PAT_A1111#Online Map
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Description:
Input our current position and a destination, an online map can recommend several paths. Now your job is to recommend two paths to your user: one is the shortest, and the other is the fastest. It is guaranteed that a path exists for any request.
Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers N (2), and M, being the total number of streets intersections on a map, and the number of streets, respectively. Then M lines follow, each describes a street in the format:
V1 V2 one-way length time
where
V1
andV2
are the indices (from 0 to N−1) of the two ends of the street;one-way
is 1 if the street is one-way fromV1
toV2
, or 0 if not;length
is the length of the street; andtime
is the time taken to pass the street.Finally a pair of source and destination is given.
Output Specification:
For each case, first print the shortest path from the source to the destination with distance
D
in the format:Distance = D: source -> v1 -> ... -> destination
Then in the next line print the fastest path with total time
T
:Time = T: source -> w1 -> ... -> destination
In case the shortest path is not unique, output the fastest one among the shortest paths, which is guaranteed to be unique. In case the fastest path is not unique, output the one that passes through the fewest intersections, which is guaranteed to be unique.
In case the shortest and the fastest paths are identical, print them in one line in the format:
Distance = D; Time = T: source -> u1 -> ... -> destination
Sample Input 1:
10 15 0 1 0 1 1 8 0 0 1 1 4 8 1 1 1 3 4 0 3 2 3 9 1 4 1 0 6 0 1 1 7 5 1 2 1 8 5 1 2 1 2 3 0 2 2 2 1 1 1 1 1 3 0 3 1 1 4 0 1 1 9 7 1 3 1 5 1 0 5 2 6 5 1 1 2 3 5
Sample Output 1:
Distance = 6: 3 -> 4 -> 8 -> 5 Time = 3: 3 -> 1 -> 5
Sample Input 2:
7 9 0 4 1 1 1 1 6 1 1 3 2 6 1 1 1 2 5 1 2 2 3 0 0 1 1 3 1 1 1 3 3 2 1 1 2 4 5 0 2 2 6 5 1 1 2 3 5
Sample Output 2:
Distance = 3; Time = 4: 3 -> 2 -> 5
Keys:
- 最短路径
Attention:
- 其实就是求两次最短路径,代码code一遍再copy一遍,考试的时候怎么快怎么来,优化代码反而容易出错
Code:
1 /* 2 Data: 2019-06-16 17:40:10 3 Problem: PAT_A1111#Online Map 4 AC: 42:06 5 6 题目大意: 7 给出当前位置和目的地,给出最短路径和最快路径 8 输入: 9 第一行给出,结点数N,边数M 10 接下来M行,v1,v2,单/双向,距离,时间 11 最后一行,起点,终点 12 输出: 13 最短距离,输出路径,不唯一则选择最快的 14 最短时间,输出路径,不唯一则选择经过结点最少的 15 */ 16 17 #include<cstdio> 18 #include<vector> 19 #include<algorithm> 20 using namespace std; 21 const int M=1e3,INF=1e9; 22 int grap[M][M],cost[M][M],vis[M],d[M]; 23 int n,v1,v2,optValue=INF,optCost=INF; 24 vector<int> pre[M],temp,opt,pro[M],fav; 25 26 void DijskraP(int s) 27 28 fill(vis,vis+M,0); 29 fill(d,d+M,INF); 30 d[s]=0; 31 for(int i=0; i<n; i++) 32 33 int u=-1,Min=INF; 34 for(int j=0; j<n; j++) 35 36 if(vis[j]==0 && d[j]<Min) 37 38 Min=d[j]; 39 u=j; 40 41 42 if(u==-1) 43 return; 44 vis[u]=1; 45 for(int v=0; v<n; v++) 46 47 if(vis[v]==0 && grap[u][v]!=INF) 48 49 if(d[u]+grap[u][v] < d[v]) 50 51 d[v] = d[u]+grap[u][v]; 52 pre[v].clear(); 53 pre[v].push_back(u); 54 55 else if(d[u]+grap[u][v] == d[v]) 56 pre[v].push_back(u); 57 58 59 60 61 62 void DFSP(int v) 63 64 if(v == v1) 65 66 temp.push_back(v); 67 int value=0; 68 for(int i=temp.size()-1; i>0; i--) 69 70 int id=temp[i],idNext=temp[i-1]; 71 value += cost[id][idNext]; 72 73 if(value < optValue) 74 75 optValue = value; 76 opt = temp; 77 78 temp.pop_back(); 79 return; 80 81 temp.push_back(v); 82 for(int i=0; i<pre[v].size(); i++) 83 DFSP(pre[v][i]); 84 temp.pop_back(); 85 86 87 void DijskraC(int s) 88 89 fill(vis,vis+M,0); 90 fill(d,d+M,INF); 91 d[s]=0; 92 for(int i=0; i<n; i++) 93 94 int u=-1,Min=INF; 95 for(int j=0; j<n; j++) 96 97 if(vis[j]==0 && d[j]<Min) 98 99 Min=d[j]; 100 u=j; 101 102 103 if(u==-1) 104 return; 105 vis[u]=1; 106 for(int v=0; v<n; v++) 107 108 if(vis[v]==0 && cost[u][v]!=INF) 109 110 if(d[u]+cost[u][v] < d[v]) 111 112 d[v] = d[u]+cost[u][v]; 113 pro[v].clear(); 114 pro[v].push_back(u); 115 116 else if(d[u]+cost[u][v] == d[v]) 117 pro[v].push_back(u); 118 119 120 121 122 123 void DFSC(int v) 124 125 if(v == v1) 126 127 temp.push_back(v); 128 if(temp.size() < optCost) 129 130 optCost = temp.size(); 131 fav = temp; 132 133 temp.pop_back(); 134 return; 135 136 temp.push_back(v); 137 for(int i=0; i<pro[v].size(); i++) 138 DFSC(pro[v][i]); 139 temp.pop_back(); 140 141 142 int main() 143 144 #ifdef ONLINE_JUDGE 145 #else 146 freopen("Test.txt", "r", stdin); 147 #endif 148 149 fill(grap[0],grap[0]+M*M,INF); 150 fill(cost[0],cost[0]+M*M,INF); 151 152 int m,one; 153 scanf("%d%d", &n,&m); 154 for(int i=0; i<m; i++) 155 156 scanf("%d%d%d", &v1,&v2,&one); 157 scanf("%d%d", &grap[v1][v2],&cost[v1][v2]); 158 if(!one) 159 160 grap[v2][v1]=grap[v1][v2]; 161 cost[v2][v1]=cost[v1][v2]; 162 163 164 scanf("%d%d",&v1,&v2); 165 DijskraP(v1); 166 DFSP(v2); 167 printf("Distance = %d", d[v2]); 168 DijskraC(v1); 169 DFSC(v2); 170 if(opt == fav) 171 172 printf("; Time = %d: %d",d[v2],opt[opt.size()-1]); 173 for(int i=opt.size()-2; i>=0; i--) 174 printf(" -> %d", opt[i]); 175 176 else 177 178 printf(": %d", opt[opt.size()-1]); 179 for(int i=opt.size()-2; i>=0; i--) 180 printf(" -> %d", opt[i]); 181 printf("\n"); 182 printf("Time = %d: %d", d[v2],fav[fav.size()-1]); 183 for(int i=fav.size()-2; i>=0; i--) 184 printf(" -> %d", fav[i]); 185 186 187 188 return 0; 189
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