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EXAMPLE 11.19 Evaluating an Expression from Its Postfix Representation
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Figure 11.20 shows the evaluation of the expression in Example 11.18 using 2 for x, 3 for y, and 1 for z:
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Figure 11.20 Evaluating a postfix expression
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A BinaryTree CLASS Here is a class for binary trees that directly implements the recursive definition. (See page 200.) By extending the AbstractCollection class, it remains consistent with the Java Collections Framework. (See 4.)
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EXAMPLE 11.20 A BinaryTree Class
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public class BinaryTree<E> extends AbstractCollection { protected E root; protected BinaryTree<E> left, right, parent; protected int size; public BinaryTree() { } public BinaryTree(E root) { this.root = root; size = 1; } public BinaryTree(E root, BinaryTree<E> left, BinaryTree<E> right) { this(root); if (left != null) { this.left = left; left.parent = this; size += left.size(); } if (right != null) { this.right = right; right.parent = this; size += right.size(); } } public boolean equals(Object object) { if (object == this) { return true; } else if (!(object instanceof BinaryTree)) { return false; } BinaryTree that = (BinaryTree)object; return that.root.equals(this.root) && that.left.equals(this.left) && that.right.equals(this.right) && that.parent.equals(this.parent) && that.size == this.size; } public int hashCode() { return root.hashCode() + left.hashCode() + right.hashCode() + size; } public int size() { return size; } public Iterator iterator() { return new java.util.Iterator() { // anonymous inner class private boolean rootDone; private Iterator lIt, rIt; // child iterators
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public boolean hasNext() { return !rootDone || lIt != null && lIt.hasNext() || rIt != null && rIt.hasNext(); } public Object next() { if (rootDone) { if (lIt != null && lIt.hasNext()) { return lIt.next(); } if (rIt != null && rIt.hasNext()) { return rIt.next(); } return null; } if (left != null) { lIt = left.iterator(); } if (right != null) { rIt = right.iterator(); } rootDone = true; return root; } public void remove() { throw new UnsupportedOperationException(); } };
} } The java.util.AbstractCollection class requires the four methods that are defined here: equals(), hashCode(), iterator(), and size().1 The iterator() method overrides the empty version that is defined in the AbstractCollection class. Its job is to build an iterator object that can traverse its BinaryTree object. To do that, it creates its own anonymous inner Iterator class using the Java return new construct at line 47. The body of this
anonymous class is defined between the braces that immediately follow the invocation of the constructor Iterator(). Note that this block must be followed by a semicolon because it is actually the end of the return statement. The complete construct looks like a method definition, but it is not. It really is a complete class definition embedded within a return statement. To return an Iterator object, this anonymous class must implement the Iterator interface. (See page 77.) This requires definitions for the three methods
public boolean hasNext() ... public Object next() ... public void remove() ... This implementation is recursive. The hasNext() method invokes the hasNext() methods of iterators on the two subtrees, and the next() method invokes the next() methods of those two iterators, named lIt and rIt. The other local variable is a flag named rootDone that keeps track of whether the root
object has been visited yet by the iterator. The hasNext() method returns true unless all three parts of the tree have been visited: the root, the left subtree, and the right subtree. It does that by using the lIt and rIt iterators recursively.
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