A1072. Gas Station (30)

A gas station has to be built at such a location that the minimum distance between the station and any of the residential housing is as far away as possible. However it must guarantee that all the houses are in its service range.

Now given the map of the city and several candidate locations for the gas station, you are supposed to give the best recommendation. If there are more than one solution, output the one with the smallest average distance to all the houses. If such a solution is still not unique, output the one with the smallest index number.

Input Specification:

Each input file contains one test case. For each case, the first line contains 4 positive integers: N (<= 10³), the total number of houses; M (<= 10), the total number of the candidate locations for the gas stations; K (<= 10⁴), the number of roads connecting the houses and the gas stations; and D_S, the maximum service range of the gas station. It is hence assumed that all the houses are numbered from 1 to N, and all the candidate locations are numbered from G1 to GM.

Then K lines follow, each describes a road in the format
P1 P2 Dist
where P1 and P2 are the two ends of a road which can be either house numbers or gas station numbers, and Dist is the integer length of the road.

Output Specification:

For each test case, print in the first line the index number of the best location. In the next line, print the minimum and the average distances between the solution and all the houses. The numbers in a line must be separated by a space and be accurate up to 1 decimal place. If the solution does not exist, simply output “No Solution”.

Sample Input 1:

4 3 11 5
1 2 2
1 4 2
1 G1 4
1 G2 3
2 3 2
2 G2 1
3 4 2
3 G3 2
4 G1 3
G2 G1 1
G3 G2 2

Sample Output 1:

G1
2.0 3.3

Sample Input 2:

2 1 2 10
1 G1 9
2 G1 20

Sample Output 2:

No Solution

  1 // hahaha.cpp : 定义控制台应用程序的入口点。
  2 //
  3
  4 #include "stdafx.h"
  5 #include <stdio.h>
  6 #include <iostream>
  7 #include <vector>
  8 #include <map>
  9 #include <string>
 10 #include <cstdio>
 11 #include <set>
 12 #include <algorithm>
 13 #include <string.h>
 14 using namespace std;
 15 const int maxn=1020;
 16 int n,m,k,ds;
 17
 18 int G[maxn][maxn];
 19
 20 int getid(char a[])
 21 {
 22  int len=strlen(a);
 23  int id=0;
 24  for(int i=0;i<len;i++)
 25  {
 26  if(a[i]!=‘G‘)
 27  {
 28    id=id*10+a[i]-‘0‘;
 29  }
 30  }
 31 if(a[0]==‘G‘)return id+n;
 32 else
 33  return id;
 34 }
 35 const int INF=1000000000;
 36 int d[maxn];
 37 int vis[maxn]={false};
 38 void dij(int s)
 39 {
 40   memset(vis,false,sizeof(vis));
 41   fill(d,d+maxn,INF);
 42   d[s]=0;
 43   for(int i=1;i<=m+n;i++)
 44   {
 45         int u=-1,min=INF;
 46         for(int j=1;j<=m+n;j++)
 47             {
 48                 if(d[j]<min && vis[j]==false)
 49                     {
 50                     u=j;
 51                     min=d[j];
 52                     }
 53             }
 54                 if(u==-1)return;
 55                 vis[u]=true;
 56                 for(int k=1;k<=n+m;k++)
 57                 {
 58                     if(vis[k]==false&&G[u][k]!=INF)
 59                     {
 60                         if(G[u][k]+d[u]<d[k])
 61                         {
 62                             d[k]=G[k][u]+d[u];
 63                         }
 64                     }
 65                 }
 66     }
 67 }
 68
 69
 70
 71 int main()
 72 {
 73     scanf("%d %d %d %d",&n,&m,&k,&ds);
 74
 75     fill(G[0],G[0]+maxn*maxn,INF);
 76     for(int i=0;i<k;i++)
 77     {
 78     char p1[15],p2[15];
 79     int dist;
 80     scanf("%s %s %d",p1,p2,&dist);
 81     int id1=getid(p1);
 82     int id2=getid(p2);
 83     G[id1][id2]=dist;
 84     G[id2][id1]=dist;
 85
 86     }
 87     //输入完毕
 88
 89     //处理图,对加油站处理，求平均距离，和最大的最近距离
 90     double ansdis=-1,ansavg=INF;
 91     int ansid=-1;
 92     for(int i=n+1;i<=n+m;i++)
 93     {
 94         double mindis=INF,avg=0;
 95         bool flag=false;
 96         double sum=0;
 97         dij(i);
 98         for(int j=1;j<=n;j++)
 99         {
100             if(d[j]>ds)
101             {
102             flag=true;
103             break;
104             }
105             if(d[j]<mindis)mindis=d[j];
106             sum+=d[j];
107         }
108         if(flag==true)continue;
109
110      avg=sum/n;
111      if(mindis>ansdis)
112      {
113      ansid=i;
114      ansdis=mindis;
115      ansavg=avg;
116      }
117      else if(mindis==ansdis&&avg<ansavg)
118      {
119         ansid=i;
120         ansavg=avg;
121      }
122 }
123
124      if(ansid==-1)printf("No Solution\n");
125      else
126          {
127          printf("G%d\n",ansid-n);
128          printf("%.1f %.1f\n",ansdis,ansavg);
129          }
130     return 0;
131 }