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Monday, 27 February 2017

Chapter 29 Exercise 6, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

29.6 (Weighted 4 * 4 16 tails model) The weighted nine tails problem in the text
uses a 3 * 3 matrix. Assume that you have 16 coins placed in a 4 * 4 matrix.
Create a new model class named WeightedTailModel16 . Create an instance
of the model and save the object into a file named WeightedTailModel16.dat.


import java.io.BufferedOutputStream;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.ObjectOutputStream;
import java.io.Serializable;
import java.util.ArrayList;
import java.util.List;
import java.util.PriorityQueue;

public class Exercise06 {

 public static void main(String[] args) throws FileNotFoundException, IOException {
  WeightedTailModel16 model = new WeightedTailModel16();
  ObjectOutputStream output = new ObjectOutputStream( new BufferedOutputStream(new FileOutputStream(new File("tmp/WeightedTailModel16.dat"))));
  output.writeObject(model);
  output.close();
 }

 static class WeightedTailModel16 extends TailModel16 implements Serializable {
  private static final long serialVersionUID = -6982578972643959605L;

  /** Construct a model */
  public WeightedTailModel16() {
   List<WeightedEdge> edges = getEdges();
   WeightedGraph<Integer> graph = new WeightedGraph<Integer>(edges, NUMBER_OF_NODES);
   tree = graph.getShortestPath(65535);
  }
  
  /** Create all edges for the graph */
  private List<WeightedEdge> getEdges() {
   // Store edges
   List<WeightedEdge> edges = new ArrayList<WeightedEdge>();

   for (int u = 0; u < NUMBER_OF_NODES; u++) {
    for (int k = 0; k < 16; k++) {
     char[] node = getNode(u); // Get the node for vertex u
     if (node[k] == 'H') {
      int v = getFlippedNode(node, k);
      int numberOfFlips = getNumberOfFlips(u, v);

      // Add edge (v, u) for a legal move from node u to node
      // v
      edges.add(new WeightedEdge(v, u, numberOfFlips));
     }
    }
   }

   return edges;
  }

  private static int getNumberOfFlips(int u, int v) {
   char[] node1 = getNode(u);
   char[] node2 = getNode(v);

   int count = 0; // Count the number of different cells
   for (int i = 0; i < node1.length; i++){
    if (node1[i] != node2[i]) {
     count++;
    }
   }

   return count;
  }

  @SuppressWarnings("unchecked")
  public int getNumberOfFlips(int u) {
   return (int) ((WeightedGraph<Integer>.ShortestPathTree) tree).getCost(u);
  }
 }

 static class WeightedGraph<V> extends AbstractGraph<V>  implements Serializable  {
  private static final long serialVersionUID = 8513410105553915338L;
  // Priority adjacency lists
  private List<PriorityQueue<WeightedEdge>> queues = new ArrayList<PriorityQueue<WeightedEdge>>();

  /** Construct a WeightedGraph from edges and vertices in arrays */
  public WeightedGraph() {
  }

  /** Construct a WeightedGraph from edges and vertices in arrays */
  public WeightedGraph(int[][] edges, V[] vertices) {
   super(edges, vertices);
   createQueues(edges, vertices.length);
  }

  /** Construct a WeightedGraph from edges and vertices in List */
  public WeightedGraph(int[][] edges, int numberOfVertices) {
   super(edges, numberOfVertices);
   createQueues(edges, numberOfVertices);
  }

  /** Construct a WeightedGraph for vertices 0, 1, 2 and edge list */
  @SuppressWarnings({ "rawtypes", "unchecked" })
  public WeightedGraph(List<WeightedEdge> edges, List<V> vertices) {
   super((List) edges, vertices);
   createQueues(edges, vertices.size());
  }

  /** Construct a WeightedGraph from vertices 0, 1, and edge array */
  @SuppressWarnings({ "rawtypes", "unchecked" })
  public WeightedGraph(List<WeightedEdge> edges, int numberOfVertices) {
   super((List) edges, numberOfVertices);
   createQueues(edges, numberOfVertices);
  }

  /** Create priority adjacency lists from edge arrays */
  private void createQueues(int[][] edges, int numberOfVertices) {
   for (int i = 0; i < numberOfVertices; i++) {
    queues.add(new PriorityQueue<WeightedEdge>()); // Create a queue
   }

   for (int i = 0; i < edges.length; i++) {
    int u = edges[i][0];
    int v = edges[i][1];
    int weight = edges[i][2];
    // Insert an edge into the queue
    queues.get(u).offer(new WeightedEdge(u, v, weight));
   }
  }

  /** Create priority adjacency lists from edge lists */
  private void createQueues(List<WeightedEdge> edges, int numberOfVertices) {
   for (int i = 0; i < numberOfVertices; i++) {
    queues.add(new PriorityQueue<WeightedEdge>()); // Create a queue
   }

   for (WeightedEdge edge : edges) {
    queues.get(edge.u).offer(edge); // Insert an edge into the queue
   }
  }

  /** Display edges with weights */
  public void printWeightedEdges() {
   for (int i = 0; i < queues.size(); i++) {
    System.out.print(getVertex(i) + " (" + i + "): ");
    for (WeightedEdge edge : queues.get(i)) {
     System.out.print("(" + edge.u + ", " + edge.v + ", "
       + edge.weight + ") ");
    }
    System.out.println();
   }
  }

  /** Get the edges from the weighted graph */
  public List<PriorityQueue<WeightedEdge>> getWeightedEdges() {
   return queues;
  }

  /** Clears the weighted graph */
  public void clear() {
   vertices.clear();
   neighbors.clear();
   queues.clear();
  }

  /** Add vertices to the weighted graph */
  public void addVertex(V vertex) {
   super.addVertex(vertex);
   queues.add(new PriorityQueue<WeightedEdge>());
  }

  /** Add edges to the weighted graph */
  public void addEdge(int u, int v, double weight) {
   super.addEdge(u, v);
   queues.get(u).add(new WeightedEdge(u, v, weight));
   queues.get(v).add(new WeightedEdge(v, u, weight));
  }

  /** Get a minimum spanning tree rooted at vertex 0 */
  public MST getMinimumSpanningTree() {
   return getMinimumSpanningTree(0);
  }

  /** Get a minimum spanning tree rooted at a specified vertex */
  public MST getMinimumSpanningTree(int startingVertex) {
   List<Integer> T = new ArrayList<Integer>();
   // T initially contains the startingVertex;
   T.add(startingVertex);

   int numberOfVertices = vertices.size(); // Number of vertices
   int[] parent = new int[numberOfVertices]; // Parent of a vertex
   // Initially set the parent of all vertices to -1
   for (int i = 0; i < parent.length; i++)
    parent[i] = -1;
   double totalWeight = 0; // Total weight of the tree thus far

   // Clone the priority queue, so to keep the original queue intact
   List<PriorityQueue<WeightedEdge>> queues = deepClone(this.queues);

   // All vertices are found?
   while (T.size() < numberOfVertices) {
    // Search for the vertex with the smallest edge adjacent to
    // a vertex in T
    int v = -1;
    double smallestWeight = Double.MAX_VALUE;
    for (int u : T) {
     while (!queues.get(u).isEmpty()
       && T.contains(queues.get(u).peek().v)) {
      // Remove the edge from queues[u] if the adjacent
      // vertex of u is already in T
      queues.get(u).remove();
     }

     if (queues.get(u).isEmpty()) {
      continue; // Consider the next vertex in T
     }

     // Current smallest weight on an edge adjacent to u
     WeightedEdge edge = queues.get(u).peek();
     if (edge.weight < smallestWeight) {
      v = edge.v;
      smallestWeight = edge.weight;
      // If v is added to the tree, u will be its parent
      parent[v] = u;
     }
    } // End of for

    if (v != -1)
     T.add(v); // Add a new vertex to the tree
    else
     break; // The tree is not connected, a partial MST is found

    totalWeight += smallestWeight;
   } // End of while

   return new MST(startingVertex, parent, T, totalWeight);
  }

  /** Clone an array of queues */
  private List<PriorityQueue<WeightedEdge>> deepClone(
    List<PriorityQueue<WeightedEdge>> queues) {
   List<PriorityQueue<WeightedEdge>> copiedQueues = new ArrayList<PriorityQueue<WeightedEdge>>();

   for (int i = 0; i < queues.size(); i++) {
    copiedQueues.add(new PriorityQueue<WeightedEdge>());
    for (WeightedEdge e : queues.get(i)) {
     copiedQueues.get(i).add(e);
    }
   }

   return copiedQueues;
  }

  /** MST is an inner class in WeightedGraph */
  @SuppressWarnings("serial")
  public class MST extends Tree implements Serializable{
   private double totalWeight; // Total weight of all edges in the tree

   public MST(int root, int[] parent, List<Integer> searchOrder,
     double totalWeight) {
    super(root, parent, searchOrder);
    this.totalWeight = totalWeight;
   }

   public double getTotalWeight() {
    return totalWeight;
   }
  }

  /** Find single source shortest paths */
  public ShortestPathTree getShortestPath(int sourceVertex) {
   // T stores the vertices whose path found so far
   List<Integer> T = new ArrayList<Integer>();
   // T initially contains the sourceVertex;
   T.add(sourceVertex);

   // vertices is defined in AbstractGraph
   int numberOfVertices = vertices.size();

   // parent[v] stores the previous vertex of v in the path
   int[] parent = new int[numberOfVertices];
   for (int i = 0; i < parent.length; i++) {
    parent[i] = -1;
   }
   parent[sourceVertex] = -1; // The parent of source is set to -1

   // cost[v] stores the cost of the path from v to the source
   double[] cost = new double[numberOfVertices];
   for (int i = 0; i < cost.length; i++) {
    cost[i] = Double.MAX_VALUE; // Initial cost set to infinity
   }
   cost[sourceVertex] = 0; // Cost of source is 0

   // Get a copy of queues
   List<PriorityQueue<WeightedEdge>> queues = deepClone(this.queues);

   // Expand T
   while (T.size() < numberOfVertices) {
    int v = -1; // Vertex to be determined
    double smallestCost = Double.MAX_VALUE; // Set to infinity
    for (int u : T) {
     while (!queues.get(u).isEmpty()
       && T.contains(queues.get(u).peek().v)) {
      queues.get(u).remove(); // Remove the vertex in queue
            // for u
     }

     if (queues.get(u).isEmpty()) {
      // All vertices adjacent to u are in T
      continue;
     }

     WeightedEdge e = queues.get(u).peek();
     if (cost[u] + e.weight < smallestCost) {
      v = e.v;
      smallestCost = cost[u] + e.weight;
      // If v is added to the tree, u will be its parent
      parent[v] = u;
     }
    } // End of for
    
    if (v != -1) {
     T.add(v); // Add a new vertex to T
     cost[v] = smallestCost;
    } else {
     break;
    }
   } // End of while

   // Create a ShortestPathTree
   return new ShortestPathTree(sourceVertex, parent, T, cost);
  }

  /** ShortestPathTree is an inner class in WeightedGraph */
  @SuppressWarnings("serial")
  public class ShortestPathTree extends Tree  implements Serializable {
   private double[] cost; // cost[v] is the cost from v to source

   /** Construct a path */
   public ShortestPathTree(int source, int[] parent,
     List<Integer> searchOrder, double[] cost) {
    super(source, parent, searchOrder);
    this.cost = cost;
   }

   /** Return the cost for a path from the root to vertex v */
   public double getCost(int v) {
    return cost[v];
   }

   /** Print paths from all vertices to the source */
   public void printAllPaths() {
    System.out.println("All shortest paths from "
      + vertices.get(getRoot()) + " are:");
    for (int i = 0; i < cost.length; i++) {
     printPath(i); // Print a path from i to the source
     System.out.println("(cost: " + cost[i] + ")"); // Path cost
    }
   }
  }
 }

 static class WeightedEdge extends AbstractGraph.Edge implements Comparable<WeightedEdge>, Serializable {
  private static final long serialVersionUID = 2199172417762473324L;
  public double weight; // The weight on edge (u, v)

  /** Create a weighted edge on (u, v) */
  public WeightedEdge(int u, int v, double weight) {
   super(u, v);
   this.weight = weight;
  }

  /** Compare two edges on weights */
  public int compareTo(WeightedEdge edge) {
   if (weight > edge.weight) {
    return 1;
   } else if (weight == edge.weight) {
    return 0;
   } else {
    return -1;
   }
  }

  @Override
  public boolean equals(Object obj) {
   if (obj instanceof WeightedEdge) {
    WeightedEdge that = (WeightedEdge) obj;
    return (u == that.u) && (v == that.v)
      && (weight == that.weight);
   } else {
    return false;
   }
  }

  @Override
  public String toString() {
   return "(" + u + ", " + v + ", " + weight + ")";
  }
 }

 static class TailModel16 implements Serializable {
  private static final long serialVersionUID = -4344466083913492090L;
  public final static int NUMBER_OF_NODES = 65536;
  protected AbstractGraph<Integer>.Tree tree; // Define a tree

  /** Construct a model */
  public TailModel16() {
   // Create edges
   List<AbstractGraph.Edge> edges = getEdges();

   // Create a graph
   UnweightedGraph<Integer> graph = new UnweightedGraph<Integer>(
     edges, NUMBER_OF_NODES);

   // Obtain a BSF tree rooted at the target node
   tree = graph.bfs(65535);
  }

  /** Create all edges for the graph */
  private List<AbstractGraph.Edge> getEdges() {
   List<AbstractGraph.Edge> edges = new ArrayList<AbstractGraph.Edge>(); // Store
                     // edges

   for (int u = 0; u < NUMBER_OF_NODES; u++) {
    for (int k = 0; k < 16; k++) {
     char[] node = getNode(u); // Get the node for vertex u
     if (node[k] == 'H') {
      int v = getFlippedNode(node, k);
      // Add edge (v, u) for a legal move from node u to node
      // v
      edges.add(new AbstractGraph.Edge(v, u));
     }
    }
   }

   return edges;
  }

  public static int getFlippedNode(char[] node, int position) {
   int row = position / 4;
   int column = position % 4;

   flipACell(node, row, column);
   flipACell(node, row - 1, column);
   flipACell(node, row + 1, column);
   flipACell(node, row, column - 1);
   flipACell(node, row, column + 1);
   /*flipACell(node, row + 1, column + 1);
   flipACell(node, row + 1, column - 1);
   flipACell(node, row - 1, column - 1);
   flipACell(node, row - 1, column + 1);*/

   return getIndex(node);
  }

  public static void flipACell(char[] node, int row, int column) {
   if (row >= 0 && row <= 3 && column >= 0 && column <= 3) {
    // Within the boundary
    if (node[row * 4 + column] == 'H')
     node[row * 4 + column] = 'T'; // Flip from H to T
    else
     node[row * 4 + column] = 'H'; // Flip from T to H
   }
  }

  public static int getIndex(char[] node) {
   int result = 0;

   for (int i = 0; i < 16; i++)
    if (node[i] == 'T')
     result = result * 2 + 1;
    else
     result = result * 2 + 0;

   return result;
  }

  public static char[] getNode(int index) {
   char[] result = new char[16];

   for (int i = 0; i < 16; i++) {
    int digit = index % 2;
    if (digit == 0)
     result[15 - i] = 'H';
    else
     result[15 - i] = 'T';
    index = index / 2;
   }

   return result;
  }

  public List<Integer> getShortestPath(int nodeIndex) {
   List<Integer> result =  tree.getPath(nodeIndex);
   if((result.size() == 1) &&(nodeIndex != NUMBER_OF_NODES - 1)) {
    return null;
   } else {
    return result;
   }
  }

  public static void printNode(char[] node) {
   for (int i = 0; i < 16; i++)
    if (i % 4 != 3)
     System.out.print(node[i]);
    else
     System.out.println(node[i]);

   System.out.println();
  }
 }

 static class UnweightedGraph<V> extends AbstractGraph<V> {
  private static final long serialVersionUID = -7293149551075817791L;

  /** Construct an empty graph */
  public UnweightedGraph() {
  }

  /** Construct a graph from edges and vertices stored in arrays */
  public UnweightedGraph(int[][] edges, V[] vertices) {
   super(edges, vertices);
  }

  /** Construct a graph from edges and vertices stored in List */
  public UnweightedGraph(List<Edge> edges, List<V> vertices) {
   super(edges, vertices);
  }

  /** Construct a graph for integer vertices 0, 1, 2 and edge list */
  public UnweightedGraph(List<Edge> edges, int numberOfVertices) {
   super(edges, numberOfVertices);
  }

  /** Construct a graph from integer vertices 0, 1, and edge array */
  public UnweightedGraph(int[][] edges, int numberOfVertices) {
   super(edges, numberOfVertices);
  }
 }

 static abstract class AbstractGraph<V> implements Graph<V>, Serializable {
  private static final long serialVersionUID = -376810429873935051L;
  protected List<V> vertices = new ArrayList<V>(); // Store vertices
  protected List<List<Integer>> neighbors = new ArrayList<List<Integer>>(); // Adjacency
                     // lists

  /** Construct an empty graph */
  protected AbstractGraph() {
  }

  /** Construct a graph from edges and vertices stored in arrays */
  protected AbstractGraph(int[][] edges, V[] vertices) {
   for (int i = 0; i < vertices.length; i++)
    this.vertices.add(vertices[i]);

   createAdjacencyLists(edges, vertices.length);
  }

  /** Construct a graph from edges and vertices stored in List */
  protected AbstractGraph(List<Edge> edges, List<V> vertices) {
   for (int i = 0; i < vertices.size(); i++)
    this.vertices.add(vertices.get(i));

   createAdjacencyLists(edges, vertices.size());
  }

  /** Construct a graph for integer vertices 0, 1, 2 and edge list */
  @SuppressWarnings("unchecked")
  protected AbstractGraph(List<Edge> edges, int numberOfVertices) {
   for (int i = 0; i < numberOfVertices; i++)
    vertices.add((V) (new Integer(i))); // vertices is {0, 1, ...}

   createAdjacencyLists(edges, numberOfVertices);
  }

  /** Construct a graph from integer vertices 0, 1, and edge array */
  @SuppressWarnings("unchecked")
  protected AbstractGraph(int[][] edges, int numberOfVertices) {
   for (int i = 0; i < numberOfVertices; i++)
    vertices.add((V) (new Integer(i))); // vertices is {0, 1, ...}

   createAdjacencyLists(edges, numberOfVertices);
  }

  /** Create adjacency lists for each vertex */
  private void createAdjacencyLists(int[][] edges, int numberOfVertices) {
   // Create a linked list
   for (int i = 0; i < numberOfVertices; i++) {
    neighbors.add(new ArrayList<Integer>());
   }

   for (int i = 0; i < edges.length; i++) {
    int u = edges[i][0];
    int v = edges[i][1];
    neighbors.get(u).add(v);
   }
  }

  /** Create adjacency lists for each vertex */
  private void createAdjacencyLists(List<Edge> edges, int numberOfVertices) {
   // Create a linked list for each vertex
   for (int i = 0; i < numberOfVertices; i++) {
    neighbors.add(new ArrayList<Integer>());
   }

   for (Edge edge : edges) {
    neighbors.get(edge.u).add(edge.v);
   }
  }

  @Override
  /** Return the number of vertices in the graph */
  public int getSize() {
   return vertices.size();
  }

  @Override
  /** Return the vertices in the graph */
  public List<V> getVertices() {
   return vertices;
  }

  @Override
  /** Return the object for the specified vertex */
  public V getVertex(int index) {
   return vertices.get(index);
  }

  @Override
  /** Return the index for the specified vertex object */
  public int getIndex(V v) {
   return vertices.indexOf(v);
  }

  @Override
  /** Return the neighbors of the specified vertex */
  public List<Integer> getNeighbors(int index) {
   return neighbors.get(index);
  }

  @Override
  /** Return the degree for a specified vertex */
  public int getDegree(int v) {
   return neighbors.get(v).size();
  }

  @Override
  /** Print the edges */
  public void printEdges() {
   for (int u = 0; u < neighbors.size(); u++) {
    System.out.print(getVertex(u) + " (" + u + "): ");
    for (int j = 0; j < neighbors.get(u).size(); j++) {
     System.out.print("(" + u + ", " + neighbors.get(u).get(j)
       + ") ");
    }
    System.out.println();
   }
  }

  @Override
  /** Clear graph */
  public void clear() {
   vertices.clear();
   neighbors.clear();
  }

  @Override
  /** Add a vertex to the graph */
  public void addVertex(V vertex) {
   vertices.add(vertex);
   neighbors.add(new ArrayList<Integer>());
  }

  @Override
  /** Add an edge to the graph */
  public void addEdge(int u, int v) {
   neighbors.get(u).add(v);
   neighbors.get(v).add(u);
  }

  /** Edge inner class inside the AbstractGraph class */
  public static class Edge  implements Serializable {
   private static final long serialVersionUID = -4933360745330399905L;
   public int u; // Starting vertex of the edge
   public int v; // Ending vertex of the edge

   /** Construct an edge for (u, v) */
   public Edge(int u, int v) {
    this.u = u;
    this.v = v;
   }
  }

  @Override
  /** Obtain a DFS tree starting from vertex v */
  /** To be discussed in Section 27.6 */
  public Tree dfs(int v) {
   List<Integer> searchOrder = new ArrayList<Integer>();
   int[] parent = new int[vertices.size()];
   for (int i = 0; i < parent.length; i++)
    parent[i] = -1; // Initialize parent[i] to -1

   // Mark visited vertices
   boolean[] isVisited = new boolean[vertices.size()];

   // Recursively search
   dfs(v, parent, searchOrder, isVisited);

   // Return a search tree
   return new Tree(v, parent, searchOrder);
  }

  /** Recursive method for DFS search */
  private void dfs(int v, int[] parent, List<Integer> searchOrder,
    boolean[] isVisited) {
   // Store the visited vertex
   searchOrder.add(v);
   isVisited[v] = true; // Vertex v visited

   for (int i : neighbors.get(v)) {
    if (!isVisited[i]) {
     parent[i] = v; // The parent of vertex i is v
     dfs(i, parent, searchOrder, isVisited); // Recursive search
    }
   }
  }

  @Override
  /** Starting bfs search from vertex v */
  /** To be discussed in Section 27.7 */
  public Tree bfs(int v) {
   List<Integer> searchOrder = new ArrayList<Integer>();
   int[] parent = new int[vertices.size()];
   for (int i = 0; i < parent.length; i++)
    parent[i] = -1; // Initialize parent[i] to -1

   java.util.LinkedList<Integer> queue = new java.util.LinkedList<Integer>(); // list
                      // used
                      // as
                      // a
                      // queue
   boolean[] isVisited = new boolean[vertices.size()];
   queue.offer(v); // Enqueue v
   isVisited[v] = true; // Mark it visited

   while (!queue.isEmpty()) {
    int u = queue.poll(); // Dequeue to u
    searchOrder.add(u); // u searched
    for (int w : neighbors.get(u)) {
     if (!isVisited[w]) {
      queue.offer(w); // Enqueue w
      parent[w] = u; // The parent of w is u
      isVisited[w] = true; // Mark it visited
     }
    }
   }

   return new Tree(v, parent, searchOrder);
  }

  /** Tree inner class inside the AbstractGraph class */
  /** To be discussed in Section 27.5 */
  public class Tree implements Serializable{
   private static final long serialVersionUID = 405899566931047214L;
   private int root; // The root of the tree
   private int[] parent; // Store the parent of each vertex
   private List<Integer> searchOrder; // Store the search order

   /** Construct a tree with root, parent, and searchOrder */
   public Tree(int root, int[] parent, List<Integer> searchOrder) {
    this.root = root;
    this.parent = parent;
    this.searchOrder = searchOrder;
   }

   /** Return the root of the tree */
   public int getRoot() {
    return root;
   }

   /** Return the parent of vertex v */
   public int getParent(int v) {
    return parent[v];
   }

   /** Return an array representing search order */
   public List<Integer> getSearchOrder() {
    return searchOrder;
   }

   /** Return number of vertices found */
   public int getNumberOfVerticesFound() {
    return searchOrder.size();
   }

   /** Return the path of vertices from a vertex to the root */
   public List<V> getPath(int index) {
    ArrayList<V> path = new ArrayList<V>();
    do {
     path.add(vertices.get(index));
     index = parent[index];
    } while (index != -1);

    return path;
   }

   /** Print a path from the root to vertex v */
   public void printPath(int index) {
    List<V> path = getPath(index);
    System.out.print("A path from " + vertices.get(root) + " to "
      + vertices.get(index) + ": ");
    for (int i = path.size() - 1; i >= 0; i--)
     System.out.print(path.get(i) + " ");
   }

   /** Print the whole tree */
   public void printTree() {
    System.out.println("Root is: " + vertices.get(root));
    System.out.print("Edges: ");
    for (int i = 0; i < parent.length; i++) {
     if (parent[i] != -1) {
      // Display an edge
      System.out.print("(" + vertices.get(parent[i]) + ", "
        + vertices.get(i) + ") ");
     }
    }
    System.out.println();
   }
  }
 }

 interface Graph<V> {
  /** Return the number of vertices in the graph */
  public int getSize();

  /** Return the vertices in the graph */
  public java.util.List<V> getVertices();

  /** Return the object for the specified vertex index */
  public V getVertex(int index);

  /** Return the index for the specified vertex object */
  public int getIndex(V v);

  /** Return the neighbors of vertex with the specified index */
  public java.util.List<Integer> getNeighbors(int index);

  /** Return the degree for a specified vertex */
  public int getDegree(int v);

  /** Print the edges */
  public void printEdges();

  /** Clear graph */
  public void clear();

  /** Add a vertex to the graph */
  public void addVertex(V vertex);

  /** Add an edge to the graph */
  public void addEdge(int u, int v);

  /** Obtain a depth-first search tree */
  public AbstractGraph<V>.Tree dfs(int v);

  /** Obtain a breadth-first search tree */
  public AbstractGraph<V>.Tree bfs(int v);
 }

}

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