c＃使用邻接列表的DFS拓扑排序有向图

Question

我正在尝试在下图中完成拓扑排序（摘自Steven Skiena的算法设计手册）。
Graph to be Sorted根据book的答案是H，A ，B，D，E，G，I，J，C，F但我不断得到A，B，D，E，C，F，H，G，I，J。

我不明白当拓扑排序意味着具有到目标节点的有向边的起始节点应该首先出现时，H如何能够前进到前面。书中给出的答案是否可以实现甚至是正确的？ 这种图形是否可以进行拓扑排序（因为它不是非循环的）？ 下面是使用邻接列表的通用图表

public class Node<T>
{
    public T Id { get; set; }
    public LinkedList<Node<T>> Adjacent { get; set; }

    public Node(T _id)
    {
        this.Id = _id;
        this.Adjacent = new LinkedList<Node<T>>();
    }
}

public class Graph<T>
{
    private Dictionary<T, Node<T>> nodeLookup = new Dictionary<T, Node<T>>();

    public Node<T> GetNode(T id)
    {
        if (!nodeLookup.ContainsKey(id))
        {
            Node<T> s = new Node<T>(id);
            nodeLookup.Add(id, s);
        }

        return nodeLookup.Single(x => x.Key.ToString() == id.ToString()).Value;
    }

    public void AddEdgeDirected(T source, T destination)
    {
        Node<T> s = GetNode(source);
        Node<T> d = GetNode(destination);

        s.Adjacent.AddLast(d);
    }

    public void PrintGraph()
    {
        Console.WriteLine("-------------------------------------- Print Graph");
        foreach (KeyValuePair<T, Node<T>> kvp in nodeLookup)
        {
            Node<T> val = kvp.Value;
            Console.Write($"[{val.Id}]: ");
            foreach (Node<T> adj in val.Adjacent)
            {
                Console.Write($"-> {adj.Id}");
            }
            Console.WriteLine();
        }
    }

    public List<Node<T>> GetAllVertices()
    {
        List<Node<T>> result = new List<Node<T>>();

        foreach (KeyValuePair<T, Node<T>> kvp in nodeLookup)
        {
            result.Add(kvp.Value);
        }

        return result;
    }
}

下面是排序算法，它打印出排序列表。它使用HashSet来查找节点是否已被访问，并在没有更多节点访问时使用数组插入节点Id。 它使用DFSTopSortUtil中的递归来获取索引，以将节点键插入结果数组中的正确位置。

public static class TopologicalSort<T>
{
    public static void DFSTopSort(Graph<T> graph)
    {
        List<Node<T>> vertices = graph.GetAllVertices();
        int numVertices = graph.GetAllVertices().Count;
        HashSet<T> visited = new HashSet<T>();
        T[] result = new T[numVertices];
        int n = numVertices - 1; //largest topNum  

        foreach (Node<T> node in vertices)
        {
            if (!visited.Contains(node.Id))
            {
                n = DFSTopSortUtil(node, visited, result, n, vertices);
            }
        }

        Console.Write("\nTopSort_03 - Print: ");
        Console.Write("\n\t");
        result.Reverse();
        foreach (T val in result)
        {
            Console.Write($"->{val}");
        }
        Console.WriteLine();
    }

    private static int DFSTopSortUtil(Node<T> node, HashSet<T> visited, T[] result, int n, List<Node<T>> vertices)
    {
        visited.Add(node.Id);

        foreach (Node<T> child in node.Adjacent)
        {
            if (!visited.Contains(child.Id))
            {
                n = DFSTopSortUtil(child, visited, result, n, vertices);
            }
        }
        result[n] = node.Id;
        return n - 1;
    }
}

这是主要方法和图表创建

class Program
{
    static void Main(string[] args)
    {
        Graph<string> graph = new Graph<string>();
        AutoCreateGraph_TopSort_Directed(graph);
        graph.PrintGraph();
        TopologicalSort<string>.DFSTopSort(graph);
    }

    public static void AutoCreateGraph_TopSort_Directed(Graph<string> graph)
    {
        graph.AddEdgeDirected("A", "B");
        graph.AddEdgeDirected("B", "C");
        graph.AddEdgeDirected("C", "F");
        graph.AddEdgeDirected("F", "H");
        graph.AddEdgeDirected("H", "G");
        graph.AddEdgeDirected("G", "F");

        graph.AddEdgeDirected("G", "I");
        graph.AddEdgeDirected("I", "J");
        graph.AddEdgeDirected("H", "J");

        graph.AddEdgeDirected("B", "E");
        graph.AddEdgeDirected("E", "C");
        graph.AddEdgeDirected("E", "F");
        graph.AddEdgeDirected("E", "G");

        graph.AddEdgeDirected("B", "D");
        graph.AddEdgeDirected("D", "E");
        graph.AddEdgeDirected("D", "G");

        graph.AddEdgeDirected("A", "D");
    }
}