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
;    //存放从start到其他各点的最短路径
String[] path=new String
; //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
;   //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]);
}
}

}