二叉树遍历递归和非递归算法总结

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import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.Stack;

/**
* A BinaryTree consists of "nodes"--each "node" is itself a BinaryTree. Each
* node has a parent (unless it is the root), may have a left child, and may
* have a right child. This class implements loop-free binary trees, allowing
* shared subtrees.
*
* @author David Matuszek
* @version Jan 25, 2004
* @param <V>
*            The type of values contained in this BinaryTree.
*/
public class BinaryTree<V>
{
    /**
     * The value (data) in this node of the binary tree; may be of any object
     * type.
     */
    public V value;
    private BinaryTree<V> leftChild;
    private BinaryTree<V> rightChild;

    /**
     * Constructor for BinaryTree.
     *
     * @param value
     *            The value to be placed in the root.
     * @param leftChild
     *            The left child of the root (may be null).
     * @param rightChild
     *            The right child of the root (may be null).
     */
    public BinaryTree(V value, BinaryTree<V> leftChild, BinaryTree<V> rightChild)
    {
this.value = value;
this.leftChild = leftChild;
this.rightChild = rightChild;
    }

    /**
     * Constructor for a BinaryTree leaf node (that is, with no children).
     *
     * @param value
     *            The value to be placed in the root.
     */
    public BinaryTree(V value)
    {
this(value, null, null);
    }

    /**
     * Getter method for the value in this BinaryTree node.
     *
     * @return The value in this node.
     */
    public V getValue()
    {
return value;
    }

    /**
     * Getter method for left child of this BinaryTree node.
     *
     * @return The left child (<code>null</code> if no left child).
     */
    public BinaryTree<V> getLeftChild()
    {
return leftChild;
    }

    /**
     * Getter method for right child of this BinaryTree node.
     *
     * @return The right child (<code>null</code> if no right child).
     */
    public BinaryTree<V> getRightChild()
    {
return rightChild;
    }

    /**
     * Sets the left child of this BinaryTree node to be the given subtree. If
     * the node previously had a left child, it is discarded. Throws an
     * <code>IllegalArgumentException</code> if the operation would cause a loop
     * in the binary tree.
     *
     * @param subtree
     *            The node to be added as the new left child.
     * @throws IllegalArgumentException
     *             If the operation would cause a loop in the binary tree.
     */
    public void setLeftChild(BinaryTree<V> subtree)
    throws IllegalArgumentException
    {
if (contains(subtree, this))
{
    throw new IllegalArgumentException("Subtree " + this
    + " already contains " + subtree);
}
leftChild = subtree;
    }

    /**
     * Sets the right child of this BinaryTree node to be the given subtree. If
     * the node previously had a right child, it is discarded. Throws an
     * <code>IllegalArgumentException</code> if the operation would cause a loop
     * in the binary tree.
     *
     * @param subtree
     *            The node to be added as the new right child.
     * @throws IllegalArgumentException
     *             If the operation would cause a loop in the binary tree.
     */
    public void setRightChild(BinaryTree<V> subtree)
    throws IllegalArgumentException
    {
if (contains(subtree, this))
{
    throw new IllegalArgumentException("Subtree " + this
    + " already contains " + subtree);
}
rightChild = subtree;
    }

    /**
     * Sets the value in this BinaryTree node.
     *
     * @param value
     *            The new value.
     */
    public void setValue(V value)
    {
this.value = value;
    }

    /**
     * Tests whether this node is a leaf node.
     *
     * @return <code>true</code> if this BinaryTree node has no children.
     */
    public boolean isLeaf()
    {
return leftChild == null && rightChild == null;
    }

    /**
     * Tests whether this BinaryTree is equal to the given object. To be
     * considered equal, the object must be a BinaryTree, and the two binary
     * trees must have equal values in their roots, equal left subtrees, and
     * equal right subtrees.
     *
     * @return <code>true</code> if the binary trees are equal.
     * @see java.lang.Object#equals(java.lang.Object)
     */
    public boolean equals(Object o)
    {
if (o == null || !(o instanceof BinaryTree))
{
    return false;
}
BinaryTree<?> otherTree = (BinaryTree<?>) o;
return equals(value, otherTree.value)
&& equals(leftChild, otherTree.getLeftChild())
&& equals(rightChild, otherTree.getRightChild());
    }

    /**
     * Tests whether its two arguments are equal. This method simply checks for
     * <code>null</code> before calling <code>equals(Object)</code> so as to
     * avoid possible <code>NullPointerException</code>s.
     *
     * @param x
     *            The first object to be tested.
     * @param y
     *            The second object to be tested.
     * @return <code>true</code> if the two objects are equal.
     */
    private boolean equals(Object x, Object y)
    {
if (x == null)
    return y == null;
return x.equals(y);
    }

    /**
     * Tests whether the <code>tree</code> argument contains within itself the
     * <code>targetNode</code> argument.
     *
     * @param tree
     *            The root of the binary tree to search.
     * @param targetNode
     *            The node to be searched for.
     * @return <code>true</code> if the <code>targetNode</code> argument can be
     *         found within the binary tree rooted at <code>tree</code>.
     */
    protected static <T> boolean contains(BinaryTree<T> tree,
    BinaryTree<T> targetNode)
    {
if (tree == null)
    return false;
if (tree == targetNode)
    return true;
return contains(tree.getLeftChild(), targetNode)
|| contains(tree.getRightChild(), targetNode);
    }

    /**
     * Returns a String representation of this BinaryTree.
     *
     * @see java.lang.Object#toString()
     * @return A String representation of this BinaryTree.
     */
    @Override
    public String toString()
    {
if (isLeaf())
{
    return value.toString();
} else
{
    String root, left = "null", right = "null";
    root = value.toString();
    if (getLeftChild() != null)
    {
left = getLeftChild().toString();
    }
    if (getRightChild() != null)
    {
right = getRightChild().toString();
    }
    return root + " (" + left + ", " + right + ")";
}
    }

    /**
     * Computes a hash code for the complete binary tree rooted at this
     * BinaryTree node.
     *
     * @return A hash code for the binary tree with this root.
     * @see java.lang.Object#hashCode()
     */
    public int hashCode()
    {
int result = value.hashCode();
if (leftChild != null)
{
    result += 3 * leftChild.hashCode();
}
if (rightChild != null)
{
    result += 7 * rightChild.hashCode();
}
return result;
    }

    /**
     * Prints the binary tree rooted at this BinaryTree node.
     */
    public void print()
    {
print(this, 0);
    }

    private void print(BinaryTree<V> root, int indent)
    {
for (int i = 0; i < indent; i++)
{
    System.out.print("   ");
}
if (root == null)
{
    System.out.println("null");
    return;
}
System.out.println(root.value);
if (root.isLeaf())
    return;
print(root.leftChild, indent + 1);
print(root.rightChild, indent + 1);
    }

    // -------------------------- Methods added for Assignment 3, CIT 594-2008

    /**
     * Returns the leftmost descendant of this binary tree. That is, return the
     * leaf that is the left child of the left child of ... the left child of
     * this binary tree. If this binary tree has no left child, return this
     * binary tree.
     *
     * @return The leftmost descendant of this BinaryTree.
     */
    public BinaryTree<V> leftmostDescendant()
    {
if (this.leftChild == null)
    return this;
else
    return leftChild.leftmostDescendant();
    }

    /**
     * Returns the rightmost descendant of this binary tree. That is, return the
     * leaf that is the right child of the right child of ... the right child of
     * this binary tree. If this binary tree has no right child, return this
     * binary tree.
     *
     * @return The rightmost descendant of this BinaryTree.
     */
    public BinaryTree<V> rightmostDescendant()
    {
if (this.rightChild == null)
    return this;
else
    return rightChild.rightmostDescendant();
    }

    /**
     * Returns the total number of nodes in this binary tree (include the root
     * in the count).
     *
     * @return The number of nodes in this BinaryTree.
     */
    public int numberOfNodes()
    {
int leftCount = this.leftChild == null ? 0 : leftChild.numberOfNodes();
int rightCount = this.rightChild == null ? 0 : rightChild
.numberOfNodes();
return 1 + leftCount + rightCount;
    }

    /**
     * Returns the depth of this binary tree. The depth of a binary tree is the
     * length of the longest path from this node to a leaf. The depth of a
     * binary tree with no descendants (that is, just a leaf) is zero.
     *
     * @return The depth of this BinaryTree.
     */
    public int depth()
    {
int leftDepth = this.leftChild == null ? 0 : leftChild.depth() + 1;
int rightDepth = this.rightChild == null ? 0 : rightChild.depth() + 1;
return Math.max(leftDepth, rightDepth);
    }

    /**
     * Returns true if and only if some node in this binary tree contains a
     * value that is equal to the parameter.
     *
     * @param value
     *            The value to be searched for.
     * @return <code>true</code> if this BinaryTree contains an equal value.
     */
    public boolean containsEqualValue(V value)
    {
if (this.value == null && value == null)
    return true;
if (this.value != null && this.value.equals(value))
    return true;
if (leftChild != null && leftChild.containsEqualValue(value))
    return true;
if (rightChild != null && rightChild.containsEqualValue(value))
    return true;
return false;
    }

    /**
     * Returns true if and only if some node in this binary tree contains the
     * same object (not just an equal object) as the one given for the value
     * parameter.
     *
     * @param value
     *            The value to be searched for.
     * @return <code>true</code> if this BinaryTree contains the identical
     *         value.
     */
    public boolean containsSameValue(V value)
    {
if (this.value == null && value == null)
    return true;
if (this.value != null && this.value == value)
    return true;
if (leftChild != null && leftChild.containsSameValue(value))
    return true;
if (rightChild != null && rightChild.containsSameValue(value))
    return true;
return false;
    }

    /**
     * Returns a Set of all the leaves of this binary tree.
     *
     * @return The leaves of this BinaryTree.
     */
    public Set<BinaryTree<V>> leaves()
    {
Set<BinaryTree<V>> set = new HashSet<BinaryTree<V>>();
if (this.isLeaf())
{
    set.add(this);
}
if (leftChild != null)
{
    set.addAll(leftChild.leaves());
}
if (rightChild != null)
{
    set.addAll(rightChild.leaves());
}
return set;
    }

    /**
     * Returns a Set of the values (of type V) in this binary tree.
     *
     * @return The values in this BinaryTree.
     */
    public Set<V> valuesOf()
    {
Set<V> values = new HashSet<V>();
values.add(this.value);
if (leftChild != null)
{
    values.addAll(leftChild.valuesOf());
}
if (rightChild != null)
{
    values.addAll(rightChild.valuesOf());
}
return values;
    }

    /**
     * Returns a List of the values (of type V) in the leaves of this binary
     * tree, in left-to-right order.
     *
     * @return The values in the leaves of this BinaryTree.
     */
    public List<V> fringe()
    {
List<V> values = new ArrayList<V>();
if (this.isLeaf())
{
    values.add(this.value);
    return values;
}
if (leftChild != null)
{
    values.addAll(leftChild.fringe());
}
if (rightChild != null)
{
    values.addAll(rightChild.fringe());
}
return values;
    }

    /**
     * Returns a new BinaryTree equal to (but not the same as) this binary tree.
     * Every node in this new BinaryTree will be created by the copy method;
     * values will be identical (==) to values in the given binary tree.
     *
     * @return An exact copy of this BinaryTree; the values in the new
     *         BinaryTree are == to the values in this BinaryTree.
     */
    public BinaryTree<V> copy()
    {
BinaryTree<V> left = null, right = null;
if (this.leftChild != null)
{
    left = this.leftChild.copy();
}
if (this.rightChild != null)
{
    right = this.rightChild.copy();
}
return new BinaryTree<V>(this.value, left, right);
    }

    /**
     * Returns a new binary tree which is the mirror image of the binary tree
     * whose root is at this binary tree. That is, for every node in the new
     * binary tree, its children are in reverse order (left child becomes right
     * child, right child becomes left child).
     *
     * @return A mirror image copy of this BinaryTree; values in the new
     *         BinaryTree are == to the values in this BinaryTree.
     */
    public BinaryTree<V> reverse()
    {
BinaryTree<V> left = null, right = null;
if (this.leftChild != null)
{
    left = this.leftChild.reverse();
}
if (this.rightChild != null)
{
    right = this.rightChild.reverse();
}
return new BinaryTree<V>(this.value, right, left);
    }

    /**
     * Rearranges the binary tree rooted at this binary tree to be the mirror
     * image of its original structure. No new BinaryTree nodes are created in
     * this process.
     */
    public void reverseInPlace()
    {
if (this.leftChild != null)
{
    leftChild.reverseInPlace();
}
if (this.rightChild != null)
{
    rightChild.reverseInPlace();
}
BinaryTree<V> temp = this.leftChild;
this.setLeftChild(this.rightChild);
this.setRightChild(temp);
    }

    public void preOrderTraverseIterative()
    {
Stack<BinaryTree<V>> stack = new Stack<BinaryTree<V>>();
BinaryTree<V> subTree = this;

while (!stack.empty() || subTree != null)
{
    if (subTree != null)
    {
stack.push(subTree);
System.out.print(subTree.value + ", ");
subTree = subTree.leftChild;
    } else
    {
subTree = stack.pop();
subTree = subTree.rightChild;
    }
}
    }

    public void preOrderTraverse()
    {
preOrderTraverse(this);
    }

    private void preOrderTraverse(BinaryTree<V> subTree)
    {
if (subTree != null)
{
    System.out.print(subTree.value + ", ");
    preOrderTraverse(subTree.leftChild);
    preOrderTraverse(subTree.rightChild);
}
    }

    public void inOrderTraverseIterative()
    {
Stack<BinaryTree<V>> stack = new Stack<BinaryTree<V>>();
BinaryTree<V> subTree = this;

while (!stack.empty() || subTree != null)
{
    if (subTree != null)
    {
stack.push(subTree);
subTree = subTree.leftChild;

    } else
    {
subTree = stack.pop();
System.out.print(subTree.value + ", ");
subTree = subTree.rightChild;
    }
}
    }

    public void inOrderTraverse()
    {
inOrderTraverse(this);
    }

    private void inOrderTraverse(BinaryTree<V> subTree)
    {
if (subTree != null)
{
    inOrderTraverse(subTree.leftChild);
    System.out.print(subTree.value + ", ");
    inOrderTraverse(subTree.rightChild);
}
    }

    public void postOrderTraverseIterative()
    {
Stack<BinaryTree<V>> stack = new Stack<BinaryTree<V>>();
Stack<BinaryTree<V>> result = new Stack<BinaryTree<V>>();
BinaryTree<V> current;
stack.push(this);

while (!stack.empty())
{
    current = stack.pop();
    result.push(current);

    if (current.leftChild != null)
stack.push(current.leftChild);

    if (current.rightChild != null)
stack.push(current.rightChild);
}

while (!result.empty())
{
    System.out.print(result.pop().value + ", ");
}
    }

    public void postOrderTraverse()
    {
postOrderTraverse(this);
    }

    private void postOrderTraverse(BinaryTree<V> subTree)
    {
if (subTree != null)
{
    postOrderTraverse(subTree.leftChild);
    postOrderTraverse(subTree.rightChild);
    System.out.print(subTree.value + ", ");
}
    }
public void display()
    {
Stack<BinaryTree<V>> stack = new Stack<BinaryTree<V>>();
stack.push(this);
int nBlanks = 32;
boolean isRowEmpty = false;
while (isRowEmpty == false)
{
    Stack<BinaryTree<V>> localStack = new Stack<BinaryTree<V>>();
    isRowEmpty = true;

    for (int j = 0; j < nBlanks; j++)
System.out.print(' ');

    while (stack.isEmpty() == false)
    {
BinaryTree<V> subTree = stack.pop();
if (subTree != null)
{
    System.out.print(subTree.value);
    localStack.push(subTree.leftChild);
    localStack.push(subTree.rightChild);

    if (subTree.leftChild != null || subTree.rightChild != null)
isRowEmpty = false;
} else
{
    System.out.print("--");
    localStack.push(null);
    localStack.push(null);
}
for (int j = 0; j < nBlanks * 2 - 2; j++)
    System.out.print(' ');
    }
    System.out.println();
    nBlanks /= 2;
    while (localStack.isEmpty() == false)
stack.push(localStack.pop());
}
    }
}