单位正方形里的照明 · n = 35
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 = 35
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
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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
347.195206
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347.191734→347.195206
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": "347.195206",
"lights": [
[
"0.055412914",
"0.972909248"
],
[
"0.943605845",
"0.972909248"
],
[
"0.231387538",
"0.960152213"
],
[
"0.768121841",
"0.959661593"
],
[
"0.404512521",
"0.954023535"
],
[
"0.594996858",
"0.954023535"
],
[
"0.499754690",
"0.866582841"
],
[
"0.941938232",
"0.834828617"
],
[
"0.057080527",
"0.834337997"
],
[
"0.265506014",
"0.750086490"
],
[
"0.733022124",
"0.749595870"
],
[
"0.959372288",
"0.675186328"
],
[
"0.498773449",
"0.675608207"
],
[
"0.040137091",
"0.674205087"
],
[
"0.751850438",
"0.565081919"
],
[
"0.247658941",
"0.563610057"
],
[
"0.500735931",
"0.533517738"
],
[
"0.962386875",
"0.501418066"
],
[
"0.036631884",
"0.500927445"
],
[
"0.274601971",
"0.420122416"
],
[
"0.725398029",
"0.419141175"
],
[
"0.947498413",
"0.330883979"
],
[
"0.052501587",
"0.330393358"
],
[
"0.499264069",
"0.320847410"
],
[
"0.264921303",
"0.229849397"
],
[
"0.735078697",
"0.229849397"
],
[
"0.049721585",
"0.169546454"
],
[
"0.949787794",
"0.169055834"
],
[
"0.501226551",
"0.118923926"
],
[
"0.407875721",
"0.054421208"
],
[
"0.590652417",
"0.053439967"
],
[
"0.233566392",
"0.034114785"
],
[
"0.765942987",
"0.034114785"
],
[
"0.056731568",
"0.025723974"
],
[
"0.942777811",
"0.025302041"
]
]
}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": 35
}当前第一名的答案
{
"intensity": "347.195206",
"lights": [
[
"0.055412914",
"0.972909248"
],
[
"0.943605845",
"0.972909248"
],
[
"0.231387538",
"0.960152213"
],
[
"0.768121841",
"0.959661593"
],
[
"0.404512521",
"0.954023535"
],
[
"0.594996858",
"0.954023535"
],
[
"0.499754690",
"0.866582841"
],
[
"0.941938232",
"0.834828617"
],
[
"0.057080527",
"0.834337997"
],
[
"0.265506014",
"0.750086490"
],
[
"0.733022124",
"0.749595870"
],
[
"0.959372288",
"0.675186328"
],
[
"0.498773449",
"0.675608207"
],
[
"0.040137091",
"0.674205087"
],
[
"0.751850438",
"0.565081919"
],
[
"0.247658941",
"0.563610057"
],
[
"0.500735931",
"0.533517738"
],
[
"0.962386875",
"0.501418066"
],
[
"0.036631884",
"0.500927445"
],
[
"0.274601971",
"0.420122416"
],
[
"0.725398029",
"0.419141175"
],
[
"0.947498413",
"0.330883979"
],
[
"0.052501587",
"0.330393358"
],
[
"0.499264069",
"0.320847410"
],
[
"0.264921303",
"0.229849397"
],
[
"0.735078697",
"0.229849397"
],
[
"0.049721585",
"0.169546454"
],
[
"0.949787794",
"0.169055834"
],
[
"0.501226551",
"0.118923926"
],
[
"0.407875721",
"0.054421208"
],
[
"0.590652417",
"0.053439967"
],
[
"0.233566392",
"0.034114785"
],
[
"0.765942987",
"0.034114785"
],
[
"0.056731568",
"0.025723974"
],
[
"0.942777811",
"0.025302041"
]
]
}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？