dijkstra 求最短路径

dijkstra算法写起来很容易，但是理解，证明它的正确性却不容易。

#include"Graph.h" #include<assert.h> #include<iostream> #include<fstream> #include<limits> using namespace std; const int MAX=std::numeric_limits<int>:: max(); int main() { ifstream cin("input.txt"); int vertex_num=5; Graph<char,int> myGraph(vertex_num); myGraph.Init(cin); //myGraph.RandInit(); int *visited=new int[vertex_num]; int *dis=new int[vertex_num]; int *output=new int[vertex_num]; visited[0]=1; output[0]=0; for(int i=1;i<vertex_num;i++) { dis[i]=myGraph.getWeight(0,i); visited[i]=0; output[i]=0; } for(int i=1;i<vertex_num;i++) { int min=MAX; int min_index=-1; for(int j=0;j<vertex_num;j++) { if(visited[j]==0&&dis[j]<min) { min=dis[j]; min_index=j; } } visited[min_index]=1; for(int j=0;j<vertex_num;j++) { int temp_weight; if(visited[j]==0&&(temp_weight=myGraph.getWeight(min_index,j))<MAX&&dis[j]>dis[min_index]+temp_weight) { dis[j]=dis[min_index]+temp_weight; output[j]=min_index; } } } for(int i=1;i<vertex_num;i++) { int j=i; cout<<j<<"到0的路径是长度:"<<dis[j]<<"路径是:"; while(j!=0) { cout<<j<<" "; j=output[j]; } cout<<0<<endl; } return 0; }