exercise2.tex

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\title{\coursename~Quiz 2: Due by \DueDate{\coursedate}{16}}
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% ========== Begin answering questions here

\section*{Exercises}

\begin{enumerate}
\item Programming on paper (2 credits): \\
Write a program that computes the median of the elements in a vector.

\item Interpreting programs (2 credits): \\
What does this program do?
\lstinputlisting{code/exercise2-1.cpp}


\end{enumerate}

\section*{Programming exercises}

\begin{enumerate}

\item Monte Carlo method: (4 credits)\\
In Lecture 2, we discussed the Monte Carlo Method to estimate the value of $\pi$ by
\begin{enumerate}
\item Read $n_{\text{total}}$ from the terminal
\item Generate random coordinates $(x,y)\in [0,1]$
\item Check if $x^2+y^2 \leq 1$
\begin{itemize}
\item Update $N_c$ if $\leq 1$
\end{itemize}
\item Increment $n$ 
\item If $n$ < $n_{\text{total}}$ go to (b)
\item Calculate $\pi \approx 4 \sfrac{N_c}{n_\text{total}}$
\item Print result
\end{enumerate}

\item Measuring time: (2 credits)\\
To measure the computation time, one can use the timers \lstinline|std::chrono::high_resolution_clock| of the \lstinline|#include <chrono>| header\footnote{\url{https://en.cppreference.com/w/cpp/chrono/high_resolution_clock}}.
\begin{lstlisting}
// Get starting timepoint 
auto start = std::chrono::high_resolution_clock::now(); 
// Do work
// Stop timer
auto stop = high_resolution_clock::now();
// Get the duration
auto duration = duration_cast<microseconds>(stop - start); 
// Print the execution time  
cout << "Time taken by function: "
     << duration.count() << " microseconds" << endl; 
\end{lstlisting} 
Write a program that fills a vector and a list with $n$ elements and measure the execution time of both and print them to the terminal. 

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\end{enumerate}

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