Prim算法在Java中的实现

Question

我试图在Java中实现Prim的算法，用于我的图形HashMap LinkedList和一个包含连接顶点和权重的类Edge：

adjacencyList = new HashMap<T, LinkedList<Edge<T>>>();

我的想法是，从一个给定的顶点开始：1）将所有顶点保存到一个LinkedList中，这样每次访问它们时我都可以删除它们2）将路径保存到另一个LinkedList中，这样我就可以得到我的最终MST 3）使用PriorityQueue找到最小权重

最后我需要MST，边数和总重量。我很困惑如何返回MST，我的代码中几乎没有错误，我不知道如何修复它们！

首先，我得到了这个错误：

    Prim.java:21: error: no suitable method found for addAll(LinkedList<Edge<T>>)
        unvisited.addAll(graph.getVertices());
                 ^
    method Collection.addAll(Collection<? extends T>) is not applicable
      (argument mismatch; LinkedList<Edge<T>> cannot be converted to Collection<? extends T>)
    method List.addAll(Collection<? extends T>) is not applicable
      (argument mismatch; LinkedList<Edge<T>> cannot be converted to Collection<? extends T>)
    method AbstractCollection.addAll(Collection<? extends T>) is not applicable
      (argument mismatch; LinkedList<Edge<T>> cannot be converted to Collection<? extends T>)
    method LinkedList.addAll(Collection<? extends T>) is not applicable
      (argument mismatch; LinkedList<Edge<T>> cannot be converted to Collection<? extends T>)
  where T is a type-variable: T extends Comparable<T> declared in class Prim

问题似乎出在我的getVerites（）方法（返回图的所有顶点）中，因为它返回一个Set

public class Graph<T extends Comparable<T>> {
    .
    .
    public Set<T> getVertices() {
            if (adjacencyList.isEmpty()) {
                System.out.println("Error message.\n");
                return null;
            } else
                return adjacencyList.keySet();
        }
    }

第二个错误是：

   Prim.java:28: error: incompatible types: T cannot be converted to Edge<T>
            for (Edge<T> edge : graph.getAdjacentVertices(source)) {
                                                          ^
  where T is a type-variable:
    T extends Comparable<T> declared in class Prim
Note: Some messages have been simplified; recompile with -Xdiags:verbose to get full output

我可以通过铸造Edge来修复它

普里姆的：

public class Prim<T extends Comparable<T>> {
    public <SHOULD I RETURN graph ?> minimumSpanningTree(Graph<Edge<T>> graph, T vertex) {
        //ArgumentException

        double weight = 0;
        T source = vertex;

        LinkedList<T> vertexSet = new LinkedList<>();
        LinkedList<Edge<T>> path = new LinkedList<>();

        vertexSet.addAll(graph.getVertices()); //unvisited ERROR HERE
        vertexSet.remove(source);

        double numberOfVertices = graph.getVertices().size();
        PriorityQueue<Edge<T>> priorityQueue = new PriorityQueue<>();

        while (!vertexSet.isEmpty()) {
            for (Edge<T> edge : graph.getAdjacentVertices(source)) {//ERROR
               if (vertexSet.contains(edge.getDestination())) 
                    priorityQueue.insert(edge);
            }
            Edge<T> minWeight = priorityQueue.extractMin();
            weight += minWeight.getWeight();
            path.add(HERE I SHOULD PUT MST PATH BUT I DON'T KNOW HOW!!);

            source = minWeight.getDestination();
            vertexSet.remove(source);
        }
        return <graph??>;
    }
}

正如我之前所说的，我不知道我是否应该返回一个图作为MST（可能是我作为输入删除最昂贵的边给出的图）或一个名为path的LinkedList，它以最小的权重保存路径。我也不知道如何在MST中找到边的数量；我应该为每个顶点（HashMap的键集）找到LinkedList的大小（这是它的值）并将它们相加吗？

编辑：getAdjamentVerites方法

public LinkedList<T> getAdjacentVertices(T vertex) {
    if (adjacencyList.isEmpty() || adjacencyList.containsKey(vertex) == false) {
        System.out.println("Error msg.\n");
        return null;
    } else {
        LinkedList<T> allAdjacents = new LinkedList<>();
        for (Edge<T> edge : adjacencyList.get(vertex)) {
            allAdjacents.add(edge.getDestination());
        }
        return allAdjacents;
    }
}




Answer 1

1） 我猜错误不在getVertices（）中，而是在边上，您的图形被定义为泛型

我建议您将Graph定义为Graph

例如（蒙住眼睛）：

public class Graph<T> {
    Map<T, Edge<T>> adjacencyList;
    public Set<T> getVertices() {
        if (adjacencyList.isEmpty()) {
            System.out.println("Error message.\n");
            return null;
        } else {
            return adjacencyList.keySet();
        }
    }
}

Graph<Point> p;
List<Point> points = new LinkedList<>();
points.addAll(p.getVertices());

2）1的变体。在这种情况下，您将返回一个列表

for (Edge<T> edge : graph.getAdjacentVertices(source))

getAdJacentVerques的返回值应该是一个枚举

LinkedList<Edge<T>> allAdjacents = new LinkedList<>();
for (Edge<T> edge : adjacencyList.get(vertex)) {
    allAdjacents.add(edge);
}
return allAdjacents;