%
% 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 4, 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 --  Connected Components }
{INSERT COLLABORATORS HERE}
%Write `none' if solved alone.

	ALGORITHM DESCRIPTION HERE
	
	JUSTIFY $O(V+E)$ RUNNING TIME / CORRECTNESS

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\answer{2 --  Eliminating Cycles }
{INSERT COLLABORATORS HERE}
%Write `none' if solved alone.

	
	%%% helper code
	%%% use this to draw example graphs / counterexample graphs
	
	\setlength{\unitlength}{1mm}
	\begin{picture}(40, 40)  % area of the drawing
	
	  % vertices
	  
	  \put(10, 10){\circle*{1}}
	  \put(20, 10){\circle*{1}}
	  \put(30, 10){\circle*{1}}
	  
	  \put(10, 20){\circle*{1}}
	  \put(20, 20){\circle*{1}}
	  \put(30, 20){\circle*{1}}
	
	  \put(10, 30){\circle*{1}}
	  \put(20, 30){\circle*{1}}
	  \put(30, 30){\circle*{1}}
	
	  % edges
	
	  \put(10, 10){\vector(1, 0){9}}
	  \put(10, 10){\vector(0, 1){9}}
	  \put(10, 10){\vector(1, 1){9}}
	\end{picture}
	
	%%% end helper code

\begin{enumerate}[(a)]

	\item
	
		PROVE STATEMENT
		
			OR
			
		GIVE (simple) COUNTEREXAMPLE
		
	\item

		PROVE STATEMENT
		
			OR
			
		GIVE (simple) COUNTEREXAMPLE
					
\end{enumerate}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\answer{3 --  Graphs and Matrices }
{INSERT COLLABORATORS HERE}
%Write `none' if solved alone.

\begin{itemize}

	\item
		
		WAY 1 IN WHICH ENTRIES OF A RELATE TO PROPERTIES OF G
		
	\item
	
		WAY 2 IN WHICH ENTRIES OF A RELATE TO PROPERTIES OF G					
		
\end{itemize}

\end{document}

