HDU4081 Qin Shi Huang's National Road System 2017-05-10 23:16 41人阅读 评论(0) 收藏
Qin Shi Huang's National Road System
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768
K (Java/Others)
Total Submission(s): 7672 Accepted Submission(s): 2693
kingdoms and became the first emperor of a unified China in 221 BC. That was Qin dynasty ---- the first imperial dynasty of China(not to be confused with the Qing Dynasty, the last dynasty of China). So Ying Zheng named himself "Qin Shi Huang" because "Shi
Huang" means "the first emperor" in Chinese.

Qin Shi Huang undertook gigantic projects, including the first version of the Great Wall of China, the now famous city-sized mausoleum guarded by a life-sized Terracotta Army, and a massive national road system. There is a story about the road system:
There were n cities in China and Qin Shi Huang wanted them all be connected by n-1 roads, in order that he could go to every city from the capital city Xianyang.
Although Qin Shi Huang was a tyrant, he wanted the total length of all roads to be minimum,so that the road system may not cost too many people's life. A daoshi (some kind of monk) named Xu Fu told Qin Shi Huang that he could build a road by magic and that
magic road would cost no money and no labor. But Xu Fu could only build ONE magic road for Qin Shi Huang. So Qin Shi Huang had to decide where to build the magic road. Qin Shi Huang wanted the total length of all none magic roads to be as small as possible,
but Xu Fu wanted the magic road to benefit as many people as possible ---- So Qin Shi Huang decided that the value of A/B (the ratio of A to B) must be the maximum, which A is the total population of the two cites connected by the magic road, and B is the
total length of none magic roads.
Would you help Qin Shi Huang?
A city can be considered as a point, and a road can be considered as a line segment connecting two points.
For each test case:
The first line is an integer n meaning that there are n cities(2 < n <= 1000).
Then n lines follow. Each line contains three integers X, Y and P ( 0 <= X, Y <= 1000, 0 < P < 100000). (X, Y) is the coordinate of a city and P is the population of that city.
It is guaranteed that each city has a distinct location.
2
4
1 1 20
1 2 30
200 2 80
200 1 100
3
1 1 20
1 2 30
2 2 40
65.00
70.00
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <string>
#include <set>
#include <map>
#include <queue> using namespace std;
#define inf 0x3f3f3f3f
int n;
struct node
{
int u,v;
double w;
} p[1000006],mst[1006];
int pre[1006],cnt;
int a[1006]; bool cmp(node a,node b)
{
return a.w<b.w;
} void init()
{
for(int i=0; i<1005; i++)
pre[i]=i;
}
int fin(int x)
{
return pre[x]==x?x:pre[x]=fin(pre[x]);
} double kruskal()
{
init();
double cost=0;
int ans=0;
for(int i=0; i<cnt; i++)
{
int a=fin(p[i].u);
int b=fin(p[i].v);
if(a!=b)
{
pre[a]=b;
cost+=p[i].w;
mst[ans].u=p[i].u,mst[ans].v=p[i].v,mst[ans].w=p[i].w;
ans++;
}
if(ans==n-1)
break;
}
return cost;
} int main()
{ int x[1005],y[1005],T;
scanf("%d",&T);
while(T--)
{
scanf("%d",&n);
for(int i=0; i<n; i++)
scanf("%d%d%d",&x[i],&y[i],&a[i]);
cnt=0;
memset(p,0,sizeof p);
memset(mst,0,sizeof mst);
for(int i=0; i<n; i++)
for(int j=i+1; j<n; j++)
{
p[cnt].u=i,p[cnt].v=j,p[cnt++].w=sqrt((double)((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j])));
}
sort(p,p+cnt,cmp);
double mincost=kruskal();
double ans=-1;
for(int i=0; i<n-1; i++)
{
init();
for(int j=0; j<n-1; j++)
{
if(i==j)
continue;
int aa=fin(mst[j].u);
int bb=fin(mst[j].v);
if(aa!=bb)
{
pre[aa]=bb;
}
}
int xx=fin(mst[i].u);
int yy=fin(mst[i].v);
int x1=-1,x2=-1;
mincost-=mst[i].w;
for(int j=0; j<n; j++)
if(fin(j)!=xx)
x1=max(x1,a[j]);
for(int j=0; j<n; j++)
if(fin(j)!=yy)
x2=max(x2,a[j]);
ans=max(ans,(x1+x2)*1.0/mincost);
mincost+=mst[i].w;
}
printf("%.2f\n",ans);
}
return 0;
}
HDU4081 Qin Shi Huang's National Road System 2017-05-10 23:16 41人阅读 评论(0) 收藏的更多相关文章
- HDU4081 Qin Shi Huang's National Road System —— 次小生成树变形
题目链接:https://vjudge.net/problem/HDU-4081 Qin Shi Huang's National Road System Time Limit: 2000/1000 ...
- HDU4081:Qin Shi Huang's National Road System (任意两点间的最小瓶颈路)
Qin Shi Huang's National Road System Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/3 ...
- hdu-4081 Qin Shi Huang's National Road System(最小生成树+bfs)
题目链接: Qin Shi Huang's National Road System Time Limit: 2000/1000 MS (Java/Others) Memory Limit: ...
- HDU4081 Qin Shi Huang's National Road System(次小生成树)
枚举作为magic road的边,然后求出A/B. A/B得在大概O(1)的时间复杂度求出,关键是B,B是包含magic road的最小生成树. 这么求得: 先在原图求MST,边总和记为s,顺便求出M ...
- hdu4081 Qin Shi Huang's National Road System 次小生成树
先发发牢骚:图论500题上说这题是最小生成树+DFS,网上搜题解也有人这么做.但是其实就是次小生成树.次小生成树完全当模版题.其中有一个小细节没注意,导致我几个小时一直在找错.有了模版要会用模版,然后 ...
- HDU4081 Qin Shi Huang's National Road System
先求最小生成树 再遍历每一对顶点,如果该顶点之间的边属于最小生成树,则剪掉这对顶点在最小生成树里的最长路径 否则直接剪掉连接这对顶点的边~ 用prim算法求最小生成树最长路径的模板~ #include ...
- hdu 4081 Qin Shi Huang's National Road System (次小生成树)
Qin Shi Huang's National Road System Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/3 ...
- UValive 5713 Qin Shi Huang's National Road System
Qin Shi Huang's National Road System Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/3 ...
- hdu 4081 Qin Shi Huang's National Road System (次小生成树的变形)
题目:Qin Shi Huang's National Road System Qin Shi Huang's National Road System Time Limit: 2000/1000 M ...
随机推荐
- 【Java】JavaIO(二)、节点流
一.InputStream & outputStream Java字节流主要是以InputStream (输入流),outputStream(输出流)为基类,本身是抽象类不能创建实例,但是是字 ...
- EasyUI 导出页面到Excel中
<script type="text/javascript"> <!-- js --> /*================================ ...
- Xcrysden-2
XCrySDen -- (X-Window) CRYstalline Structures and DENsities Introduction to use. XCrySDen is a cryst ...
- MVVM 的理解
MVVM 是 Model - View - ViewModel 的缩写 可以看到他和之前的MVC很像,的确有人称之为一个加强优化版的MVC. 是一种模块化开发代码分层的思想或者框架! MVVM 的优点 ...
- Spring AOP开发
--------------------siwuxie095 Spring AOP 开发 1.在 Spring 中进行 ...
- js td innerHTML
用value不好使,用innerHTML可以.JS:document.getElementById("aa").innerHTML="单元格"; body:&l ...
- swift中UITextView的使用
https://blog.csdn.net/potato512/article/details/52692604
- Navicat Premium11连接Oracle出现ORA-28547:connection to server failed
环境描述:本地Oracle正常安装,中途没有出现任何异常.确保Oracle的主要服务都启动了.1.OracleServiceORCL2.OracleOraDb11g_home1TNSListener ...
- php使用jquery Form ajax 提交表单,并上传文件
在html5中我们通过FormData就可以ajax上传文件数据,不过因为兼容问题.我们选用jquery.form.min.js来进行ajax的表单提交. 一.jquery.form.js下载地址 ...
- PL/Sql快速执行 insert语句的.sql文件
当全是 insert语句的.sql文件太大时(insert 语句条数太大),直接打开执行sql文件,pl/sql会卡死. 这是可以用pl/sql的命令窗口来执行.sql文件,操作步骤如下: 1.新建命 ...