\documentclass[12pt]{article}
\usepackage[pdftitle={tut0},pdfsubject={Tutorial 0},pdfauthor={Wei Sun}]{hyperref}

%amsmath is a packaged use for typesetting math
%amsfonts is required for special fonts, e.g. blackboard bold (for denoting real numbers, etc.)
\usepackage{amsmath,amsfonts}

%tikz is the package used for trees
\usepackage{tikz}

\begin{document}
\begin{center}
{\Large\bf University of Waterloo}\\
\vspace{3mm}
{\Large\bf CS240R Spring 2017}\\
\vspace{2mm}
{\Large\bf Tutorial 0}\\
\vspace{3mm}
\textbf{Monday, May 8}
\end{center}

\section*{Problem 1 - Mathematics}

Prove log(n!) $\in$ O(n*log(n))

\section*{Example 2 - Trees}
Try adding the letters Z, A, and C to the tree below. \\

\begin{center}
\begin{tikzpicture}[
  level distance=45 pt,
  every node/.style={circle,draw},
  level 1/.style={sibling distance=200 pt},
  level 2/.style={sibling distance=100 pt},
  level 3/.style={sibling distance=60 pt}
]
  \node {M$_0$}
    child {node {F$_0$}
      child {node {C$_0$}}
      child {node {I$_0$}}
    }
    child {node {T$_0$}
      child {node {Q$_0$}}
      child {node {W$_0$}}
    };
\end{tikzpicture}
\end{center}

{\it Hint: For nodes with only one child, you may wish to use ``child[missing]'' for the non-existent child.}

\section*{Example 3 - Plots}

Plot the following points below, the first one has already been done for you. Only show the resulting plot.\\
Points: (2,7), (1,3), (3,1), (7,7)

\begin{center}
\begin{tikzpicture}
		\draw[thick,]  (0,9) -- (0,0) node[left] {0};
		\draw[thick,]  (0,0) -- (9,0) node[below] {9};
		\draw[thick,]  (9,9) -- (9,0) node[left] {};
		\draw[thick,]  (9,9) -- (0,9) node[left] {9};
		
		\fill (2, 7) circle[radius=2.5pt] node[right]{(2, 7)};
\end{tikzpicture}
\end{center}

\section*{Review}

Please review the concepts of best case and worst case and understand the distinction
between cases and bounds. Order notation deals with the concept of bounds, where big O
is an upper bound and $\Omega$ is a lower bound.

\end{document}