Java：引用图形中的边

Question

I am modifying a graph implementation to compute the all pairs shortest path matrix using Floyd's algorithm . The graph has both adjacency linked list and matrix implementations. For now I am using adjacency matrix because it its needed for this algorithm.

abstract public class GraphMatrix<V,E> extends AbstractStructure<V> implements Graph<V,E>{
/**
 * Number of vertices in graph.
 */
protected int size;          // allocation size for graph
/**
 * The edge data.  Every edge appears on one (directed)
 * or two (undirected) locations within graph.
 */
protected Object data[][];     // matrix - array of arrays
/**
 * Translation between vertex labels and vertex structures.
 */
protected Map<V,GraphMatrixVertex<V>> dict;   // labels -> vertices
/**
 * List of free vertex indices within graph.
 */
protected List<Integer> freeList;    // available indices in matrix
 /**
 * Whether or not graph is directed.
 */
protected boolean directed;  // graph is directed

/**
 * Constructor of directed/undirected GraphMatrix. Protected constructor.
 *
 * @param size Maximum size of graph.
 * @param dir True if graph is to be directed.
 */
protected GraphMatrix(int size, boolean dir)
{
    this.size = size; // set maximum size
    directed = dir;   // fix direction of edges
    // the following constructs a size x size matrix
    data = new Object[size][size];
    // label to index translation table
    dict = new Hashtable<V,GraphMatrixVertex<V>>(size);
    // put all indices in the free list
    freeList = new SinglyLinkedList<Integer>();
    for (int row = size-1; row >= 0; row--)
        freeList.add(new Integer(row));
}

.
.
.

public Object[][] AllPairsShortestPath()
{
    //First, data array needs to be copied to a new array so that it is not corrupted.
    Object[][] weight_matrix = data.clone();
    for(int k = 0; k < size; k++)
    {
        for(int i = 0; i < size; i++)
        {
            for(int j = 0; j < size; j++)
            {
                if((weight_matrix + weight_matrix[k][j])<weight_matrix[i][j])
                {
                  //New shorter path is found   
                }
            }
        }
    }
    return weight_matrix;       
}

My question is how can I reference the weight_matrix elements so that they can be compared? Here is the edge class that is in the Object matrix:

public class Edge<V,E>
{
/**
 * Two element array of vertex labels.
 * When necessary, first element is source.
 */
protected V here, there;    // labels of adjacent vertices
/**
 * Label associated with edge.  May be null.
 */
protected E label;     // edge label
/**
 * Whether or not this edge has been visited.
 */
protected boolean visited;  // this edge visited
/**
 * Whether or not this edge is directed.
 */
protected boolean directed; // this edge directed

/**
 * Construct a (possibly directed) edge between two labeled
 * vertices.  When edge is directed, vtx1 specifies source.
 * When undirected, order of vertices is unimportant.  Label
 * on edge is any type, and may be null.
 * Edge is initially unvisited.
 *
 * @post edge associates vtx1 and vtx2; labeled with label
 *       directed if "directed" set true
 *
 * @param vtx1 The label of a vertex (source if directed).
 * @param vtx2 The label of another vertex (destination if directed).
 * @param label The label associated with the edge.
 * @param directed True iff this edge is directed.
 */
public Edge(V vtx1, V vtx2, E label,
            boolean directed)
{
    here = vtx1;
    there = vtx2;
    this.label = label;
    visited = false;
    this.directed = directed;
}

/**
 * Returns the first vertex (or source if directed).
 *
 * @post returns first node in edge
 * 
 * @return A vertex; if directed, the source.
 */
public V here()
{
    return here;
}

/**
 * Returns the second vertex (or source if undirected).
 *
 * @post returns second node in edge
 * 
 * @return A vertex; if directed, the destination.
 */
public V there()
{
    return there;
}

/**
 * Sets the label associated with the edge.  May be null.
 *
 * @post sets label of this edge to label 
 * 
 * @param label Any object to label edge, or null.
 */
public void setLabel(E label)
{
    this.label = label;
}

/**
 * Get label associated with edge.
 *
 * @post returns label associated with this edge
 * 
 * @return The label found on the edge.
 */
public E label()
{
    return label;
}

/**
 * Test and set visited flag on vertex.
 *
 * @post visits edge, returns whether previously visited
 * 
 * @return True iff edge was visited previously.
 */
public boolean visit()
{
    boolean was = visited;
    visited = true;
    return was;
}

/**
 * Check to see if edge has been visited.
 *
 * @post returns true iff edge has been visited
 * 
 * @return True iff the edge has been visited.
 */
public boolean isVisited()
{
    return visited;
}

/**
 * Check to see if edge is directed.
 *
 * @post returns true iff edge is directed
 * 
 * @return True iff the edge has been visited.
 */
public boolean isDirected()
{
    return directed;
}

/**
 * Clear the visited flag associated with edge.
 *
 * @post resets edge's visited flag to initial state
 */
public void reset()
{
    visited = false;
}

/**
 * Returns hashcode associated with edge.
 *
 * @post returns suitable hashcode
 * 
 * @return An integer code suitable for hashing.
 */
public int hashCode()
{
    if (directed) return here().hashCode()-there().hashCode();
    else          return here().hashCode()^there().hashCode();
}

/**
 * Test for equality of edges.  Undirected edges are equal if
 * they connect the same vertices.  Directed edges must have same
 * direction.
 *
 * @post returns true iff edges connect same vertices
 * 
 * @param o The other edge.
 * @return True iff this edge is equal to other edge.
 */
public boolean equals(Object o)
{
    Edge<?,?> e = (Edge<?,?>)o;
    return ((here().equals(e.here()) && 
             there().equals(e.there())) ||
            (!directed &&
             (here().equals(e.there()) && 
              there().equals(e.here()))));
}

/**
 * Construct a string representation of edge.
 *
 * @post returns string representation of edge
 * 
 * @return String representing edge.
 */
public String toString()
{
    StringBuffer s = new StringBuffer();
    s.append("<Edge:");
    if (visited) s.append(" visited");
    s.append(" "+here());
    if (directed) s.append(" ->");
    else s.append(" <->");
    s.append(" "+there()+">");
    return s.toString();
}
}

Answer 1

I guess ((weight_matrix + weight_matrix[k][j])<weight_matrix[i][j])

is not what you want. IIRC, Floyd's as follows:

((weight_matrix[i][k] + weight_matrix[k][j])<weight_matrix[i][j])

IF YOUR weight_matrix were a matrix of weights (take a look here for more floyd). Size, in this implementation, would be the number of vertices you got on the graph.

If each edge had a weight, you could do

(( ((Edge)weight_matrix[i][k]).getValue() + ((Edge)weight_matrix[k][j]).getValue()) < ((Edge)weight_matrix[i][j]).getValue())

If all edge weights are equal, you could tell getValue() to return 1 always, and voilá.