Questionnaire-2024/bdds/0003.tex

\item \lect Given the following \textit{Binary Decision Diagram (BDD)} that represents the formula $f$. Compute its disjunctive normal form \DNF{f}.
  \TODONOTE{THIS IS BULLCRAP.}
\begin{center}
\begin{forest}
for tree={circle, draw, no edge,
            minimum size=2em,
            inner sep=0pt,
            s sep=2mm,
            l sep=4mm}
[$f$, rectangle, draw,  tikz={\draw [line] () to (a.north);}
    [$a$, name=a, tikz={\draw [line] () to (b.north east); \draw [dot=.5] () to (c2.north west);}
        [$b$, name=b, tikz={\draw [dot=.5, bend left] () to (c1.north east); \draw [line, bend right] () to (c1.north west);}
            [$c$, name=c1, s sep=20mm, tikz={\draw [line] () to (one.north); \draw [dot=.5] () to (e.north west);}
                [,phantom]
                [$e$, name=e, s sep=10mm, tikz={\draw [line, bend left] () to (one.north east); \draw [dot=.5, bend left] () to (one.east);}
                    [$1$, rectangle, draw, name=one]
                    [$0$, rectangle, draw, name=zero]
                ]
            ]
        ]
        [$c$, name=c2, tikz={\draw [line, bend right] () to (e.north); \draw [dot=.5, bend left] () to (d.north);}
            [,phantom]
            [$d$, name=d, tikz={\draw [line] () to (e.north east); \draw[dot=.5] () to (zero.north);
}
                [,phantom]
                [,phantom]
            ]
        ]
    ]
]
\end{forest}
\end{center}