算法<九>Dijkstra算法(迪杰斯特拉算法)

package com.example.demo.SortAlgorithm;
/*
 *
 * @Author: i_heh
 * @Date: 2019/7/5
 * @Time: 14:25
 * @Description: 迪杰斯特拉算法
 *
 */
public class Dijkstra {

    private static int N = 1000;
    private static int[][] Graph = {
            {0, 1, 5, N, N, N, N, N, N},
            {1, 0, 3, 7, 5, N, N, N, N},
            {5, 3, 0, N, 1, 7, N, N, N},
            {N, 7, N, 0, 2, N, 3, N, N},
            {N, 5, 1, 2, 0, 3, 6, 9, N},
            {N, N, 7, N, 3, 0, N, 5, N},
            {N, N, N, 3, 6, N, 0, 2, 7},
            {N, N, N, N, 9, 5, 2, 0, 4},
            {N, N, N, N, N, N, 7, 4, 0}};

    public static void main(String[] args) {
        dijkstra(0, Graph);
    }

    /**
     * Dijkstra最短路径。
     * 即图中"节点vs"到其它各个节点的最短路径。
     *
     * @param vs    起始节点
     * @param Graph 图
     */
    public static void dijkstra(int vs, int[][] Graph) {
        int NUM = Graph[0].length;
        // 前驱节点数组
        int[] prenode = new int[NUM];
        // 最短距离数组
        int[] mindist = new int[NUM];
        // 该节点是否已经找到最短路径
        boolean[] find = new boolean[NUM];

        int vnear = 0;

        for (int i = 0; i < mindist.length; i++) {
            prenode[i] = i;
            mindist[i] = Graph[vs][i];
            find[i] = false;
        }
        find[vs] = true;
        for (int v = 1; v < Graph.length; v++) {
            // 每次循环求得距离vs最近的节点vnear和最短距离min
            int min = N;
            for (int j = 0; j < Graph.length; j++) {
                if (!find[j] && mindist[j] < min) {
                    min = mindist[j];
                    vnear = j;
                }
            }
            find[vnear] = true;
            // 根据vnear修正vs到其他所有节点的前驱节点及距离
            for (int k = 0; k < Graph.length; k++) {
                if (!find[k] && (min + Graph[vnear][k]) < mindist[k]) {
                    prenode[k] = vnear;
                    mindist[k] = min + Graph[vnear][k];
                }
            }
        }
        for (int i = 0; i < NUM; i++) {
            System.out.println("v" + vs + "...v" + prenode[i] + "->v" + i + ", s=" + mindist[i]);
        }
    }
}