\@writefile{lof}{\contentsline{figure}{\numberline{5.2}{\ignorespaces Absolute error of the expected shortest path distance as the sample size increases.\relax}}{3}}
%\textsc{Nick Trefethen's Problem Solving Squad} \hfill \normalsize{Wednesday 10th May 2017} \\ [25pt] % Your university, school and/or department name(s)
%\horrule{0.5pt} \\[0.2cm] % Thin top horizontal rule
%\large Problem 2 \hfill Thomas Roy and Caoimhe Rooney\\ % The assignment title
\parbox{0.5\linewidth}{\textit{"It does not matter how slowly you go as long as you do not stop."}\\
- Confucius}
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\section{Problem Recap}
\textit{"n points are placed at random on the square $[0,1]^2$ (uniform measure). From each point after the first, the shortest possible line is joined to a previous point without crossing any of the lines already drawn. After $n=100$ points, what is the expected minimal length of a curve connecting $(0.0)$ to $(0.5,0.5)$ without crossing any lines?"}
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@@ -154,6 +167,26 @@ We wrote an algorithm in \texttt{MATLAB} which constructed a graph of $n=100$ no
\item Use Dijkstra's algorithm to find the shortest path.
