The `Insert` member function of the `BST` class
is defined in Program .
This function takes as its lone argument a reference to
the object instance which is to be inserted into the binary search tree.
It is assumed in this implementation that duplicate keys are not permitted.
I.e., all of the keys contained in the tree are unique.

**Program:** `BST` Class `Insert`, `AttachKey` and `Balance` Member Function Definitions

The `Insert` routine behaves like the `Find` routine
until it arrives at an external, empty node.
Once the empty node has been found,
it is transformed into an internal node
by calling the `AttachKey` function.
`AttachKey` works as follows:
A pointer to the object being inserted
is saved in the `key` member variable
and two new empty binary trees are attached to the node.

Notice that after the insertion is done,
the function `Balance` is called.
However, as shown in Program ,
the `BST::Balance` function does nothing.
Section describes the class `AVLTree`
which is derived from the `BST` class
and which inherits the `Insert` function but
overrides the `Balance` operation.

The asymptotic running time of the `Insert` member function
is the same as that of `Find` for an unsuccessful search.
I.e., in the worst case the running time is
and the average case running time is

where is the average depth of an external
node in a binary search tree with *n* internal nodes.
When , the worst case running time is *O*(*n*)
and the average case is .

Copyright © 1997 by Bruno R. Preiss, P.Eng. All rights reserved.