PAT_A1087#All Roads Lead to Rome
Source:
Description:
Indeed there are many different tourist routes from our city to Rome. You are supposed to find your clients the route with the least cost while gaining the most happiness.
Input Specification:
Each input file contains one test case. For each case, the first line contains 2 positive integers N (2), the number of cities, and K, the total number of routes between pairs of cities; followed by the name of the starting city. The next N−1 lines each gives the name of a city and an integer that represents the happiness one can gain from that city, except the starting city. Then Klines follow, each describes a route between two cities in the format
City1 City2 Cost
. Here the name of a city is a string of 3 capital English letters, and the destination is alwaysROM
which represents Rome.
Output Specification:
For each test case, we are supposed to find the route with the least cost. If such a route is not unique, the one with the maximum happiness will be recommanded. If such a route is still not unique, then we output the one with the maximum average happiness -- it is guaranteed by the judge that such a solution exists and is unique.
Hence in the first line of output, you must print 4 numbers: the number of different routes with the least cost, the cost, the happiness, and the average happiness (take the integer part only) of the recommanded route. Then in the next line, you are supposed to print the route in the format
City1->City2->...->ROM
.
Sample Input:
6 7 HZH ROM 100 PKN 40 GDN 55 PRS 95 BLN 80 ROM GDN 1 BLN ROM 1 HZH PKN 1 PRS ROM 2 BLN HZH 2 PKN GDN 1 HZH PRS 1
Sample Output:
3 3 195 97 HZH->PRS->ROM
Keys:
Attention:
- 结点编号从1开始,因为映射判定的条件是结点编号==0
Code:
1 /* 2 Data: 2019-08-27 19:12:20 3 Problem: PAT_A1087#All Roads Lead to Rome 4 AC: 37:38 5 6 题目大意: 7 从起点至终点ROM花费最少且最幸福的一条路, 8 若不唯一,给出平均幸福指数最高的路径 9 10 输入: 11 第一行给出,城市数N,路径数K,起点城市 12 接下来N-1行,城市名,幸福指数 13 接下来K行,v1,v2,cost 14 输出: 15 最短路径数目,花费,幸福指数,平均幸福指数(整数部分,除去起点) 16 起点至终点的路径 17 */ 18 #include<cstdio> 19 #include<string> 20 #include<vector> 21 #include<map> 22 #include<iostream> 23 #include<algorithm> 24 using namespace std; 25 const int M=1e3,INF=1e9; 26 int n,m,v1,v2,t,grap[M][M],d[M],w[M],vis[M],pt=1,optH=0,cnt=0; 27 vector<int> pre[M],path,optPath; 28 map<string,int> mp; 29 string city[M]; 30 31 int ToInt(string s) 32 { 33 if(mp[s] == 0) 34 { 35 city[pt]=s; 36 mp[s]=pt++; 37 } 38 return mp[s]; 39 } 40 41 void Dijskra(int s) 42 { 43 fill(vis,vis+M,0); 44 fill(d,d+M,INF); 45 d[s]=0; 46 for(int i=1; i<=n; i++) 47 { 48 int u=-1,Min=INF; 49 for(int j=1; j<=n; j++) 50 { 51 if(vis[j]==0 && d[j]<Min) 52 { 53 u = j; 54 Min=d[j]; 55 } 56 } 57 if(u==-1) 58 break; 59 vis[u]=1; 60 for(int v=1; v<=n; v++) 61 { 62 if(vis[v]==0 && grap[u][v]!=INF) 63 { 64 if(d[u]+grap[u][v]<d[v]) 65 { 66 pre[v].clear(); 67 pre[v].push_back(u); 68 d[v] = d[u]+grap[u][v]; 69 } 70 else if(d[u]+grap[u][v]==d[v]) 71 pre[v].push_back(u); 72 } 73 } 74 } 75 } 76 77 void DFS(int v) 78 { 79 if(v == 1) 80 { 81 cnt++; 82 int happy=0; 83 for(int i=0; i<path.size(); i++) 84 happy+=w[path[i]]; 85 if(happy > optH) 86 { 87 optH = happy; 88 optPath = path; 89 } 90 else if(happy==optH && path.size()<optPath.size()) 91 optPath = path; 92 return; 93 } 94 path.push_back(v); 95 for(int i=0; i<pre[v].size(); i++) 96 DFS(pre[v][i]); 97 path.pop_back(); 98 } 99 100 int main() 101 { 102 #ifdef ONLINE_JUDGE 103 #else 104 freopen("Test.txt", "r", stdin); 105 #endif // ONLINE_JUDGE 106 107 string s1,s2; 108 cin >> n >> m >> s1; 109 ToInt(s1); 110 for(int i=1; i<n; i++) 111 { 112 cin >> s1; 113 v1 = ToInt(s1); 114 scanf("%d", &w[v1]); 115 if(s1 == "ROM") 116 t = v1; 117 } 118 fill(grap[0],grap[0]+M*M,INF); 119 for(int i=0; i<m; i++) 120 { 121 cin >> s1 >> s2; 122 v1 = ToInt(s1); 123 v2 = ToInt(s2); 124 scanf("%d", &grap[v1][v2]); 125 grap[v2][v1]=grap[v1][v2]; 126 } 127 Dijskra(1); 128 DFS(t); 129 printf("%d %d %d %d\n", cnt,d[t],optH,optH/optPath.size()); 130 printf("%s", city[1].c_str()); 131 for(int i=optPath.size()-1; i>=0; i--) 132 printf("->%s", city[optPath[i]].c_str()); 133 134 return 0; 135 }