\documentclass[12pt]{article}

\usepackage{fullpage}

\begin{document}
\begin{center}
\bf
Algorithms Section 2\\
Spring 2003\\
\rm
Homework 6b\\
Due Tuesday, March 11\\
\end{center}

\begin{enumerate}

\item \textbf{[75 Points] Implementing B-Trees!}
In this assignment you will implement B-Trees.  In particular, your implementation should assume that $t=2$.  Your code should have a \texttt{Node} element similar to the one suggested in the 
lecture notes.  Your program should support the operations \texttt{insert(x)}, which inserts the integer \texttt{x}  into the tree, and \texttt{find(x)} which returns a boolean indicating whether or not \texttt{x}
is in the tree.  For insertion, use the second method described in class (in which insertion is done in a single pass down the tree).  In addition, your program should have a method called
\texttt{height()} which returns the height of the tree.  (A tree with a single node has height 0.)
Please do this programming exercise without looking at the book.   The book's pseudocode isn't particularly clean or clear.

You should turn in a copy of your code and a sample run of a test program which inserts the 
even numbers from 0 to 20 (in order) into the tree.  
Next, invoke the \texttt{height()} method and print the height of your tree.
Then, the test program tests to see if
each number from 0 to 20 (odd and even) is in the tree and prints ``true'' or ``false'' for
each such query.

\end{enumerate}


\end{document}

