dijkstra求最短路
dijkstra和Prim很像，区别在于Prim在找到离MST最近的结点后把它加入MST并更新与此结点相邻的结点离MST的最短距离；而dijsktra中，找到当前离起点最近的结点后，更新与它相邻的结点距离起点的最短距离和最短路径。
代码如下：
1 //dijkstra 2 #include <iostream> 3 #include <cstring> 4 #include <vector> 5 using namespace std; 6 7 const int INF=0x3f3f3f3f; 8 9 struct Edge{ 10 int vertex, weight; 11 }; 12 13 class Graph{ 14 private: 15 int n; 16 vector<Edge> *edges; 17 bool *visited; 18 public: 19 int *prev; //stores index of previous node 20 int *dist; //stores min dist of a node to the starting node 21 Graph(int input_n){ 22 n=input_n; 23 edges=new vector<Edge>[n]; 24 prev=new int[n]; 25 dist=new int[n]; 26 visited=new bool[n]; 27 memset(prev,-1,n*sizeof(int)); 28 memset(visited,0,n); 29 memset(dist,0x3f,n*sizeof(int)); 30 } 31 ~Graph(){ 32 delete[] edges; 33 delete[] visited; 34 delete[] prev; 35 delete[] dist; 36 } 37 void insert(int x, int y, int weight){ 38 edges[x].push_back(Edge{y,weight}); 39 edges[y].push_back(Edge{x,weight}); 40 } 41 void dijkstra(int start_v){ 42 dist[start_v]=0; 43 //every time settle one vertex 44 for(int i=0;i<n;i++){ 45 int min_dist=INF, min_vertex = 0; 46 //find the current nearest vertex 47 for(int j=0;j<n;j++){ 48 if(!visited[j]&&dist[j]<min_dist){ 49 min_dist=dist[j]; 50 min_vertex=j; 51 } 52 } 53 visited[min_vertex]=1; 54 //update shortest dist of adjcent vertices 55 //and update previous node, which is min_vertex 56 for(Edge &j: edges[min_vertex]){ 57 if(min_dist+j.weight<dist[j.vertex]){ 58 dist[j.vertex]=min_dist+j.weight; 59 prev[j.vertex]=min_vertex; 60 } 61 } 62 } 63 } 64 void printPath(int cur_v){ 65 if(prev[cur_v]!=-1){ 66 printPath(prev[cur_v]); 67 } 68 cout<<cur_v<<" "; 69 } 70 }; 71 72 int main() { 73 int n, m; 74 cin >> n >> m; 75 Graph g(n); 76 for (int i = 0; i < m; i++) { 77 int a, b, c; 78 cin >> a >> b >> c; 79 g.insert(a, b, c); 80 } 81 g.dijkstra(0); 82 for (int i = 0; i < n; i++) { 83 cout << i << ": " << g.dist[i] << endl; 84 } 85 for(int i=0;i<n;i++){ 86 g.printPath(i); 87 cout<<endl; 88 } 89 return 0; 90 }
