+\subsection{Brute Force}
+The first approach was to implement a brute force algorithm which calculates
+every possible combination of pets and children and then takes the one with the
+highest value. This corresponds with the pseudocode specified in
+Listing~\ref{lst:brute_force}. The algorithm, due to calculating all the values
+has a minimal complexity of $n!$. This is because there are $n!$ permutations
+possible for $n$ children.
+\begin{lstlisting}[
+ caption={Brute Force approach},
+ label={lst:brute_force},
+ keywords={[3]loop,put,return}
+]
+n! - loop over all permutations
+c1 - put compatibility in list
+c1 - return maximum compatibility rating from list
+\end{lstlisting}
+
+
+\subsection{Improvements}