一 问题描述

小明为位置1，求他到其他各顶点的距离。

二 实现

package graph.dijkstra;

import java.util.Scanner;
import java.util.Stack;

public class Dijkstra {
    static final int MaxVnum = 100;  // 顶点数最大值
    static final int INF = 0x3f3f3f3f; //无穷大
    static final int dist[] = new int[MaxVnum]; // 最短距离
    static final int p[] = new int[MaxVnum]; // 前驱数组
    static final boolean flag[] = new boolean[MaxVnum]; // 如果 s[i] 等于 true，说明顶点 i 已经加入到集合 S ;否则顶点 i 属于集合 V-S

    static int locatevex(AMGraph G, char x) {
        for (int i = 0; i < G.vexnum; i++) // 查找顶点信息的下标
            if (x == G.Vex[i])
                return i;
        return -1; // 没找到
    }

    static void CreateAMGraph(AMGraph G) {
        Scanner scanner = new Scanner(System.in);
        int i, j;
        char u, v;
        int w;
        System.out.println("请输入顶点数：");
        G.vexnum = scanner.nextInt();
        System.out.println("请输入边数:");
        G.edgenum = scanner.nextInt();
        System.out.println("请输入顶点信息:");

        // 输入顶点信息，存入顶点信息数组
        for (int k = 0; k < G.vexnum; k++) {
            G.Vex[k] = scanner.next().charAt(0);
        }
        //初始化邻接矩阵所有值为0，如果是网，则初始化邻接矩阵为无穷大
        for (int m = 0; m < G.vexnum; m++)
            for (int n = 0; n < G.vexnum; n++)
                G.Edge[m][n] = INF;

        System.out.println("请输入每条边依附的两个顶点及权值：");
        while (G.edgenum-- > 0) {
            u = scanner.next().charAt(0);
            v = scanner.next().charAt(0);
            w = scanner.nextInt();

            i = locatevex(G, u);// 查找顶点 u 的存储下标
            j = locatevex(G, v);// 查找顶点 v 的存储下标
            if (i != -1 && j != -1)
                G.Edge[i][j] = w; //有向图邻接矩阵
            else {
                System.out.println("输入顶点信息错！请重新输入！");
                G.edgenum++; // 本次输入不算
            }
        }
    }

    static void print(AMGraph G) { // 输出邻接矩阵
        System.out.println("图的邻接矩阵为：");
        for (int i = 0; i < G.vexnum; i++) {
            for (int j = 0; j < G.vexnum; j++)
                System.out.print(G.Edge[i][j] + "\t");
            System.out.println();
        }
    }

    public static void main(String[] args) {
        AMGraph G = new AMGraph();
        int st;
        char u;
        CreateAMGraph(G);
        System.out.println("请输入源点的信息:");
        Scanner scanner = new Scanner(System.in);
        u = scanner.next().charAt(0);
        ;
        st = locatevex(G, u);//查找源点u的存储下标
        Dijkstra(G, st);
        System.out.println("小明所在的位置:" + u);

        for (int i = 0; i < G.vexnum; i++) {
            System.out.print("小明:" + u + " - " + "要去的位置:" + G.Vex[i]);

            if (dist[i] == INF)
                System.out.print(" sorry,无路可达");
            else
                System.out.println(" 最短距离为:" + dist[i]);
        }
        findpath(G, u);
    }

    public static void Dijkstra(AMGraph G, int u) {
        for (int i = 0; i < G.vexnum; i++) {
            dist[i] = G.Edge[u][i]; //初始化源点u到其他各个顶点的最短路径长度
            flag[i] = false;
            if (dist[i] == INF)
                p[i] = -1; //源点u到该顶点的路径长度为无穷大，说明顶点i与源点u不相邻
            else
                p[i] = u; //说明顶点i与源点u相邻，设置顶点i的前驱p[i]=u
        }
        dist[u] = 0;
        flag[u] = true;   //初始时，集合S中只有一个元素：源点u
        for (int i = 0; i < G.vexnum; i++) {
            int temp = INF, t = u;
            for (int j = 0; j < G.vexnum; j++) //在集合V-S中寻找距离源点u最近的顶点t
                if (!flag[j] && dist[j] < temp) {
                    t = j;
                    temp = dist[j];
                }
            if (t == u) return; //找不到t，跳出循环
            flag[t] = true;  //否则，将t加入集合
            for (int j = 0; j < G.vexnum; j++)//更新V-S中与t相邻接的顶点到源点u的距离
                if (!flag[j] && G.Edge[t][j] < INF)
                    if (dist[j] > (dist[t] + G.Edge[t][j])) {
                        dist[j] = dist[t] + G.Edge[t][j];
                        p[j] = t;
                    }
        }
    }

    public static void findpath(AMGraph G, char u) {
        int x;
        Stack<Integer> S = new Stack<>();
        System.out.println("源点为：" + u);

        for (int i = 0; i < G.vexnum; i++) {
            x = p[i];
            if (x == -1 && u != G.Vex[i]) {
                System.out.println("源点到其它各顶点最短路径为：" + u + "--" + G.Vex[i] + "    sorry,无路可达");
                continue;
            }
            while (x != -1) {
                S.push(x);
                x = p[x];
            }
            System.out.println("源点到其它各顶点最短路径为：");
            while (!S.empty()) {
                System.out.print(G.Vex[S.peek()] + "--");
                S.pop();
            }
            System.out.println(G.Vex[i] + "    最短距离为：" + dist[i]);
        }
    }
}

class AMGraph {
    char Vex[] = new char[Dijkstra.MaxVnum];
    int Edge[][] = new int[Dijkstra.MaxVnum][Dijkstra.MaxVnum];
    int vexnum; // 顶点数
    int edgenum; // 边数
}

三 测试