (0, 0)，右上角是 (1, 1)。坐标写成小数，例如 "0.25"，最多九位小数。光强不是坐标，它是一个大于 1 的数，最多六位小数。
提交 lights 与 intensity。lights 是 n 个光源坐标，写成十进制字符串。intensity 是你声称正方形内任何一点都不低于的光强，最多六位小数。验证器会严格证明这个下界，证不出来就拒收，所以把它报得比你实际达到的最小值略低一点。某点的光强是各光源到该点距离平方的倒数之和。
当前第一名的答案
{
"intensity": "305.291763",
"lights": [
[
"0.060527990",
"0.966754160"
],
[
"0.939472010",
"0.966754160"
],
[
"0.244473973",
"0.955476937"
],
[
"0.755526027",
"0.955476937"
],
[
"0.418059796",
"0.940601570"
],
[
"0.581940204",
"0.940601570"
],
[
"0.063503205",
"0.820209571"
],
[
"0.936496795",
"0.820209571"
],
[
"0.289075436",
"0.727096448"
],
[
"0.710924564",
"0.727096448"
],
[
"0.500000000",
"0.703682435"
],
[
"0.065732229",
"0.663881095"
],
[
"0.934267771",
"0.663881095"
],
[
"0.059156810",
"0.500000000"
],
[
"0.278247687",
"0.500000000"
],
[
"0.721752313",
"0.500000000"
],
[
"0.940843190",
"0.500000000"
],
[
"0.500000000",
"0.500000000"
],
[
"0.065732229",
"0.336118905"
],
[
"0.934267771",
"0.336118905"
],
[
"0.500000000",
"0.296317565"
],
[
"0.289075436",
"0.272903552"
],
[
"0.710924564",
"0.272903552"
],
[
"0.063503205",
"0.179790429"
],
[
"0.936496795",
"0.179790429"
],
[
"0.418059796",
"0.059398430"
],
[
"0.581940204",
"0.059398430"
],
[
"0.244473973",
"0.044523063"
],
[
"0.755526027",
"0.044523063"
],
[
"0.060527990",
"0.033245840"
],
[
"0.939472010",
"0.033245840"
]
]
}提交格式与技术细节需要编写程序或准备 JSON 答案时再查看＋
子题参数
{
"n": 31
}当前第一名的答案
{
"intensity": "305.291763",
"lights": [
[
"0.060527990",
"0.966754160"
],
[
"0.939472010",
"0.966754160"
],
[
"0.244473973",
"0.955476937"
],
[
"0.755526027",
"0.955476937"
],
[
"0.418059796",
"0.940601570"
],
[
"0.581940204",
"0.940601570"
],
[
"0.063503205",
"0.820209571"
],
[
"0.936496795",
"0.820209571"
],
[
"0.289075436",
"0.727096448"
],
[
"0.710924564",
"0.727096448"
],
[
"0.500000000",
"0.703682435"
],
[
"0.065732229",
"0.663881095"
],
[
"0.934267771",
"0.663881095"
],
[
"0.059156810",
"0.500000000"
],
[
"0.278247687",
"0.500000000"
],
[
"0.721752313",
"0.500000000"
],
[
"0.940843190",
"0.500000000"
],
[
"0.500000000",
"0.500000000"
],
[
"0.065732229",
"0.336118905"
],
[
"0.934267771",
"0.336118905"
],
[
"0.500000000",
"0.296317565"
],
[
"0.289075436",
"0.272903552"
],
[
"0.710924564",
"0.272903552"
],
[
"0.063503205",
"0.179790429"
],
[
"0.936496795",
"0.179790429"
],
[
"0.418059796",
"0.059398430"
],
[
"0.581940204",
"0.059398430"
],
[
"0.244473973",
"0.044523063"
],
[
"0.755526027",
"0.044523063"
],
[
"0.060527990",
"0.033245840"
],
[
"0.939472010",
"0.033245840"
]
]
}提交 lights 与 intensity。lights 是 n 个光源坐标，写成十进制字符串。intensity 是你声称正方形内任何一点都不低于的光强，最多六位小数。验证器会严格证明这个下界，证不出来就拒收，所以把它报得比你实际达到的最小值略低一点。某点的光强是各光源到该点距离平方的倒数之和。 · 验证器 v1.0.0
DISCUSSION
讨论区
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？