This is an individual problem set. Choose any one of the following three options.

Option 1: (10 Points up to 14 Points) Immutable BSTs

...
    public void put(Key key, Value val);
    public void deleteMin();
    public void deleteMax();
    public void delete(Key key);        // Hibbard Deletion
...

By altering the interface somewhat, we can specify immutable or persistent BSTs in which alterations to a BST construct a new BST. The following BST interface can be used as a specification for immutable BSTs.

public interface BST<Key extends Comparable<Key>, Value> { 
    public boolean isEmpty();
    public int size();
    public boolean contains(Key key);
    public Value get(Key key);
    public BST<Key, Value> put(Key key, Value val);
    public BST<Key, Value> deleteMin();
    public BST<Key, Value> delete(Key key);    // Hibbard Deletion
    public Key min();
    public String toString();
    public Key floor(Key key);
    public int height(); 
}

public class Empty<Key, Value> implements Map<Key, Value> { ... }
public class Binding<Key, Value> implements Map<Key, Value> { ... }

Notes

1. Like the SW implementation of mutable BSTs, your implementation should throw a NoSuchElementException if a client attempts to delete a key/value pair that doesn't exist in the BST.

2. The toString function should return a simple string representation of the tree. Consider using -- for empty trees and (left, key, val, right) for non-empty trees.

3. As usual, your classes should include main functions that serve as a unit test for the class.

Extra Credit

1. (1 Point) Implement the public Key select(int k); operation. See SW for a description.

2. (1 Point) Implement the public int rank(Key key); operation. See SW for a description.

3. (2 Point) Implement the public Iterable<Key> keys(); operation. See SW for a description.

Option 2: (16 Points) Implement the Immutable Red/Black tree ADT.

public interface RedBlack<Key extends Comparable<Key>, Value> { 
    public boolean isEmpty();
    public int size();
    public boolean contains(Key key);
    public Value get(Key key);
    public RedBlack<Key, Value> put(Key key, Value val);
    public String toString();
}

Option 3: (10 Points) The Great-Tree List Recursion Problem