最短路径(邻接矩阵)-Dijkstra算法

    Dijkstra算法又叫作迪杰斯特拉算法，是利用"贪心法"(在对问题进行求解时，总是做出在当前看来最好的选择策略)设计算法的一个成功范例。

        适用条件:带权无环和无负权值

       举个栗子:

  

 

   Dijkstra算法的代码实现如下:

package com.threeTop.www;

import java.util.Stack;

/**
 * 邻接矩阵存储方式的Dijkstra算法
 * @author wjgs
 *
 */
public class Dijkstra {
	
	    //通过下标映射元素值
		private int[] mapping;
		
		//图的二维数组
		private int[][] matrix;
		
		/**
		 * 初始化图的顶点
		 * @param vertexes 顶点数组
		 */
		 public Dijkstra(int []vertexes)
		 {
			 
			 int length=vertexes.length;
			 mapping=new int[length];
			 matrix=new int[length][length]; //图的二维矩阵
			 for(int i=0;imapping.length-1||y>mapping.length-1)
			 {
				 throw new IndexOutOfBoundsException("边的顶点不存在!");
			 }
			
			 //增加边的权值
			 matrix[x][y]=value;
			 
		 }
		 
		 /**
		  * Dijkstra算法实现到各点的最短路径
		  * @param start
		  */
		 
		 public void dijkstra(int start)
		 {
			 int length =mapping.length;
			 int x=-1;   //记录起始点
			 for(int i=0;i0)
				 {
					 path[i]=x;
				 }
				 else
				 {
					 //不可达，则赋前一个顶点下标为-1
					 path[i]=-1;
				 }
			 }
			 
			 //先把起始顶点加入s
			 s[x]=1;
			 
			 for(int i=0;istack=new Stack();
			 for(int i=0;i"+mapping[i]+"  最短路径长度:"+distance[x][i]);
					 
					 //path存储路径，可以逆序输出，可以借助栈实现正序输出
					 System.out.print("逆序最短路径输出:");
					 int index=i;
					 while(index!=-1)
					 {
						 System.out.print(mapping[index]+" ");
						 stack.push(mapping[index]);
						 index=path[index];
					 }
					 System.out.print("正序最短路径输出:");
					 while(!stack.isEmpty())
					 {
						 System.out.print(stack.pop()+" ");
					 }
					 System.out.println();
				 }
			 }
			
			 
		 }
		 

	public static void main(String[] args) {
		int[] vetexes={1,2,3,4,5,6};
		Dijkstra graph=new Dijkstra(vetexes);
		graph.addEdge(1, 2,16);graph.addEdge(2, 1,16);
		graph.addEdge(1, 3,1);graph.addEdge(3, 1,1);
		graph.addEdge(1, 5,12);graph.addEdge(5, 1,12);
		graph.addEdge(1, 6,15);graph.addEdge(6, 1,15);
		graph.addEdge(2, 4,2);graph.addEdge(4, 2,2);
		graph.addEdge(2, 6,8);graph.addEdge(6, 2,8);
		graph.addEdge(3, 5,5);graph.addEdge(5, 3,5);
		graph.addEdge(4, 6,3);graph.addEdge(6, 4,3);
		graph.addEdge(5, 6,8);graph.addEdge(6, 5,8);
		graph.addEdge(4, 5,9);graph.addEdge(5, 4,9);
		graph.dijkstra(1);

	}

}