\documentclass[12pt]{article}

\usepackage{fullpage,amsmath,amsfonts,hyperref}

\begin{document}

\title{Algorithms and Data Structures}
\author{Summer Semester 2025}
\date{For discussion on Wednesday, May 7, 2025}
\maketitle

\begin{enumerate}

\item For each of the five algorithms from GTG p.~143, state the
expected running time in big-Oh notation.  You can also find the
program code in the book's github repository at
\begin{center}
\url{https://github.com/mjwestcott/Goodrich/blob/master/ch03/exercises.py}
\end{center}

\item (GTG Exercise C-3.35) Assuming it is possible to sort $n$
numbers in $O(n \log n)$ time, show that it is possible to solve the
three-way set disjointness problem in $O(n \log n)$ time.

\item (GTG Exercise C-3.36) Describe an efficient algorithm for
finding the ten largest elements in a sequence of size $n$. What is
the running time of your algorithm?

\item (GTG Exercise C-3.37) Give an example of a positive function
$f (n)$ such that $f (n)$ is neither $O(n)$ nor $\Omega(n)$.

\item (GTG Exercise R-4.1) Describe a recursive algorithm for finding
the maximum element in a sequence, $S$, of $n$ elements. What is your
running time and space usage?

\item (GTG Exercise C-4.15) Write a recursive function that will
output all the subsets of a set of $n$ elements (without repeating any
subsets).



\end{enumerate}
\end{document}
