1072.Gas Station

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【题意】

找一个到所有房屋最短距离最远，平均距离最近，且覆盖所有房屋的加油站

【思路】

把住房和加油站都视作普通节点，对每个加油站用一次Dijkstra算法即可

【注意点】

此题Dijkstra算法中可以不用遍历到每个点，只要把所有房屋都访问到了就可以了，即使有些加油站访问不到或者超出了服务范围也不要紧。

#include <iostream>#include <string>#include <vector>#include <algorithm>#include <cstdlib>#include <cstdio>using namespace std;#define MAXIMUM 0x0fffffffint n,m,k,ds;vector<bool> visited;vector<int> dist;vector<vector<int>> weight;typedef struct{int index;int minDist;float avgDist;}gasStation;bool cmp(gasStation g1, gasStation g2){if(g1.minDist>g2.minDist){return 1;}else if(g1.minDist==g2.minDist && g1.avgDist<g2.avgDist){return 1;}else if(g1.minDist==g2.minDist && g1.avgDist==g2.avgDist && g1.index<g2.index){return 1;}else{return 0;}}int lable2index(string lable){int index = 0;if(lable[0]=='G'){for(int i=1; i<lable.length(); i++){index = index*10+lable[i]-'0';}index += n-1;}else{for(int i=0; i<lable.length(); i++){index = index*10+lable[i]-'0';}index--;}return index;}int main(int argc, char const *argv[]){cin >> n >> m >> k >> ds;visited.resize(n+m);dist.resize(n+m);weight.resize(n+m,vector<int>(n+m));for(int i=0; i<n+m; i++){for(int j=0; j<=i; j++){if(i==j){weight[i][j] = 0;}else{weight[i][j] = weight[j][i] = MAXIMUM;}}}//0~n-1:residential housing//n~n+m-1:gas stationfor(int i=0; i<k; i++){string ends[2];int d,index[2];cin >> ends[0] >> ends[1] >> d;index[0] = lable2index(ends[0]);index[1] = lable2index(ends[1]);weight[index[0]][index[1]] = weight[index[1]][index[0]] = d;}vector<gasStation> stations;//Dijkstrafor(int gasIndex=n; gasIndex<n+m; gasIndex++){visited.assign(n+m,0);dist.assign(n+m,MAXIMUM);visited[gasIndex] = 1;dist[gasIndex] = 0;bool valid = 1;int minDist = MAXIMUM;float avgDist = 0.0;int cnt = n;int index = gasIndex;//并不需要把每个节点都遍历到，只需要把n个城市遍历到即可while(cnt){int min = MAXIMUM;int nextIndex;for(int j=0; j<n+m; j++){if(!visited[j]){if(dist[index]+weight[index][j]<dist[j]){dist[j] = dist[index]+weight[index][j];}if(dist[j]<min){min = dist[j];nextIndex = j;}}}if(min>ds){valid = 0;break;}index = nextIndex;visited[index] = 1;//编号小于n的点代表住房if(index<n){cnt--;if(dist[index]<minDist){minDist = dist[index];}avgDist += dist[index];}}avgDist /= n;if(valid){gasStation tmp;tmp.index = gasIndex;tmp.minDist = minDist;tmp.avgDist = avgDist;stations.push_back(tmp);}}if(stations.empty()){cout << "No Solution";}else{sort(stations.begin(),stations.end(),cmp);cout << 'G' << stations[0].index-n+1 << endl;printf("%d.0 %.1f", stations[0].minDist, stations[0].avgDist);}system("pause");return 0;}

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