\nonumber & \qquad\qquad\qquad \vee c_iy>c_jy+c_jh\\
\nonumber & \qquad\qquad\qquad \vee c_iy+c_jh<c_jh\Bigr)\Biggr)\wedge\\
\bigwedge_{i\in PC}\bigwedge_{j\in PC}\Biggl( & i=j\\
- \nonumber & \vee c_ix+\frac{c_iw}{2}-c_jx+\frac{c_jw}{2}>15\\
- \nonumber & \vee c_jx+\frac{c_jw}{2}-c_ix+\frac{c_iw}{2}>15\\
- \nonumber & \vee c_iy+\frac{c_ih}{2}-c_jy+\frac{c_jh}{2}>15\\
- \nonumber & \vee c_jy+\frac{c_jh}{2}-c_iy+\frac{c_ih}{2}>15\Biggr)\wedge\\
+ \nonumber & \vee c_ix+\frac{c_iw}{2}-c_jx+\frac{c_jw}{2}>17\\
+ \nonumber & \vee c_jx+\frac{c_jw}{2}-c_ix+\frac{c_iw}{2}>17\\
+ \nonumber & \vee c_iy+\frac{c_ih}{2}-c_jy+\frac{c_jh}{2}>17\\
+ \nonumber & \vee c_jy+\frac{c_jh}{2}-c_iy+\frac{c_ih}{2}>17\Biggr)\wedge\\
\bigwedge_{i\in RC}\bigvee_{j\in PC}\neg\Biggl(
& (c_ix-1>c_jx+c_jw\\
\nonumber & \vee c_ix+1+c_jw<c_jx\\
\nonumber & \vee c_iy+1+c_jh<c_jh\Biggr)
\end{align}
+All subformulas describe a constraint from the problem description and can be
+separated in three groups. Subformulas going over all components, only power
+components and only regular components.
+\begin{itemize}
+ \item\textbf{All}
+ \begin{enumerate}
+ \setcounter{enumi}{7}
+ \item Describes that the width and the height of the component can be
+ swapped(in case of rotation).
+ \item Constrains location of the components in regard to the size of
+ the chip.
+ \item Makes sure the components do not overlap by defining for all
+ pairs of components that they either are strictly right, strictly
+ left, strictly above or strictly below the other.
+ \end{enumerate}
+ \item\textbf{Power only}
+ \begin{enumerate}
+ \setcounter{enumi}{10}
+ \item Power components must be at least $17$ block away from
+ other power components. This is defined by saying that the
+ difference between the center of each pair of components is
+ bigger then $17$.
+ \end{enumerate}
+ \item\textbf{Regular only}
+ \begin{enumerate}
+ \setcounter{enumi}{11}
+ \item Regular components must be connected to a power
+ components. This is described using the method from the
+ overalap calculation in a negated way. Every regular
+ component must have overlap with a power component that
+ has been enlarged by $1$.
+ \end{enumerate}
+\end{itemize}
+
\subsection{SMT format solution}
+The formula is easily convertable via a Python script to SMT format and said
+script is listed in Listing~\ref{listing:2.py}. The Python script optimizes a
+little bit from the original formula by leaving out the overlap checking
+between the same components. When we run the file a solution is found within
+$30$ seconds.
+
+\subsection{Solution}
+Figure~\ref{fig:s2} shows the configuration found by the solver. Light gray
+components are regular components and darker gray components are power
+components.
+
+\begin{figure}[H]
+ \includegraphics[scale=0.75]{s2.png}
+ \label{fig:s2}
+ \caption{Solution visualization for problem 2}
+\end{figure}