Implementation of Trees

How can we implement a tree in a Java program?  As with linked lists, there are a variety of implementation techniques, using either a nested TreeNode class or a recursive definition.  We will focus on the recursive version.

Implementing Binary Trees

class BinaryTree {
    Object data;
    BinaryTree left,right;

    BinaryTree(){
        data = null;
        left = right = null;
    }

    BinaryTree(Object obj){
        data = obj;
        left = new BinaryTree();
        right = new BinaryTree();
    }

    BinaryTree(Object obj, BinaryTree left, BinaryTree right){
        data = obj;
        this.left = left;
        this.right = right;
    }

    boolean isEmpty(){
        return left==null && right==null;
    }

    Object getData(){
        return data;
    }

    BinaryTree getLeft(){
        return left;
    }

    BinaryTree getRight(){
        return right;
    }


}

example  Count the number of nodes in a given BinaryTree

int nodeCount(BinaryTree tree){
    if(tree.isEmpty())
        return 0;
    else
        return 1 + nodeCount(tree.getLeft()) + nodeCount(tree.getRight());
}

example  Display the contents of a BinaryTree using an inorder traversal.

void inorderDisplay(BinaryTree tree){
    if(!tree.isEmpty()){
        inorderDisplay(tree.getLeft());
        System.out.println(tree.getData());
        inorderDisplay(tree.getRight());
    }
}

Implementing Non-binary Trees

class Tree {

    Object root;
    List children;

    Tree(Object root){
        this.root = root;
        children = new ArrayList();  // or LinkedList
     }

    Tree(Object root, List children){
        this.root = root;
        this.children = children;
    }

    Object getRoot(){
        return root;
        }

    List getChildren(){
        return children;
        }

}

example  Count the nodes in a given tree

int nodeCount(Tree t){
    int count = 1;  // count the root
    Iterator i = t.getChildren().iterator();
    while(i.hasNext())
        count += nodeCount((Tree)i.next());
    return count;
}

example  Display the contents of a given tree in preorder sequence

void preorderDisplay(Tree t){
    System.out.println(t.getRoot().toString());
    Iterator i = t.getChildren().iterator();
    while(i.hasNext())
        preorderDisplay((Tree)i.next());
}

example  Modify the display method so that the children of a node are indented

void preorderDisplay(Tree t, int indentation){
    for(int i=0;i<3*indentation;i++)
        System.out.print(" ");
    Iterator i = t.getChildren().iterator();
    while(i.hasNext())
        preorderDisplay((Tree)i.next(), indentation+1);
}

void preorderDisplay(Tree t){
    preorderDisplay(t,0);
}

Tree Iterators

We can define an iterator method for a tree or binary tree.  Actually, we could define four different iterators, one for each traversal ordering.  Here are two for binary trees:

  Iterator iterator(){
        class BreadthFirstIterator implements Iterator {
            Queue q = new Queue();

            BreadthFirstIterator(BinaryTree b){
                if(!b.isEmpty())
                    q.enqueue(b);
            }

            boolean hasNext(){
                return !q.isEmpty();
                }

            Object next() {
                BinaryTree b = (BinaryTree) q.dequeue();
                if(!b.left.isEmpty())
                    q.enqueue(b.left);
                if(!b.right.isEmpty())
                    q.enqueue(b.right);
                return b.data;
                }
            }

        return new BreadthFirstIterator(this);
    }

  Iterator iterator(){
        class PreorderIterator implements Iterator {
            Stack s = new Stack();

            PreorderIterator(BinaryTree b){
                if(!b.isEmpty())
                    s.push(b);
            }

            boolean hasNext(){
                return !s.isEmpty();
                }

            Object next() {
                BinaryTree b = (BinaryTree) s.pop();
                if(!b.right.isEmpty())
                    s.push(b.right);
                if(!b.left.isEmpty())
                    s.push(b.left);
                return b.data;
                }
            }

        return new PreorderIterator(this);
    }

Cloning a tree

java.util defines an interface called Clonable as follows:

interface Clonable {
    public Object clone();
}

The clone method creates and returns a copy of the object to which it is applied.

exercise  Write a clone method for binary trees:

public Object clone(){
    if(isEmpty())
        return new BinaryTree();
    else
        return new BinaryTree(data, left.clone(), right.clone());
}

Q:  What would happen if "left.clone()" and "right.clone()" were replaced by "left" and "right"?

Q:  What would happen if "data" were replaced by "data.clone()"?