1072 Gas Station

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 (≤), the total number of houses; M (≤), the total number of the candidate locations for the gas stations; K (≤), 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

题意：

　　给出m个候选的加油站建造地点，要求从中选取一个，使其距离住宅区的距离尽可能的远。如果存在相等的情况，则输出距离平均值最小的那个。

思路：

　　对每一个加油站运用Dijkstra算法求出该加油站到达其他结点的最小距离。然后在最小距离中寻找最大值。

Code：

#include <bits/stdc++.h>

using namespace std;

const int inf = 999999999;
int grap[1020][1020];
int visited[1020], dist[1020];

int main() {
    int n, m, k, ds;
    cin >> n >> m >> k >> ds;
    fill(grap[0], grap[0] + 1020 * 1020, inf);
    for (int i = 0; i < 1020; ++i) grap[i][i] = 0;
    for (int i = 0; i < k; ++i) {
        string p1, p2;
        int d;
        cin >> p1 >> p2 >> d;
        int v1, v2;
        if (p1[0] == 'G') {
            v1 = stoi(p1.substr(1)) + n;
        } else {
            v1 = stoi(p1);
        }
        if (p2[0] == 'G') {
            v2 = stoi(p2.substr(1)) + n;
        } else {
            v2 = stoi(p2);
        }
        grap[v1][v2] = grap[v2][v1] = d;
        grap[v1][v2] = grap[v2][v1] = min(d, grap[v1][v2]);
    }
    int ansid = -1;
    double ansdist = -1, ansaver = inf;
    for (int i = n + 1; i <= n + m; ++i) {
        double aver = 0, mindist = inf;
        fill(visited, visited + 1020, 0);
        fill(dist, dist + 1020, inf);
        dist[i] = 0;
        for (int j = 0; j < n + m; ++j) {
            int u = -1, minn = inf;
            for (int k = 1; k <= n + m; ++k) {
                if (visited[k] == 0 && dist[k] < minn) {
                    u = k;
                    minn = dist[k];
                }
            }
            if (u == -1) break;
            visited[u] = 1;
            for (int k = 1; k <= n + m; ++k) {
                if (visited[k] == 0 && dist[k] > dist[u] + grap[u][k])
                    dist[k] = dist[u] + grap[u][k];
            }
        }
        for (int j = 1; j <= n; ++j) {
            if (dist[j] > ds) {
                mindist = -1;
                break;
            }
            if (dist[j] < mindist) mindist = dist[j];
            aver += 1.0 * dist[j];
        }
        if (mindist == -1) continue;
        aver = aver / n;
        if (mindist > ansdist) {
            ansdist = mindist;
            ansaver = aver;
            ansid = i;
        } else if (mindist == ansdist && aver < ansaver) {
            ansaver = aver;
            ansid = i;
        }
    }

    if (ansid == -1)
        printf("No Solution
");
    else
        printf("G%d
%.1f %.1f
", ansid - n, ansdist, ansaver);

    return 0;
}

参考：

　　https://www.liuchuo.net/archives/2376