java 实现 dijkstra 算法-- 最优路径

问题

求出任意一点出发, 到指定点的最短距离和路径

算法代码

//假设起点为src, 终点为dst, 图以二维矩阵的形式存储，若graph[i][j] == 0, 代表i,j不相连
//visit[i] == 0,代表未访问,visit[i] == -1代表已访问
public static Node dijkstra(int src, int dst, int[][] graph,int[] visit){
    //节点个数
    int n = graph.length;
    PriorityQueue pq = new PriorityQueue<>(new Node());
    //将起点加入pq
    ArrayList way = new ArrayList<>();
    way.add(src); // 起点路径
    pq.add(new Node(src, 0, way));
    while (!pq.isEmpty()){
        Node t = pq.poll();
        //当前节点是终点，即可返回最短路径
        if(t.node == dst)
            //return t.cost;
            return t;
        //t节点表示还未访问
        if (visit[t.node]==0){
            //将节点设置为已访问
            visit[t.node] = -1;
            //将当前节点相连且未访问的节点遍历
            for (int i = 0; i < n; i++) {
            	// 连通 并且 未被访问
                if (graph[t.node][i]!=0 && visit[i]==0) {
                    int newCost = t.cost + graph[t.node][i];// 新距离

                    List newWay = new ArrayList<>(t.way);// 新路线
                    newWay.add(i);

                    pq.add(new Node(i, newCost,newWay));
                }
            }
        }
    }
    //return -1;
    return null;
}

//定义一个存储节点和离起点相应距离的数据结构
@Data
static class Node implements Comparator {
    public int node; // 节点下标
    public int cost; // 起始节点到当前节点的距离
    public List way; // 起始节点到当前节点的路径

    public Node(){}

    public Node(int node, int cost, List way){
        this.node = node;
        this.cost = cost;
        this.way = way;
    }
    // 小顶堆: 头部永远是 cost 最小的
    @Override
    public int compare(Node node1, Node node2){
        return node1.cost-node2.cost;
    }
}

测试代码

public static void main(String[] args) {
  
    // 测试 dijkstra 算法
    int[][] graph = new int[6][6];
    initGraph(graph);
    int[] visit = {0,0,0,0,0,0};

    //int dist = dijkstra(0, 4, graph, visit);
    Node node = dijkstra(1, 5, graph, visit);

    System.out.println(node);
}

private static void initGraph(int[][] graph) {
    // 初始图的默认值为0,表示都不相连
    for (int i = 0; i < graph.length; i++) {
        for (int j = 0; j < graph.length; j++) {
            graph[i][j] = 0;
        }
    }

    // 设置连接关系
    graph[0][1] = 7;
    graph[0][2] = 9;
    graph[0][5] = 14;

    graph[1][0] = 7;
    graph[1][2] = 10;
    graph[1][3] = 15;

    graph[2][0] = 9;
    graph[2][1] = 10;
    graph[2][3] = 11;
    graph[2][5] = 2;

    graph[3][1] = 15;
    graph[3][2] = 11;
    graph[3][4] = 6;

    graph[4][3] = 6;
    graph[4][5] = 9;

    graph[5][0] = 14;
    graph[5][2] = 2;
    graph[5][4] = 9;

}

测试结果

点1 到点5的 最短距离为12, 路径为 1,2,5