%%
%% This is file `65240.sty'
%% Source taken from Nancy Lynch's 6.5240 templates
%% It includes math macros used for the CLRS book and 6.5240 homework header.

\def\fileversion{1.0}
\def\filedate{2011/02/01}
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{65240}[\filedate{} macros for 6.5240]

\usepackage{url}
\usepackage{latexsym}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{verbatim}
\usepackage{listings}
\DeclareSymbolFont{largesymbols}{OMX}{cmex}{m}{n} % However for large sigmas we want the Computer Modern symbol
\renewcommand{\ttdefault}{cmtt}
\usepackage{array}
\usepackage{multirow}
\usepackage{color}
\usepackage{clrscode4e}
\usepackage{xspace} % xspace takes care of the \@ after a capitalized word before a period.
\usepackage{multicol}
\usepackage{graphicx}
\usepackage{fancyhdr}

\setlength{\oddsidemargin}{0pt}
\setlength{\evensidemargin}{0pt}
\setlength{\textwidth}{6.5in}
\setlength{\topmargin}{0in}
\setlength{\textheight}{8.5in}

\setlength{\parskip}{1pc}
\setlength{\parindent}{0pt}

\let\@author\@empty
\let\@pset\@empty
\let\@collab\@empty
\newcommand{\pset}[1]{\def\@pset{#1}}
\newcommand{\collab}[1]{\def\@collab{#1}}
\newcommand{\due}[1]{\def\@due{#1}}

% Command to make the header box.
\newcommand{\header}{
  \begin{center}
    \hspace*{-0.25in}\framebox[7in]{
      \vbox{
        \hbox to 6.25in { \@author \hfill \@date}
        \vspace{1mm}
        \hbox to 6.25in {\bf \hfill 6.5240 Problem Set \@pset\ \hfill}
        \vspace{1mm}
        \hbox to 6.25in { Collaborators: {\it \@collab} \hfill Due date: \@due
        }
      }
    }
  \end{center}
}

\AtBeginDocument{
  \ifx \@author \@empty
    \@latexerr{You must use \noexpand\author{name} for 6.5240 homework}
  \fi
  \ifx \@pset \@empty
    \@latexerr{You must use \noexpand\pset{number} for 6.5240 homework}
  \fi
  \ifx \@collab \@empty
    \@latexerr{You must use \noexpand\collab{names or none} for 6.5240 homework}
  \fi
  \thispagestyle{plain}
  \header
  \lhead{\@author}
  \rhead{\textbf{6.5240 Problem Set \@pset}}
  \cfoot{\thepage}
  \pagestyle{fancy}
}


% \newcommand{\handout}[1]{\thispagestyle{empty}
%  \markboth{Handout \protect\ref{#1}: \protect\ref{#1-title}}{Handout \protect\ref{#1}: \protect\ref{#1-title}}
%  \pagestyle{myheadings}\htitle{\protect\ref{#1}}{\protect\ref{#1-title}}{\protect\ref{#1-date}}}

% Ignore hboxes overfull by 1 point or less.
\hfuzz 1pt

% Formatting parameters for floats.
\setcounter{topnumber}{3}
\renewcommand\topfraction{.7}
\setcounter{bottomnumber}{1}
\renewcommand\bottomfraction{.3}
\setcounter{totalnumber}{5}
\renewcommand\textfraction{.1}
\renewcommand\floatpagefraction{.7}
\setcounter{dbltopnumber}{2}
\renewcommand\dbltopfraction{.7}
\renewcommand\dblfloatpagefraction{.7}

% % default style assignments
% \def\UrlBreaks{\do\-\do\.\do\@\do\\\do\/\do\!\do\_\do\|\do\;\do\>\do\]%
%  \do\)\do\,\do\?\do\'\do\+\do\=\do\#}%
% \def\UrlBigBreaks{\do\:\do@url@hyp}%
% \def\UrlNoBreaks{\do\(\do\[\do\{\do\<}%
% % any ordinary characters that aren't usually:
% \def\UrlOrds{\do\*\do\~\do\'\do\"}%
% \def\UrlSpecials{\do\ {\Url@space}\do\%{\Url@percent}\do\^^M{\Url@space}%
%    \Url@force@Tilde}% package option may force faked text-ascii-tilde


% Some hacks to make HTML happier.
\newcommand{\vskipargs}[1]{\vskip #1}
\newcommand{\newproc}{\hrule\vskipargs{1ex plus 0.1ex minus 0.1ex}}

% Tilde for webstuff
\newcommand{\webtilde}{\raisebox{-.8ex}\~}

% Comment out chunks.
\newcommand{\punt}[1]{}

% Footnote commands.
\newcommand{\footnotenonumber}[1]{{\def\thempfn{}\footnotetext{#1}}}
\newcommand{\footnotetight}[1]{\footnote{\renewcommand\baselinestretch{1}\footnotesize #1}}

%% Math Stuff, Symbols

% Number sets.
\newcommand{\reals}         {\mathbf{R}}%\mathbbm{R}}    %% bbm seems to produce type 3 fonts
\newcommand{\integers}      {\mathbf{Z}}
\newcommand{\naturals}      {\mathbf{N}}
\newcommand{\rationals}     {\mathbf{Q}}
\newcommand{\complex}       {\mathbf{C}}

% Useful shorthands.
\newcommand{\eps}{\varepsilon}

\newcommand{\lgg}       {\lg\lg}
\newcommand{\lggg}      {\lg\lg\lg}
\newcommand{\lgggg}     {\lg\lg\lg\lg}

\newcommand{\lnn}       {\ln\ln}
\newcommand{\lnnn}      {\ln\ln\ln}
\newcommand{\lnnnn}      {\ln\ln\ln\ln}

\newcommand{\norm}[1]       {\left\| #1\right\|}
\newcommand{\set}[1]        {\left\{ #1 \right\}}
\newcommand{\abs}[1]        {\left| #1\right|}
\newcommand{\card}[1]       {\left| #1\right|}
\newcommand{\floor}[1]      {\left\lfloor #1 \right\rfloor}
\newcommand{\ceil}[1]       {\left\lceil #1 \right\rceil}
\newcommand{\ang}[1]        {\ifmmode{\left\langle #1 \right\rangle}
                 \else{$\left\langle${#1}$\right\rangle$\xspace}\fi}
                        % the \if allows use outside mathmode,
                    % but may swallow following space there!
\newcommand{\sbrace}[1]{\left[#1\right]}
\newcommand{\cbrace}[1]{\left\{#1\right\}}
\newcommand{\paren}[1]      {\left( #1 \right)}
\newcommand{\prob}[1]       {\Pr\left\{ #1 \right\}}
\newcommand{\expect}[1]     {{\rm E}\left[ #1 \right]}
\newcommand{\expectsq}[1]   {{\rm E}^2\left[ #1 \right]}
\newcommand{\variance}[1]   {{\rm Var}\left[ #1 \right]}
\renewcommand{\choose}[2]   {{\dbinom{#1}{#2}}}

\newcommand{\goesto}     {\rightarrow}


\def\pmod#1{\allowbreak\mkern12mu({\rm mod}\,\,#1)}

\newcommand{\matx}[2]       {\left(\!\!\!\begin{array}{*{#1}{c}}#2\end{array}\!\!\!\right)}
\newcommand{\Adj}       {\mathop{\rm Adj}\nolimits}
\newcommand{\percent}[1]    {#1\%}

\newtheorem{principle}{Principle}
\newtheorem{theorem}        {Theorem}
\newtheorem{lemma}[theorem] {Lemma}
\newtheorem{corollary}[theorem] {Corollary}
\newtheorem{xample}     {Example}

\newenvironment{example}    {\begin{xample}\rm}{\end{xample}}

\newenvironment{proof}      {\noindent\textsc{Proof.}\hspace{0.5em}}{\qed\par}
\def\squarebox#1{\hbox to #1{\hfill\vbox to #1{\vfill}}}
\newcommand{\qedbox}
{\vbox{\hrule\hbox{\vrule\squarebox{.667em}\vrule}\hrule}}
\newcommand{\qed}               {\nopagebreak\mbox{}\hfill\qedbox\smallskip}
\newenvironment{proofsketch}    {\noindent\textsc{Proof Sketch.}\hspace{0.5em}}{\qed}

\newenvironment{proofidea}    {\noindent\textsc{Proof Idea.}\hspace{0.5em}}


\newcommand{\eqnref}[1]     {(\protect\ref{#1})}

\newcommand{\transpose}     {^{\mbox{\scriptsize \sf T}}}
\newcommand{\amortized}[1]  {\widehat{#1}}

\renewcommand{\cases}[1]    {\left\{ \begin{array}{ll}#1\end{array}\right.}
\newcommand{\cif}[1]        {\mbox{if $#1$}}
\newcommand{\cwhen}[1]      {\mbox{when $#1$}}
\newcommand{\cotherw}       {\mbox{otherwise}}

%Narrow arrays
\newlength{\savearraycolsep}
\newcommand{\narrowarray}[1]{\setlength{\savearraycolsep}{\arraycolsep}\setlength{\arraycolsep}{#1\arraycolsep}}
\newcommand{\normalarray}{\setlength{\arraycolsep}{\savearraycolsep}}

% definitions and special styles

\newcommand{\defn}[1]       {{\textit{\textbf{\boldmath #1}}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% The Code environment %%%
%% The following commands are so we can automatically number and symbolically reference
%% lines.
%% The ``codelinenumber'' counter counts the current line number
%\newcounter{codelinenumber}
%% The \zeroli command zeros the line number counter
%\newcommand{\zeroli}{\setcounter{codelinenumber}0}
%% The \li command bumps the counter, outputs it, and skips some space
%% It also GLOBALLY sets the value of \@currentlabel, so that the \label
%% commands on the same line work OK.  The problem otherwise is that Latex
%% uses groups on each field of a line in tabbing mode, and this causes
%% \@currentlabel to get reset as soon as a field ends (e.g. at the \').
%% Now, the label can appear after the \\, as in
%%  \li \>\>$x\gets y$ \\ \label{li:assign-x}
%%

\def\code{\lstinline[basicstyle=\ttfamily]}

%% Labels
\newcommand{\figlabel}[1]   {\label{fig:#1}}
\newcommand{\tablabel}[1]   {\label{tab:#1}}
\newcommand{\stlabel}[1]    {\label{st:#1}}
\newcommand{\thmlabel}[1]   {\label{thm:#1}}
\newcommand{\lemlabel}[1]   {\label{lem:#1}}
\newcommand{\corlabel}[1]   {\label{cor:#1}}
\newcommand{\eqlabel}[1]    {\label{eq:#1}}
\newcommand{\ineqlabel}[1]  {\label{ineq:#1}}
\newcommand{\caselabel}[1]  {\label{case:#1}}
\newcommand{\lilabel}[1]    {\label{li:#1}}

%% References

\newcommand{\chapref}[1]    {Chapter~\ref{chap:#1}}
\newcommand{\secref}[1]     {Section~\ref{sec:#1}}
\newcommand{\secreftwo}[2]  {Sections \ref{sec:#1} and~\ref{sec:#2}}
\newcommand{\secrefthree}[3]    {Sections \ref{sec:#1}, \ref{sec:#2}, and \ref{sec:#3}}
\newcommand{\secreffour}[4] {Sections \ref{sec:#1}, \ref{sec:#2}, \ref{sec:#3}, and~\ref{sec:#4}}
\newcommand{\appref}[1]     {Appendix~\ref{app:#1}}
\newcommand{\figref}[1]     {Figure~\ref{fig:#1}}
\newcommand{\figreftwo}[2]  {Figures \ref{fig:#1} and~\ref{fig:#2}}
\newcommand{\tabref}[1]     {Table~\ref{tab:#1}}
\newcommand{\stref}[1]      {Step~\ref{st:#1}}
\newcommand{\strefs}[2]     {Steps~\ref{st:#1}--\ref{st:#2}}
\newcommand{\streftwo}[2]   {Steps \ref{st:#1} and~\ref{st:#2}}
\newcommand{\thmref}[1]     {Theorem~\ref{thm:#1}}
\newcommand{\thmreftwo}[2]  {Theorems~\ref{thm:#1} and~\ref{thm:#2}}
\newcommand{\lemref}[1]     {Lemma~\ref{lem:#1}}
\newcommand{\lemreftwo}[2]  {Lemmas \ref{lem:#1} and~\ref{lem:#2}}
\newcommand{\lemrefthree}[3]    {Lemmas \ref{lem:#1}, \ref{lem:#2}, and~\ref{lem:#3}}
\newcommand{\corref}[1]     {Corollary~\ref{cor:#1}}
\renewcommand{\eqref}[1]      {Equation~(\ref{eq:#1})}
\newcommand{\eqreftwo}[2]   {Equations (\ref{eq:#1}) and~(\ref{eq:#2})}
\newcommand{\ineqref}[1]    {Inequality~(\ref{ineq:#1})}
\newcommand{\ineqreftwo}[2] {Inequalities (\ref{ineq:#1}) and~(\ref{ineq:#2})}
\newcommand{\invref}[1]     {Invariant~\ref{inv:#1}}
\newcommand{\invrefs}[2]    {Invariants \ref{inv:#1}--\ref{inv:#2}}
\newcommand{\invreftwo}[2]  {Invariants \ref{inv:#1} and~\ref{inv:#2}}
\newcommand{\defref}[1]     {Definition~\ref{def:#1}}
\newcommand{\propref}[1]    {Property~\ref{prop:#1}}
\newcommand{\caseref}[1]    {Case~\ref{case:#1}}
\newcommand{\casereftwo}[2] {Cases \ref{case:#1} and~\ref{case:#2}}
\newcommand{\liref}[1]      {line~\ref{li:#1}}
\newcommand{\Liref}[1]      {Line~\ref{li:#1}}
\newcommand{\lirefs}[2]     {lines \ref{li:#1}--\ref{li:#2}}
\newcommand{\Lirefs}[2]     {Lines \ref{li:#1}--\ref{li:#2}}
\newcommand{\lireftwo}[2]   {lines \ref{li:#1} and~\ref{li:#2}}
\newcommand{\lirefthree}[3] {lines \ref{li:#1}, \ref{li:#2}, and~\ref{li:#3}}
\newcommand{\exref}[1]      {Exercise~\ref{ex:#1}}
\newcommand{\princref}[1]   {Principle~\ref{prop:#1}}