单位正方形里的照明 · n = 30
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 = 30
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
123456789101112131415161718192021222324252627282930
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
285.333303
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285.33045→285.333303
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": "285.333303",
"lights": [
[
"0.500000000",
"0.989735375"
],
[
"0.071447475",
"0.981969854"
],
[
"0.928552525",
"0.981969854"
],
[
"0.720927993",
"0.975814320"
],
[
"0.279072007",
"0.975814320"
],
[
"0.500000000",
"0.865147870"
],
[
"0.068085758",
"0.839667355"
],
[
"0.931914242",
"0.839667355"
],
[
"0.281315293",
"0.741815526"
],
[
"0.718684707",
"0.741815526"
],
[
"0.062401882",
"0.674521768"
],
[
"0.937598118",
"0.674521768"
],
[
"0.500000000",
"0.620797675"
],
[
"0.059404278",
"0.500000000"
],
[
"0.277064310",
"0.500000000"
],
[
"0.722935690",
"0.500000000"
],
[
"0.940595722",
"0.500000000"
],
[
"0.500000000",
"0.379202325"
],
[
"0.062401882",
"0.325478232"
],
[
"0.937598118",
"0.325478232"
],
[
"0.281315293",
"0.258184474"
],
[
"0.718684707",
"0.258184474"
],
[
"0.068085758",
"0.160332645"
],
[
"0.931914242",
"0.160332645"
],
[
"0.500000000",
"0.134852130"
],
[
"0.279072007",
"0.024185680"
],
[
"0.720927993",
"0.024185680"
],
[
"0.071447475",
"0.018030146"
],
[
"0.928552525",
"0.018030146"
],
[
"0.500000000",
"0.010264625"
]
]
}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": 30
}当前第一名的答案
{
"intensity": "285.333303",
"lights": [
[
"0.500000000",
"0.989735375"
],
[
"0.071447475",
"0.981969854"
],
[
"0.928552525",
"0.981969854"
],
[
"0.720927993",
"0.975814320"
],
[
"0.279072007",
"0.975814320"
],
[
"0.500000000",
"0.865147870"
],
[
"0.068085758",
"0.839667355"
],
[
"0.931914242",
"0.839667355"
],
[
"0.281315293",
"0.741815526"
],
[
"0.718684707",
"0.741815526"
],
[
"0.062401882",
"0.674521768"
],
[
"0.937598118",
"0.674521768"
],
[
"0.500000000",
"0.620797675"
],
[
"0.059404278",
"0.500000000"
],
[
"0.277064310",
"0.500000000"
],
[
"0.722935690",
"0.500000000"
],
[
"0.940595722",
"0.500000000"
],
[
"0.500000000",
"0.379202325"
],
[
"0.062401882",
"0.325478232"
],
[
"0.937598118",
"0.325478232"
],
[
"0.281315293",
"0.258184474"
],
[
"0.718684707",
"0.258184474"
],
[
"0.068085758",
"0.160332645"
],
[
"0.931914242",
"0.160332645"
],
[
"0.500000000",
"0.134852130"
],
[
"0.279072007",
"0.024185680"
],
[
"0.720927993",
"0.024185680"
],
[
"0.071447475",
"0.018030146"
],
[
"0.928552525",
"0.018030146"
],
[
"0.500000000",
"0.010264625"
]
]
}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？