hdu 4081(次小生成树)
Qin Shi Huang's National Road System
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6407 Accepted Submission(s): 2239
the Warring States Period of ancient China(476 BC to 221 BC), there
were seven kingdoms in China ---- they were Qi, Chu, Yan, Han, Zhao, Wei
and Qin. Ying Zheng was the king of the kingdom Qin. Through 9 years of
wars, he finally conquered all six other 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.
each test case, print a line indicating the above mentioned maximum
ratio A/B. The result should be rounded to 2 digits after decimal point.
4
1 1 20
1 2 30
200 2 80
200 1 100
3
1 1 20
1 2 30
2 2 40
70.00
#include <stdio.h>
#include <algorithm>
#include <string.h>
#include <math.h>
using namespace std;
typedef double type;
const int N = ;
const double INF = ;
struct Point
{
int x,y;
} p[N];
double graph[N][N];
int person[N];
int n,m;
int pre[N];
type path[N][N],low[N]; ///path[i][j]用于记录i到j路径上的权值最大的边
bool vis[N],used[N][N];
type prim(int pos,int n){
memset(used,false,sizeof(used));
memset(vis,false,sizeof(vis));
memset(path,,sizeof(path));
vis[pos]=true;
type cost = ;
for(int i=;i<=n;i++){
low[i]= graph[pos][i];
pre[i]=;
}
low[pos]=;
for(int i=;i<n;i++){
type Min = INF;
for(int j=;j<=n;j++){
if(!vis[j]&&low[j]<Min){
pos = j;
Min = low[j];
}
}
used[pre[pos]][pos] = used[pos][pre[pos]] = true;
cost+= Min;
vis[pos] = true;
for(int j=;j<=n;j++){
if(vis[j]&&j!=pos){
path[pos][j] = path[j][pos] = max(low[pos],path[j][pre[pos]]);
}
if(!vis[j]&&low[j]>graph[pos][j]){
low[j]=graph[pos][j];
pre[j] = pos;
}
}
}
return cost;
}
double dis(Point a,Point b)
{
return sqrt(1.0*((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)));
}
void init()
{
for(int i=; i<=n; i++)
{
for(int j=; j<=n; j++)
{
if(i==j) graph[i][j] = ;
else graph[i][j] = INF;
}
}
} int main()
{
int tcase;
scanf("%d",&tcase);
while(tcase--)
{
scanf("%d",&n);
init();
for(int i=; i<=n; i++)
{
scanf("%d%d%d",&p[i].x,&p[i].y,&person[i]);
}
for(int i=;i<=n;i++){
for(int j=i+;j<=n;j++){
graph[i][j] = graph[j][i] = dis(p[i],p[j]);
}
}
double MST = prim(,n);
double Max = -;
for(int i=;i<=n;i++){ ///枚举所有的边
for(int j=;j<=n;j++){
if(i!=j){
if(used[i][j]){ ///如果枚举的边属于最小生成树,那么结果为 A/(MST-此边)
Max = max(Max,(person[i]+person[j])/(MST-graph[i][j]));
}else{ ///如果枚举的边不属于最小生成树,那么必定要删掉最小生成树中的一条边,删掉的肯定就是i-j之间最长的那条
Max = max(Max,(person[i]+person[j])/(MST-path[i][j]));
}
} }
}
printf("%.2lf\n",Max);
}
return ;
}
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