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 <= N <= 500), 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 and V2 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 from V1 to V2, or 0 if not; length is the length of the street; and time 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
1 #include <iostream> 2 #include <algorithm> 3 #include <vector> 4 using namespace std; 5 const int maxn = 510, inf = 0x7fffffff; 6 struct Arc{ 7 int v; 8 int tim, len; 9 }; 10 vector<Arc> arc[maxn]; 11 int N, M, dis[maxn], tim[maxn], pre[maxn], pathLen[maxn], S, T; 12 vector<int> disPath, timPath, tempPath; 13 14 void scan(){ 15 scanf("%d%d", &N, &M); 16 for(int i = 0; i < M; ++ i){ 17 int v1, v2, oneWay; 18 Arc t; 19 scanf("%d%d%d%d%d", &v1, &v2, &oneWay, &t.len, &t.tim); 20 t.v = v2; arc[v1].push_back(t); 21 if(!oneWay) t.v = v1, arc[v2].push_back(t); 22 } 23 scanf("%d%d", &S, &T); 24 } 25 26 void dijkstra_dis(int s){ 27 bool vis[maxn]; 28 fill(vis, vis+maxn, false); 29 fill(dis, dis+maxn, inf); 30 fill(tim, tim+maxn, inf); 31 dis[s] = tim[s] = 0; 32 for(int i = 0; i < N; ++ i){ 33 int u = -1, minDis = inf; 34 for(int j = 0; j < N; ++ j){ 35 if(!vis[j] && dis[j] < minDis){ 36 minDis = dis[j]; 37 u = j; 38 } 39 } 40 if(u == -1) return; 41 vis[u] = true; 42 for(int k = 0; k < arc[u].size(); ++ k){ 43 int v = arc[u][k].v; 44 if(!vis[v]){ 45 if(dis[u] + arc[u][k].len < dis[v]){ 46 dis[v] = dis[u] + arc[u][k].len; 47 tim[v] = tim[u] + arc[u][k].tim; 48 pre[v] = u; 49 }else if(dis[u] + arc[u][k].len == dis[v] && tim[u] + arc[u][k].tim < tim[v]){ 50 tim[v] = tim[u] + arc[u][k].tim; 51 pre[v] = u; 52 } 53 } 54 } 55 } 56 } 57 58 void dijkstra_tim(int s){ 59 bool vis[maxn]; 60 fill(vis, vis+maxn, false); 61 fill(tim, tim+maxn, inf); 62 fill(pathLen, pathLen+maxn, inf); 63 tim[s] = 0, pathLen[s] = 1; 64 for(int i = 0; i < N; i ++){ 65 int u = -1, minTim = inf; 66 for(int j = 0; j < N; j ++){ 67 if(!vis[j] && tim[j] < minTim){ 68 minTim = tim[j]; 69 u = j; 70 } 71 } 72 if(u == -1) return; 73 vis[u] = true; 74 for(int k = 0; k < arc[u].size(); k ++){ 75 int v = arc[u][k].v; 76 if(!vis[v]){ 77 if(tim[u] + arc[u][k].tim < tim[v]){ 78 tim[v] = tim[u] + arc[u][k].tim; 79 pre[v] = u; 80 pathLen[v] = pathLen[u] + 1; 81 }else if(tim[u] + arc[u][k].tim == tim[v] && pathLen[u]+1 < pathLen[v]){ 82 pre[v] = u; 83 pathLen[v] = pathLen[u] + 1; 84 } 85 } 86 } 87 } 88 } 89 90 void dfs(int t){ 91 tempPath.push_back(t); 92 if(pre[t] != -1){ 93 dfs(pre[t]); 94 } 95 } 96 97 void printPath(vector<int> &path){ 98 for(int i = path.size()-1; i >= 0; -- i){ 99 printf("%d", path[i]); 100 if(i != 0) printf(" -> "); 101 } 102 printf("\n"); 103 } 104 105 int main() 106 { 107 fill(pre, pre+maxn, -1); 108 scan(); 109 dijkstra_dis(S); 110 dfs(T); 111 disPath = tempPath; 112 fill(pre, pre+maxn, -1); 113 dijkstra_tim(S); 114 tempPath.clear();//clear data 115 dfs(T); 116 timPath = tempPath; 117 if(timPath == disPath){ 118 printf("Distance = %d; Time = %d: ", dis[T], tim[T]); 119 printPath(disPath); 120 }else{ 121 printf("Distance = %d: ", dis[T]); printPath(disPath); 122 printf("Time = %d: ", tim[T]); printPath(timPath); 123 } 124 return 0; 125 }
