A class that implements the Set interface using a binary search tree

The major hurdle is that our class does not implement Iterable. To overcome this, we augment the BinaryNode inner class by adding links to the next smallest and next largest nodes so that the iterator can efficiently return the next node (just like a linked list). Rewrite the insert method of MyBinarySearchTree to support the added links.

We first augment the data structure so that the inner class becomes:

    private static class BinaryNode
    ...{
         ...
        AnyType element;              // The data in the node
        BinaryNode<AnyType> left;     // Left child
        BinaryNode<AnyType> right;    // Right child
        BinaryNode<AnyType> smaller;  // Previous in-order element
        BinaryNode<AnyType> larger;   // Next in-order element
    }

 

Here is the insert method:

private BinaryNode<T> insert(T x, BinaryNode<T> t, BinaryNode<T> larger, BinaryNode<T> smaller)
...{
    if (t == null)
    ...{
        BinaryNode<T> n = new BinaryNode<T>(x, null, null, larger, smaller);
        if (larger != null) larger.prev = n;
        if (smaller != null) smaller.next = n;
        return n;
    }
    int compareResult = x.compareTo(t.element);
    if (compareResult < 0)
        t.left = insert(x, t.left, t, smaller);
    else if (compareResult > 0)
        t.right = insert(x, t.right, larger, t);
    else
        ; // duplicate

    return t;
}

When a new node is inserted as a left child, three things must be done to support this augmentation: its larger field must point to its parent; its smaller field must be set to its parent's smaller field; and the parent's smaller field must be set to it. A similar triplet of changes is needed when the new node is a right child.