Chapter 26 Exercise 4, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

26.4 (Parent reference for BST ) Suppose that the TreeNode class defined in BST contains a reference to the node’s parent, as shown in Programming Exercise 25.15. Implement the AVLTree class to support this change. Write a test program that adds numbers 1 , 2 , . . . , 100 to the tree and displays the paths for all leaf nodes.

import java.util.ArrayList;

public class Exercise04 {

 public static void main(String[] args) {
  AVLTree<Integer> tree = new AVLTree<Integer>();
  for (int i = 1; i <= 100; i++) {
   tree.insert(i);   
  }
  tree.displayPath();
 }
 
 static class AVLTree<E extends Comparable<E>> extends BST<E> {
  /** Create a default AVL tree */
  public AVLTree() {
  }

  /** Create an AVL tree from an array of objects */
  public AVLTree(E[] objects) {
   super(objects);
  }

  public void displayPath() {
   displayPath(root);
  }
  
  public void displayPath(TreeNode<E> node) {
   ArrayList<TreeNode<E>> list = getPath(node);
   for (TreeNode<E> treeNode : list) {
    System.out.print(treeNode.element + " ");
   }
   System.out.println();
   if(node.left != null) {
    displayPath(node.left);
   }
   if(node.right != null) {
    displayPath(node.right);
   }   
  }
  
 
  @Override
  /** Override createNewNode to create an AVLTreeNode */
  protected AVLTreeNode<E> createNewNode(E e, TreeNode<E> parent) {
   return new AVLTreeNode<E>(e, parent);
  }

  @Override
  /** Insert an element and rebalance if necessary */
  public boolean insert(E e) {
   boolean successful = super.insert(e);
   if (!successful)
    return false; // e is already in the tree
   else {
    balancePath(e); // Balance from e to the root if necessary
   }

   return true; // e is inserted
  }

  /** Update the height of a specified node */
  private void updateHeight(AVLTreeNode<E> node) {
   if (node.left == null && node.right == null) // node is a leaf
    node.height = 0;
   else if (node.left == null) // node has no left subtree
    node.height = 1 + ((AVLTreeNode<E>) (node.right)).height;
   else if (node.right == null) // node has no right subtree
    node.height = 1 + ((AVLTreeNode<E>) (node.left)).height;
   else
    node.height = 1 + Math.max(
      ((AVLTreeNode<E>) (node.right)).height,
      ((AVLTreeNode<E>) (node.left)).height);
  }

  /**
   * Balance the nodes in the path from the specified node to the root if
   * necessary
   */
  private void balancePath(E e) {
   java.util.ArrayList<TreeNode<E>> path = path(e);
   for (int i = path.size() - 1; i >= 0; i--) {
    AVLTreeNode<E> A = (AVLTreeNode<E>) (path.get(i));
    updateHeight(A);
    switch (balanceFactor(A)) {
    case -2:
     if (balanceFactor((AVLTreeNode<E>) A.left) <= 0) {
      balanceLL(A); // Perform LL rotation
     } else {
      balanceLR(A); // Perform LR rotation
     }
     break;
    case +2:
     if (balanceFactor((AVLTreeNode<E>) A.right) >= 0) {
      balanceRR(A); // Perform RR rotation
     } else {
      balanceRL(A); // Perform RL rotation
     }
    }
   }
  }

  /** Return the balance factor of the node */
  private int balanceFactor(AVLTreeNode<E> node) {
   if (node.right == null) // node has no right subtree
    return -node.height;
   else if (node.left == null) // node has no left subtree
    return +node.height;
   else
    return ((AVLTreeNode<E>) node.right).height
      - ((AVLTreeNode<E>) node.left).height;
  }

  /** Balance LL (see Figure 9.1) */
  private void balanceLL(TreeNode<E> A) {
   TreeNode<E> parentOfA = A.parent;
   TreeNode<E> B = A.left; // A is left-heavy and B is left-heavy
   A.parent = B;
   if(B.right != null) {
    B.right.parent = A;
   }
   B.parent = parentOfA;      
   if (A == root) {
    root = B;
   } else {
    if (parentOfA.left == A) {
     parentOfA.left = B;
    } else {
     parentOfA.right = B;
    }
   }

   A.left = B.right; // Make T2 the left subtree of A
   B.right = A; // Make A the left child of B
   updateHeight((AVLTreeNode<E>) A);
   updateHeight((AVLTreeNode<E>) B);
  }

  /** Balance LR (see Figure 9.1(c)) */
  private void balanceLR(TreeNode<E> A) {
   TreeNode<E> parentOfA = A.parent;
   TreeNode<E> B = A.left; // A is left-heavy
   TreeNode<E> C = B.right; // B is right-heavy
   A.parent = C;
   B.parent = C;
   if(C.left != null) {
    C.left.parent = B;
   }
   if(C.right != null) {
    C.right.parent = A;
   }
   C.parent = parentOfA;   

   if (A == root) {
    root = C;
   } else {
    if (parentOfA.left == A) {
     parentOfA.left = C;
    } else {
     parentOfA.right = C;
    }
   }

   A.left = C.right; // Make T3 the left subtree of A
   B.right = C.left; // Make T2 the right subtree of B
   C.left = B;
   C.right = A;

   // Adjust heights
   updateHeight((AVLTreeNode<E>) A);
   updateHeight((AVLTreeNode<E>) B);
   updateHeight((AVLTreeNode<E>) C);
  }

  /** Balance RR (see Figure 9.1(b)) */
  private void balanceRR(TreeNode<E> A) {
   TreeNode<E> parentOfA = A.parent;
   TreeNode<E> B = A.right; // A is right-heavy and B is right-heavy
   A.parent = B;
   if(B.left != null) {
    B.left.parent = A;
   }
   B.parent = parentOfA;
   
   if (A == root) {
    root = B;
   } else {
    if (parentOfA.left == A) {
     parentOfA.left = B;
    } else {
     parentOfA.right = B;
    }
   }

   A.right = B.left; // Make T2 the right subtree of A
   B.left = A;
   updateHeight((AVLTreeNode<E>) A);
   updateHeight((AVLTreeNode<E>) B);
  }

  /** Balance RL (see Figure 9.1(d)) */
  private void balanceRL(TreeNode<E> A) {
   TreeNode<E> parentOfA = A.parent;
   TreeNode<E> B = A.right; // A is right-heavy
   TreeNode<E> C = B.left; // B is left-heavy
   A.parent = C;
   B.parent = C;
   if(C.left != null) {
    C.left.parent = A;
   }
   if(C.right != null) {
    C.right.parent = B;
   }
   C.parent = parentOfA;
   
   if (A == root) {
    root = C;
   } else {
    if (parentOfA.left == A) {
     parentOfA.left = C;
    } else {
     parentOfA.right = C;
    }
   }

   A.right = C.left; // Make T2 the right subtree of A
   B.left = C.right; // Make T3 the left subtree of B
   C.left = A;
   C.right = B;

   // Adjust heights
   updateHeight((AVLTreeNode<E>) A);
   updateHeight((AVLTreeNode<E>) B);
   updateHeight((AVLTreeNode<E>) C);
  }

  @Override
  /** Delete an element from the binary tree.
   * Return true if the element is deleted successfully
   * Return false if the element is not in the tree */
  public boolean delete(E element) {
   if (root == null)
    return false; // Element is not in the tree

   // Locate the node to be deleted and also locate its parent node
   TreeNode<E> parent = null;
   TreeNode<E> current = root;
   while (current != null) {
    if (element.compareTo(current.element) < 0) {
     parent = current;
     current = current.left;
    } else if (element.compareTo(current.element) > 0) {
     parent = current;
     current = current.right;
    } else
     break; // Element is in the tree pointed by current
   }

   if (current == null)
    return false; // Element is not in the tree

   // Case 1: current has no left children (See Figure 23.6)
   if (current.left == null) {
    // Connect the parent with the right child of the current node
    if (parent == null) {
     root = current.right;
    } else {
     if (element.compareTo(parent.element) < 0)
      parent.left = current.right;
     else
      parent.right = current.right;

     // Balance the tree if necessary
     balancePath(parent.element);
    }
   } else {
    // Case 2: The current node has a left child
    // Locate the rightmost node in the left subtree of
    // the current node and also its parent
    TreeNode<E> parentOfRightMost = current;
    TreeNode<E> rightMost = current.left;

    while (rightMost.right != null) {
     parentOfRightMost = rightMost;
     rightMost = rightMost.right; // Keep going to the right
    }

    // Replace the element in current by the element in rightMost
    current.element = rightMost.element;

    // Eliminate rightmost node
    if (parentOfRightMost.right == rightMost)
     parentOfRightMost.right = rightMost.left;
    else
     // Special case: parentOfRightMost is current
     parentOfRightMost.left = rightMost.left;

    // Balance the tree if necessary
    balancePath(parentOfRightMost.element);
   }

   size--;
   return true; // Element inserted
  }

  /** AVLTreeNode is TreeNode plus height */
  protected static class AVLTreeNode<E extends Comparable<E>> extends BST.TreeNode<E> {
   protected int height = 0; // New data field

   public AVLTreeNode(E o, TreeNode<E> parent) {
    super(o, parent);
   }
  }
 }
 

 static class BST<E extends Comparable<E>> extends AbstractTree<E> {
  protected TreeNode<E> root;
  protected int size = 0;
  
  /** Returns the parent for the specified node. */
  public TreeNode<E> getParent(TreeNode<E> node) {
   return node.parent;
  }
  
  /** Returns the path from the specified node to the root
  * in an array list. */
  public ArrayList<TreeNode<E>> getPath(TreeNode<E> node) {
   ArrayList<TreeNode<E>> result = new ArrayList<>();
   while(node.parent != null) {
    result.add(node);
    node = node.parent;
   }
   result.add(node);
   return result;
  }
  
  
  /** Create a default binary tree */
  public BST() {
  }

  /** Create a binary tree from an array of objects */
  public BST(E[] objects) {
   for (int i = 0; i < objects.length; i++)
    insert(objects[i]);
  }

  @Override
  /** Returns true if the element is in the tree */
  public boolean search(E e) {
   TreeNode<E> current = root; // Start from the root

   while (current != null) {
    if (e.compareTo(current.element) < 0) {
     current = current.left;
    } else if (e.compareTo(current.element) > 0) {
     current = current.right;
    } else
     // element matches current.element
     return true; // Element is found
   }

   return false;
  }

  @Override
  /** Insert element o into the binary tree
   * Return true if the element is inserted successfully */
  public boolean insert(E e) {
   if (root == null)
    root = createNewNode(e, null); // Create a new root
   else {
    // Locate the parent node
    TreeNode<E> parent = null;
    TreeNode<E> current = root;
    while (current != null)
     if (e.compareTo(current.element) < 0) {
      parent = current;
      current = current.left;
     } else if (e.compareTo(current.element) > 0) {
      parent = current;
      current = current.right;
     } else
      return false; // Duplicate node not inserted

    // Create the new node and attach it to the parent node
    if (e.compareTo(parent.element) < 0)
     parent.left = createNewNode(e, parent);
    else
     parent.right = createNewNode(e, parent);
   }

   size++;
   return true; // Element inserted
  }

  protected TreeNode<E> createNewNode(E e, TreeNode<E> parent) {
   return new TreeNode<E>(e, parent);
  }

  @Override
  /** Inorder traversal from the root*/
  public void inorder() {
   inorder(root);
  }

  /** Inorder traversal from a subtree */
  protected void inorder(TreeNode<E> root) {
   if (root == null)
    return;
   inorder(root.left);
   System.out.print(root.element + " ");
   inorder(root.right);
  }

  @Override
  /** Postorder traversal from the root */
  public void postorder() {
   postorder(root);
  }

  /** Postorder traversal from a subtree */
  protected void postorder(TreeNode<E> root) {
   if (root == null)
    return;
   postorder(root.left);
   postorder(root.right);
   System.out.print(root.element + " ");
  }

  @Override
  /** Preorder traversal from the root */
  public void preorder() {
   preorder(root);
  }

  /** Preorder traversal from a subtree */
  protected void preorder(TreeNode<E> root) {
   if (root == null)
    return;
   System.out.print(root.element + " ");
   preorder(root.left);
   preorder(root.right);
  }

  /**
   * This inner class is static, because it does not access any instance
   * members defined in its outer class
   */
  public static class TreeNode<E extends Comparable<E>> {
   protected E element;
   protected TreeNode<E> left;
   protected TreeNode<E> right;
   protected TreeNode<E> parent;

   public TreeNode(E e, TreeNode<E> parent) {
    element = e;
    this.parent = parent;
   }   
  }

  @Override
  /** Get the number of nodes in the tree */
  public int getSize() {
   return size;
  }

  /** Returns the root of the tree */
  public TreeNode<E> getRoot() {
   return root;
  }

  /** Returns a path from the root leading to the specified element */
  public java.util.ArrayList<TreeNode<E>> path(E e) {
   java.util.ArrayList<TreeNode<E>> list = new java.util.ArrayList<TreeNode<E>>();
   TreeNode<E> current = root; // Start from the root

   while (current != null) {
    list.add(current); // Add the node to the list
    if (e.compareTo(current.element) < 0) {
     current = current.left;
    } else if (e.compareTo(current.element) > 0) {
     current = current.right;
    } else
     break;
   }

   return list; // Return an array of nodes
  }

  @Override
  /** Delete an element from the binary tree.
   * Return true if the element is deleted successfully
   * Return false if the element is not in the tree */
  public boolean delete(E e) {
   // Locate the node to be deleted and also locate its parent node
   TreeNode<E> parent = null;
   TreeNode<E> current = root;
   while (current != null) {
    if (e.compareTo(current.element) < 0) {
     parent = current;
     current = current.left;
    } else if (e.compareTo(current.element) > 0) {
     parent = current;
     current = current.right;
    } else
     break; // Element is in the tree pointed at by current
   }

   if (current == null)
    return false; // Element is not in the tree

   // Case 1: current has no left children
   if (current.left == null) {
    // Connect the parent with the right child of the current node
    if (parent == null) {
     root = current.right;
    } else {
     if (e.compareTo(parent.element) < 0)
      parent.left = current.right;
     else
      parent.right = current.right;
    }
   } else {
    // Case 2: The current node has a left child
    // Locate the rightmost node in the left subtree of
    // the current node and also its parent
    TreeNode<E> parentOfRightMost = current;
    TreeNode<E> rightMost = current.left;

    while (rightMost.right != null) {
     parentOfRightMost = rightMost;
     rightMost = rightMost.right; // Keep going to the right
    }

    // Replace the element in current by the element in rightMost
    current.element = rightMost.element;

    // Eliminate rightmost node
    if (parentOfRightMost.right == rightMost)
     parentOfRightMost.right = rightMost.left;
    else
     // Special case: parentOfRightMost == current
     parentOfRightMost.left = rightMost.left;
   }

   size--;
   return true; // Element inserted
  }

  @Override
  /** Obtain an iterator. Use inorder. */
  public java.util.Iterator<E> iterator() {
   return new InorderIterator();
  }

  // Inner class InorderIterator
  private class InorderIterator implements java.util.Iterator<E> {
   // Store the elements in a list
   private java.util.ArrayList<E> list = new java.util.ArrayList<E>();
   private int current = 0; // Point to the current element in list

   public InorderIterator() {
    inorder(); // Traverse binary tree and store elements in list
   }

   /** Inorder traversal from the root */
   private void inorder() {
    inorder(root);
   }

   /** Inorder traversal from a subtree */
   private void inorder(TreeNode<E> root) {
    if (root == null)
     return;
    inorder(root.left);
    list.add(root.element);
    inorder(root.right);
   }

   @Override
   /** More elements for traversing? */
   public boolean hasNext() {
    if (current < list.size())
     return true;

    return false;
   }

   @Override
   /** Get the current element and move to the next */
   public E next() {
    return list.get(current++);
   }

   @Override
   /** Remove the current element */
   public void remove() {
    delete(list.get(current)); // Delete the current element
    list.clear(); // Clear the list
    inorder(); // Rebuild the list
   }
  }

  /** Remove all elements from the tree */
  public void clear() {
   root = null;
   size = 0;
  }
 }

 static abstract class AbstractTree<E> implements Tree<E> {
  @Override
  /** Inorder traversal from the root*/
  public void inorder() {
  }

  @Override
  /** Postorder traversal from the root */
  public void postorder() {
  }

  @Override
  /** Preorder traversal from the root */
  public void preorder() {
  }

  @Override
  /** Return true if the tree is empty */
  public boolean isEmpty() {
   return getSize() == 0;
  }

  @Override
  /** Return an iterator for the tree */
  public java.util.Iterator<E> iterator() {
   return null;
  }
 }

 interface Tree<E> extends Iterable<E> {
  /** Return true if the element is in the tree */
  public boolean search(E e);

  /**
   * Insert element o into the binary tree Return true if the element is
   * inserted successfully
   */
  public boolean insert(E e);

  /**
   * Delete the specified element from the tree Return true if the element
   * is deleted successfully
   */
  public boolean delete(E e);

  /** Inorder traversal from the root */
  public void inorder();

  /** Postorder traversal from the root */
  public void postorder();

  /** Preorder traversal from the root */
  public void preorder();

  /** Get the number of nodes in the tree */
  public int getSize();

  /** Return true if the tree is empty */
  public boolean isEmpty();

  public java.util.Iterator<E> iterator();
 }
}