Question

Is it necessary to implement a BST with both keys and values? I can implement a BST that has method calls such as the following, in which it will make the comparison at each node of whether the traversal should go to the left node or right node based upon the V value:

public class BST<V>
{
    public void Insert(V value)
    {
        //implementation
    }

    public V Remove(V value)
    {
        //implementation
    }

    //other methods
}

Or, I can implement the BST such that it has the method calls like the following, in which the K keys are the comparing determination of whether to traverse to the left node or the right node:

public class BST<K key, V value>
{
    public void Insert(K key, V value)
    {
        //implementation
    }

    //which of the following would then be the appropriate method signature?
    public V Remove(K key)
    {
        //implementation
    }
    //or?
    public V Remove(V Value)
    {
        //implementation
    }

    //other methods
}

Answer 1

Not using a key but only a value is fine. However, the tree will become immutable if you do this. Modifying a value is no longer safe since it will imbalance the tree. You will have to enforce this by providing only a property getter for the node value.