summaryrefslogtreecommitdiffstats
diff options
context:
space:
mode:
authorDavid A. Madore <david+git@madore.org>2018-01-29 13:55:10 (GMT)
committerDavid A. Madore <david+git@madore.org>2018-01-29 13:55:10 (GMT)
commit7323dadb946d0e27ceadfa06d06e73fe8615539f (patch)
tree3c561f2947ebc5f84ca2164e09d0c93701d68b7d
parent6d5d3cd4a38a2b6e26b2243bc2ae993bdcfd6270 (diff)
downloadinf105-7323dadb946d0e27ceadfa06d06e73fe8615539f.zip
inf105-7323dadb946d0e27ceadfa06d06e73fe8615539f.tar.gz
inf105-7323dadb946d0e27ceadfa06d06e73fe8615539f.tar.bz2
Write answers to second exercise.
-rw-r--r--controle-20180206.tex119
1 files changed, 117 insertions, 2 deletions
diff --git a/controle-20180206.tex b/controle-20180206.tex
index 4ea67f4..be3a599 100644
--- a/controle-20180206.tex
+++ b/controle-20180206.tex
@@ -350,18 +350,133 @@ démontrer).
(c) $x\mathbin{@}y\mathbin{\#}z$, (d) $x\mathbin{@}y\mathbin{@}z$,
(e) $(x\mathbin{\#}y)\mathbin{@}z$.
+\begin{corrige}
+On obtient les arbres d'analyse suivants :
+(a) % S<S<S<T<U<V<x.>>>>#.T<U<V<y.>>>>#.T<U<V<z.>>>>
+\begin{tikzpicture}[line join=bevel,baseline=(S0.base)]
+\node (S0) at (53.333bp,0.000bp) [draw=none] {$S$};
+\node (S1) at (20.000bp,-30.000bp) [draw=none] {$S$}; \draw (S0) -- (S1);
+\node (S2) at (0.000bp,-60.000bp) [draw=none] {$S$}; \draw (S1) -- (S2);
+\node (T0) at (0.000bp,-80.000bp) [draw=none] {$T$}; \draw (S2) -- (T0);
+\node (U0) at (0.000bp,-100.000bp) [draw=none] {$U$}; \draw (T0) -- (U0);
+\node (V0) at (0.000bp,-120.000bp) [draw=none] {$V$}; \draw (U0) -- (V0);
+\node (x0) at (0.000bp,-140.000bp) [draw=none] {$x$}; \draw (V0) -- (x0);
+\node (o0) at (20.000bp,-60.000bp) [draw=none] {$\#$}; \draw (S1) -- (o0);
+\node (T1) at (40.000bp,-60.000bp) [draw=none] {$T$}; \draw (S1) -- (T1);
+\node (U1) at (40.000bp,-80.000bp) [draw=none] {$U$}; \draw (T1) -- (U1);
+\node (V1) at (40.000bp,-100.000bp) [draw=none] {$V$}; \draw (U1) -- (V1);
+\node (y0) at (40.000bp,-120.000bp) [draw=none] {$y$}; \draw (V1) -- (y0);
+\node (o1) at (60.000bp,-30.000bp) [draw=none] {$\#$}; \draw (S0) -- (o1);
+\node (T2) at (80.000bp,-30.000bp) [draw=none] {$T$}; \draw (S0) -- (T2);
+\node (U2) at (80.000bp,-50.000bp) [draw=none] {$U$}; \draw (T2) -- (U2);
+\node (V2) at (80.000bp,-70.000bp) [draw=none] {$V$}; \draw (U2) -- (V2);
+\node (z0) at (80.000bp,-90.000bp) [draw=none] {$z$}; \draw (V2) -- (z0);
+\end{tikzpicture}
+\hskip1cmplus5cmminus.5cm
+(b) % S<S<T<U<V<x.>>>>#.T<U<V<y.>>@.T<U<V<z.>>>>>
+\begin{tikzpicture}[line join=bevel,baseline=(S0.base)]
+\node (S0) at (26.667bp,0.000bp) [draw=none] {$S$};
+\node (S1) at (0.000bp,-30.000bp) [draw=none] {$S$}; \draw (S0) -- (S1);
+\node (T0) at (0.000bp,-50.000bp) [draw=none] {$T$}; \draw (S1) -- (T0);
+\node (U0) at (0.000bp,-70.000bp) [draw=none] {$U$}; \draw (T0) -- (U0);
+\node (V0) at (0.000bp,-90.000bp) [draw=none] {$V$}; \draw (U0) -- (V0);
+\node (x0) at (0.000bp,-110.000bp) [draw=none] {$x$}; \draw (V0) -- (x0);
+\node (o0) at (20.000bp,-30.000bp) [draw=none] {$\#$}; \draw (S0) -- (o0);
+\node (T1) at (60.000bp,-30.000bp) [draw=none] {$T$}; \draw (S0) -- (T1);
+\node (U1) at (40.000bp,-60.000bp) [draw=none] {$U$}; \draw (T1) -- (U1);
+\node (V1) at (40.000bp,-80.000bp) [draw=none] {$V$}; \draw (U1) -- (V1);
+\node (y0) at (40.000bp,-100.000bp) [draw=none] {$y$}; \draw (V1) -- (y0);
+\node (o1) at (60.000bp,-60.000bp) [draw=none] {$@$}; \draw (T1) -- (o1);
+\node (T2) at (80.000bp,-60.000bp) [draw=none] {$T$}; \draw (T1) -- (T2);
+\node (U2) at (80.000bp,-80.000bp) [draw=none] {$U$}; \draw (T2) -- (U2);
+\node (V2) at (80.000bp,-100.000bp) [draw=none] {$V$}; \draw (U2) -- (V2);
+\node (z0) at (80.000bp,-120.000bp) [draw=none] {$z$}; \draw (V2) -- (z0);
+\end{tikzpicture}
+\hskip1cmplus5cmminus.5cm
+(c) % S<S<T<U<V<x.>>@.T<U<V<y.>>>>>#.T<U<V<z.>>>>
+\begin{tikzpicture}[line join=bevel,baseline=(S0.base)]
+\node (S0) at (53.333bp,0.000bp) [draw=none] {$S$};
+\node (S1) at (20.000bp,-30.000bp) [draw=none] {$S$}; \draw (S0) -- (S1);
+\node (T0) at (20.000bp,-50.000bp) [draw=none] {$T$}; \draw (S1) -- (T0);
+\node (U0) at (0.000bp,-80.000bp) [draw=none] {$U$}; \draw (T0) -- (U0);
+\node (V0) at (0.000bp,-100.000bp) [draw=none] {$V$}; \draw (U0) -- (V0);
+\node (x0) at (0.000bp,-120.000bp) [draw=none] {$x$}; \draw (V0) -- (x0);
+\node (o0) at (20.000bp,-80.000bp) [draw=none] {$@$}; \draw (T0) -- (o0);
+\node (T1) at (40.000bp,-80.000bp) [draw=none] {$T$}; \draw (T0) -- (T1);
+\node (U1) at (40.000bp,-100.000bp) [draw=none] {$U$}; \draw (T1) -- (U1);
+\node (V1) at (40.000bp,-120.000bp) [draw=none] {$V$}; \draw (U1) -- (V1);
+\node (y0) at (40.000bp,-140.000bp) [draw=none] {$y$}; \draw (V1) -- (y0);
+\node (o1) at (60.000bp,-30.000bp) [draw=none] {$\#$}; \draw (S0) -- (o1);
+\node (T2) at (80.000bp,-30.000bp) [draw=none] {$T$}; \draw (S0) -- (T2);
+\node (U2) at (80.000bp,-50.000bp) [draw=none] {$U$}; \draw (T2) -- (U2);
+\node (V2) at (80.000bp,-70.000bp) [draw=none] {$V$}; \draw (U2) -- (V2);
+\node (z0) at (80.000bp,-90.000bp) [draw=none] {$z$}; \draw (V2) -- (z0);
+\end{tikzpicture}
+\hskip1cmplus5cmminus.5cm
+(d) % S<T<U<V<x.>>@.T<U<V<y.>>@.T<U<V<z.>>>>>>
+\begin{tikzpicture}[line join=bevel,baseline=(S0.base)]
+\node (S0) at (26.667bp,0.000bp) [draw=none] {$S$};
+\node (T0) at (26.667bp,-20.000bp) [draw=none] {$T$}; \draw (S0) -- (T0);
+\node (U0) at (0.000bp,-50.000bp) [draw=none] {$U$}; \draw (T0) -- (U0);
+\node (V0) at (0.000bp,-70.000bp) [draw=none] {$V$}; \draw (U0) -- (V0);
+\node (x0) at (0.000bp,-90.000bp) [draw=none] {$x$}; \draw (V0) -- (x0);
+\node (o0) at (20.000bp,-50.000bp) [draw=none] {$@$}; \draw (T0) -- (o0);
+\node (T1) at (60.000bp,-50.000bp) [draw=none] {$T$}; \draw (T0) -- (T1);
+\node (U1) at (40.000bp,-80.000bp) [draw=none] {$U$}; \draw (T1) -- (U1);
+\node (V1) at (40.000bp,-100.000bp) [draw=none] {$V$}; \draw (U1) -- (V1);
+\node (y0) at (40.000bp,-120.000bp) [draw=none] {$y$}; \draw (V1) -- (y0);
+\node (o1) at (60.000bp,-80.000bp) [draw=none] {$@$}; \draw (T1) -- (o1);
+\node (T2) at (80.000bp,-80.000bp) [draw=none] {$T$}; \draw (T1) -- (T2);
+\node (U2) at (80.000bp,-100.000bp) [draw=none] {$U$}; \draw (T2) -- (U2);
+\node (V2) at (80.000bp,-120.000bp) [draw=none] {$V$}; \draw (U2) -- (V2);
+\node (z0) at (80.000bp,-140.000bp) [draw=none] {$z$}; \draw (V2) -- (z0);
+\end{tikzpicture}
+\hskip1cmplus5cmminus.5cm
+(e) % S<T<U<(.S<S<T<U<V<x.>>>>#.T<U<V<y.>>>>).>@.T<U<V<z.>>>>>
+\begin{tikzpicture}[line join=bevel,baseline=(S0.base)]
+\node (S0) at (86.667bp,0.000bp) [draw=none] {$S$};
+\node (T0) at (86.667bp,-20.000bp) [draw=none] {$T$}; \draw (S0) -- (T0);
+\node (U0) at (40.000bp,-50.000bp) [draw=none] {$U$}; \draw (T0) -- (U0);
+\node (p0) at (0.000bp,-80.000bp) [draw=none] {$($}; \draw (U0) -- (p0);
+\node (S1) at (40.000bp,-80.000bp) [draw=none] {$S$}; \draw (U0) -- (S1);
+\node (S2) at (20.000bp,-110.000bp) [draw=none] {$S$}; \draw (S1) -- (S2);
+\node (T1) at (20.000bp,-130.000bp) [draw=none] {$T$}; \draw (S2) -- (T1);
+\node (U1) at (20.000bp,-150.000bp) [draw=none] {$U$}; \draw (T1) -- (U1);
+\node (V0) at (20.000bp,-170.000bp) [draw=none] {$V$}; \draw (U1) -- (V0);
+\node (x0) at (20.000bp,-190.000bp) [draw=none] {$x$}; \draw (V0) -- (x0);
+\node (o0) at (40.000bp,-110.000bp) [draw=none] {$\#$}; \draw (S1) -- (o0);
+\node (T2) at (60.000bp,-110.000bp) [draw=none] {$T$}; \draw (S1) -- (T2);
+\node (U2) at (60.000bp,-130.000bp) [draw=none] {$U$}; \draw (T2) -- (U2);
+\node (V1) at (60.000bp,-150.000bp) [draw=none] {$V$}; \draw (U2) -- (V1);
+\node (y0) at (60.000bp,-170.000bp) [draw=none] {$y$}; \draw (V1) -- (y0);
+\node (p1) at (80.000bp,-80.000bp) [draw=none] {$)$}; \draw (U0) -- (p1);
+\node (o1) at (100.000bp,-50.000bp) [draw=none] {$@$}; \draw (T0) -- (o1);
+\node (T3) at (120.000bp,-50.000bp) [draw=none] {$T$}; \draw (T0) -- (T3);
+\node (U3) at (120.000bp,-70.000bp) [draw=none] {$U$}; \draw (T3) -- (U3);
+\node (V2) at (120.000bp,-90.000bp) [draw=none] {$V$}; \draw (U3) -- (V2);
+\node (z0) at (120.000bp,-110.000bp) [draw=none] {$z$}; \draw (V2) -- (z0);
+\end{tikzpicture}
+\end{corrige}
+
(2) En considérant que $(w)$ a le même effet / la même valeur
que $w$ : (a) Quelle opération parmi $\#$ et $@$ est
prioritaire\footnote{On dit qu'une opération binaire $\boxtimes$ est
\emph{prioritaire} sur $\boxplus$ lorsque « $u\boxtimes v\boxplus
w$ » se comprend comme « $(u\boxtimes v)\boxplus w$ » et
« $u\boxplus v\boxtimes w$ » comme « $u\boxplus (v\boxtimes w)$ ».}
-sur l'autre ? (b) L'opération $\#$ s'associe-t-elle\footnote{On dit
+sur l'autre ?\quad (b) L'opération $\#$ s'associe-t-elle\footnote{On dit
qu'une opération binaire $\boxdot$ \emph{s'associe à gauche} lorsque
« $u\boxdot v\boxdot w$ » se comprend comme « $(u\boxdot v)\boxdot
w$ », et \emph{s'associe à droite} lorsque « $u\boxdot v\boxdot w$ »
se comprend comme « $u\boxdot (v\boxdot w)$ ».} à gauche ou à
-droite ? (c) L'opération $@$ s'associe-t-elle à gauche ou à droite ?
+droite ?\quad (c) L'opération $@$ s'associe-t-elle à gauche ou à droite ?
+
+\begin{corrige}
+(a) Les arbres d'analyse (b) et (c) de la question (1) montrent que
+ $@$ est prioritaire sur $\#$.\quad (b) L'arbre d'analyse (a) de la
+ question (1) montre que $\#$ s'associe à gauche.\quad (c) L'arbre
+ d'analyse (d) de la question (1) montre que $@$ s'associe à droite.
+\end{corrige}
%