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Tuesday, 21 February 2017

Chapter 28 Exercise 14, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

28.14 (4 * 4 16 tails problem) Listing 28.14, NineTail.java, presents a solution for the nine tails problem. Revise this program for the 4 * 4 16 tails problem.
Note that it is possible that a solution may not exist for a starting pattern. If so,
report that no solution exists.

import java.io.Serializable;
import java.util.ArrayList;
import java.util.List;

public class Exercise14 {
  public static void main(String[] args) {
    TailModel model = new TailModel();
    System.out.println("The number of the starting patterns that have a solution: " 
        + model.tree.getNumberOfVerticesFound());
    System.out.println("The number of the starting patterns that don't have a solution: " 
        + (model.NUMBER_OF_NODES - model.tree.getNumberOfVerticesFound()));
  }
  
  static class TailModel {
    public final static int DIMENSION = 4;
    // 1 << 9 is 512; 1 << 16 is 65536;
    public final static int NUMBER_OF_NODES = 1 << DIMENSION * DIMENSION; 
    protected AbstractGraph<Integer>.Tree tree; // Define a tree

    /** Construct a model */
    public TailModel() {
      // 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(NUMBER_OF_NODES - 1);
    }

    /** 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 < DIMENSION * DIMENSION; 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 / DIMENSION;
      int column = position % DIMENSION;

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

      return getIndex(node);
    }

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

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

      for (int i = 0; i < DIMENSION * DIMENSION; 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[DIMENSION * DIMENSION];

      for (int i = 0; i < DIMENSION * DIMENSION; i++) {
        int digit = index % 2;
        if (digit == 0)
          result[DIMENSION * DIMENSION - 1 - i] = 'H';
        else
          result[DIMENSION * DIMENSION - 1 - i] = 'T';
        index = index / 2;
      }

      return result;
    }
    
    public List<Integer> getShortestPath(int nodeIndex) {
      List<Integer> path = tree.getPath(nodeIndex);
      
      if (path.size() == 1 && path.get(0) != DIMENSION * DIMENSION - 1)
        return null;
      else
        return path;
    }

    public static void printNode(char[] node) {
      for (int i = 0; i < DIMENSION * DIMENSION; i++)
        if (i % DIMENSION != DIMENSION - 1)
          System.out.print(node[i]);
        else
          System.out.println(node[i]);

      System.out.println();
    }
  }
}

import java.util.*;

public abstract class AbstractGraph<V> implements Graph<V> {
  protected List<V> vertices = new ArrayList<>(); // Store vertices
  protected List<List<Edge>> neighbors 
    = new ArrayList<>(); // Adjacency lists

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

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

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

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

  /** Create adjacency lists for each vertex */
  private void createAdjacencyLists(
      int[][] edges, int numberOfVertices) {
    for (int i = 0; i < edges.length; i++) {
      addEdge(edges[i][0], edges[i][1]);
    }
  }

  /** Create adjacency lists for each vertex */
  private void createAdjacencyLists(
      List<Edge> edges, int numberOfVertices) {
    for (Edge edge: edges) {
      addEdge(edge.u, 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) {
    List<Integer> result = new ArrayList<>();
    for (Edge e: neighbors.get(index))
      result.add(e.v);
    
    return result;
  }

  @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 (Edge e: neighbors.get(u)) {
        System.out.print("(" + getVertex(e.u) + ", " +
          getVertex(e.v) + ") ");
      }
      System.out.println();
    }
  }

  @Override /** Clear graph */
  public void clear() {
    vertices.clear();
    neighbors.clear();
  }
  
  @Override /** Add a vertex to the graph */  
  public boolean addVertex(V vertex) {
    if (!vertices.contains(vertex)) {
      vertices.add(vertex);
      neighbors.add(new ArrayList<Edge>());
      return true;
    }
    else {
      return false;
    }
  }

  /** Add an edge to the graph */  
  protected boolean addEdge(Edge e) {
    if (e.u < 0 || e.u > getSize() - 1)
      throw new IllegalArgumentException("No such index: " + e.u);

    if (e.v < 0 || e.v > getSize() - 1)
      throw new IllegalArgumentException("No such index: " + e.v);
    
    if (!neighbors.get(e.u).contains(e)) {
      neighbors.get(e.u).add(e);
      return true;
    }
    else {
      return false;
    }
  }
  
  @Override /** Add an edge to the graph */  
  public boolean addEdge(int u, int v) {
    return addEdge(new Edge(u, v));
  }
  
  /** Edge inner class inside the AbstractGraph class */
  public static class Edge {
    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;
    }
    
    public boolean equals(Object o) {
      return u == ((Edge)o).u && v == ((Edge)o).v; 
    }
  }
  
  @Override /** Obtain a DFS tree starting from vertex v */
  /** To be discussed in Section 30.6 */
  public Tree dfs(int v) {
    List<Integer> searchOrder = new ArrayList<>();
    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 u, int[] parent, List<Integer> searchOrder,
      boolean[] isVisited) {
    // Store the visited vertex
    searchOrder.add(u);
    isVisited[u] = true; // Vertex v visited

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

  @Override /** Starting bfs search from vertex v */
  /** To be discussed in Section 28.7 */
  public Tree bfs(int v) {
    List<Integer> searchOrder = new ArrayList<>();
    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<>(); // 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 (Edge e: neighbors.get(u)) {
        if (!isVisited[e.v]) {
          queue.offer(e.v); // Enqueue w
          parent[e.v] = u; // The parent of w is u
          isVisited[e.v] = true; // Mark it visited
        }
      }
    }

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

  /** Tree inner class inside the AbstractGraph class */
  /** To be discussed in Section 28.5 */
  public class Tree {
    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<>();

      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();
    }
  }
}

public 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 boolean addVertex(V vertex);

  /** Add an edge to the graph */  
  public boolean 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);
}

import java.util.*;

public class UnweightedGraph<V> extends AbstractGraph<V> {
  /** Construct an empty graph */
  public UnweightedGraph() {
  }
    
  /** Construct a graph from vertices and edges stored in arrays */
  public UnweightedGraph(V[] vertices, int[][] edges) {
    super(vertices, edges);
  }

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

  /** 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);
  }
}

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