%
% 6.006 homework template
%
% NOTE:
% Be sure to define your name with the \name command
% Be sure to use the \answer command for each of your answers 
%   (first argument: problem name
%   second argument: collaborators (write 'none' if you solved it alone))
\documentclass[12pt]{article}

\newcommand{\name}{YOUR NAME HERE}
\newcommand{\problemset}{ Problem Set 3, Part B }

%\pagestyle{headings}
\usepackage[dvips]{graphics,color}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{latexsym}
\usepackage{enumerate}
\setlength{\parskip}{1pc}
\setlength{\parindent}{0pt}
\setlength{\topmargin}{-3pc}
\setlength{\textheight}{9.5in}
\setlength{\oddsidemargin}{0pc}
\setlength{\evensidemargin}{0pc}
\setlength{\textwidth}{6.5in}

\newcommand{\answer}[2]{
\newpage
\noindent
\framebox{
	\vbox{
		6.006 Homework \hfill {\bf \problemset}
		\hfill \# #2 \\ 
		\name \hfill \today 
	}
}
\bigskip

}


\begin{document}

\answer{1 --  Find the Largest i Elements in Sorted Order }
{INSERT COLLABORATORS HERE}
%Write `none' if solved alone.

\begin{enumerate}[(a)]
	\item
	
		The running time of the algorithm is
			\begin{equation*} 
				\Theta(\text{INSERT RUNNING TIME HERE})
			\end{equation*}
		because INSERT EXPLANATION HERE
		
	\item

                EXPLAIN YOUR ALGORITHM 
	
                ANALYZE ITS RUNNING TIME
		
	\item

                EXPLAIN YOUR ALGORITHM (and analyze its running time)
                OR EXPLAIN WHY YOU CAN'T DO BETTER
	
\end{enumerate}


\answer{2 --  $d$-ary Heaps }
{INSERT COLLABORATORS HERE}
%Write `none' if solved alone.

\begin{enumerate}[(a)]
	\item
                DESCRIBE IMPLEMENTATION OF PARENT
		
	\item
                DESCRIBE IMPLEMENTATION OF CHILD

	\item
                HEIGHT OF HEAP

	\item
                ASYMPTOTIC RUNNING TIMES OF INCREASE-KEY AND HEAPIFY

                EXPLAIN WHY

	\item

                NEW HEIGHT OF HEAP

	\item

                NEW RUNNING TIMES OF INCREASE-KEY AND HEAPIFY

                EXPLAIN WHY
	
\end{enumerate}


\end{document}