单源最短路径（ Dijkstra算法）JAVA实现

单源最短路径（ Dijkstra算法）JAVA实现

package dijkstra;public class Graph {final int max=100;/* * 顶点节点 */public class VexNode{int adjvex;int data;}VexNode[] vexNodes;int[] thevexs; //顶点集合int[][] edges = new int[max][max]; //边集合/* * 创建图 */public void createGraph(Graph graph,int[][] A,int[] vexs) {thevexs=vexs;for (int i = 0; i < vexs.length; i++) {  for (int j = 0; j < vexs.length; j++) {  graph.edges[i][j] = A[i][j];}}}/* * 输出图 */public void printGraph(Graph graph) {for (int i = 0; i < graph.thevexs.length; i++) {for (int j = 0; j < graph.thevexs.length; j++) {//没有路径则输出/if (graph.edges[i][j]==1000) {System.out.printf("%4s","/"); }else {System.out.printf("%4d",graph.edges[i][j]);}}System.out.println("\n");}}}

package dijkstra;public class DijkStra {final int max = 100; public static int[] Dijsktra(Graph graph,int start){       //接受一个有向图的权重矩阵，和一个起点编号start（从0编号，顶点存在数组中）          //返回一个int[] 数组，表示从start到它的最短路径长度          int n = graph.thevexs.length;        //顶点个数          int[] shortPath = new int[n];    //存放从start到其他各点的最短路径          String[] path=new String[n]; //存放从start到其他各点的最短路径的字符串表示           for(int i=0;i<n;i++)               path[i]=new String(start+"-->"+i);          int[] visited = new int[n];   //标记当前该顶点的最短路径是否已经求出,1表示已求出                    //初始化，第一个顶点求出          shortPath[start] = 0;          visited[start] = 1;            for(int count = 1;count <= n - 1;count++)  //要加入n-1个顶点          {                 int k = -1;    //选出一个距离初始顶点start最近的未标记顶点              int dmin = Integer.MAX_VALUE;              for(int i = 0;i < n;i++)              {                              if(visited[i] == 0 && graph.edges[start][i]<dmin)                  {                      dmin = graph.edges[start][i];                                        k = i;                  }                                      }              System.out.println("k="+k);                             //将新选出的顶点标记为已求出最短路径，且到start的最短路径就是dmin              shortPath[k] = dmin;                visited[k] = 1;                  //以k为中间点，修正从start到未访问各点的距离              for(int i = 0;i < n;i++)              {                 // System.out.println("k="+k);                  if(visited[i] == 0 && graph.edges[start][k] + graph.edges[k][i] < graph.edges[start][i]){                  graph.edges[start][i] = graph.edges[start][k] + graph.edges[k][i];                                            path[i]=path[k]+"-->"+i;                                        }                                }                   }           for(int i=0;i<n;i++)             System.out.println("从"+start+"出发到"+i+"的最短路径为："+path[i]);             System.out.println("=====================================");                  return shortPath;      }  }

package dijkstra;public class Test {public static void main(String[] args) {final int INF = 1000;int[] vexs = {0,1,2,3,4,5};int[][] A ={{0,50,10,INF,INF,INF},{INF,0,15,50,10,INF},{20,INF,0,15,INF,INF},{INF,20,INF,0,35,INF},{INF,INF,INF,30,0,INF},{INF,INF,INF,3,INF,0},};Graph graph = new Graph();graph.createGraph(graph, A, vexs);graph.printGraph(graph);DijkStra dijkStra = new DijkStra();int[] shortPath = dijkStra.Dijsktra(graph, 2);      for(int i = 0;i < shortPath.length;i++)        if (shortPath[i]!=INF) {             System.out.println("从"+"2"+"出发到"+i+"的最短距离为："+shortPath[i]);          }    }       }