\documentclass[12pt]{article}
\usepackage{fullpage}
\usepackage{times}
\usepackage[normalem]{ulem}
\usepackage{fancyhdr,graphicx,amsmath,amssymb, mathtools, scrextend, titlesec, enumitem}
\usepackage[ruled,vlined]{algorithm2e}
\include{pythonlisting}
\title{Problem 4 Oscillating subsequence}
\author{Luoqi (Rocky) Wu}
\begin{document}
\maketitle
\textbf{Analysis:}
\textbf{Recurrence:}
\pagebreak
\begin{algorithm}
\caption{}
\KwIn{}
\KwOut{}
\hrulefill\\
\nl \tcp*[r]{}
\nl
\nl \For{i = 2 to k} {
\nl \For{$j = 0 to 1$}{
\nl }
}
\nl \Return{}
\end{algorithm}
\pagebreak
\textbf{Runtime Analysis:} To bound the running time， \\
\textbf{Proof of Correctness using induction:} \\
Claim: \\
Base Case: \\
Inductive Case: \\
-If \\
-If \\
We have now exhausted the sample space, \\
\end{document}
