Dijkstra.java

package test1;

import java.util.ArrayList;
import java.util.List;

public class Dijkstra {

    public static void main(String[] args) {
        //此路不通
        int m = 10000;
        int[][] weight1 = {//邻接矩阵
                {0, 3, 2000, 7, m},
                {3, 0, 4, 2, m},
                {m, 4, 0, 5, 4},
                {7, 2, 5, 0, 6},
                {m, m, 4, 6, 0}
        };

        int[][] weight2 = {
                {0, 10, m, 30, 100},
                {m, 0, 50, m, m},
                {m, m, 0, m, 10},
                {m, m, 20, 0, 60},
                {m, m, m, m, 0}
        };

        List<String> regions = new ArrayList<String>(){{
            add("A");
            add("B");
            add("C");
            add("D");
            add("E");
        }};

        int start = 0;
        int[] shortPath = minStep(weight1, start, -1, regions);
//        for (int i = 0; i < shortPath.length; i++)
//            System.out.println("从" + start + "出发到" + i + "的最短距离为：" + shortPath[i]);
    }

    public static int[] minStep(int[][] weight, int start, int end, List<String> regions) {
        //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 = weight.length;      //顶点个数
        int[] shortPath = new int[n];  //保存start到其他各点的最短路径
        String[] path = new String[n];  //保存start到其他各点最短路径的字符串表示
        for (int i = 0; i < n; i++)
            path[i] = regions.get(start) + "-->" + regions.get(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，第一个顶点已经求出
        shortPath[start] = 0;
        visited[start] = 1;

        for (int count = 1; count < n; 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 && weight[start][i] < dmin) {
                    dmin = weight[start][i];
                    k = i;
                }
            }

            //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++) {
                if (visited[i] == 0 && weight[start][k] + weight[k][i] < weight[start][i]) {
                    weight[start][i] = weight[start][k] + weight[k][i];
                    path[i] = path[k] + "-->" + regions.get(i);
                }
            }
        }
        if (end == -1) {
            for (int i = 0; i < n; i++) {
                System.out.println("从" + regions.get(start) + "出发到" + regions.get(i) + "的最短路径为：" + path[i] + "，最短距离为：" + shortPath[i]);
            }
            System.out.println("=====================================");
        } else {
            System.out.println("从" + regions.get(start) + "出发到" + regions.get(end) + "的最短路径为：" + path[end] + "，最短距离为：" + shortPath[end]);
        }
        return shortPath;
    }
}