Exercises sheet for high school students in Skoura-Boulmane , Morocco
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\lhead{
\textbf{LYCEE COLLEGIAL CHARIF IDRISSI}
}
\rhead{\textbf{INFORMATIQUE}
}
\chead{\textbf{
TCS
}}
\lfoot{}
\cfoot{\textbf{$\mathsf{2015-2016}$}}
%\rfoot{\textit{Pr. $\mathcal{A}$.Kaal}}
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%===========================================================
\begin{document}
\begin{center}
\large{\textbf{Serie N\textdegree 6: \textsc{Structures it\'eratives}}}
\end{center}
\begin{definition}[]
\hspace{2ex}Ecrire, en utilisant la boucle \textbf{Pour}, les algorithmes qui effecturent les calculs suivants
\begin{enumerate}
\item
\begin{tabular}{p{3cm}p{3cm}p{3cm}}
a) S = $\sum_{i=1}^{20} i$ & b) S = $\sum_{i=1}^{20} i^2$ & c) S = $ \sum_{i=1}^{20} i^i$
\end{tabular}
\item
\begin{tabular}{p{3cm}p{3cm}p{3cm}}
a) P = $\prod_{k=1}^{20} k$ & b) P = $ \prod_{k=1}^{20} k^2$ &c) P = $ \prod_{k=1}^{20} k^k $\\
\end{tabular}
\end{enumerate}
\end{definition}
\begin{definition}
\hspace{2ex} Ecrire les boucles appropri\'es pour cacluler chacune des expressions ci-desosus\\
\begin{enumerate}
\item
\begin{tabular}{p{7cm}p{7cm}}
a) $s= 1^2-2^2+\dots +19^2-20^2$ & b)$ s = 1^1 - 2^2 + \dots +19^{19} -20^{20}$ \\
\end{tabular}
\item
\begin{tabular}{p{7cm}p{7cm}}
a) $s= 1^2\times (-2)^2 \times \dots \times 19^2 \times (-20)^{2}$&b)$ p = 1^1 \times 2^2 + \dots +19^{19} \times 20^{20}$ \\
\end{tabular}
\item
\begin{tabular}{p{7cm}p{7cm}}
a) $s= \sqrt{1}+\sqrt{2}+\dots +\sqrt{19}+\sqrt{20}$ &b)$ s = \dfrac{1^1}{\sqrt{2}} + \dfrac{2^2}{\sqrt{3}} + \dots +\dfrac{19^{19}}{\sqrt{20}}$ \\
\end{tabular}
\end{enumerate}
\end{definition}
\begin{definition}[]
\begin{minipage}{0.7\textwidth}
\hspace{2ex}Ex\'ecuter l'algorithme ci-contre avec les entr\'ee de la ligne 1 du tableau ci-dessous et compl\'eter la ligne 2.\\[2ex]
\begin{tabular}{c|c|c|c|c|c|c}
Ex\'ecution \HandRight & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$N$ & 7 & 11 & 13 & 25 & 37 & 38 \\
\hline
$p$ & ... & ... & ... & ... & ... & ... \\
\hline
\end{tabular}
\vspace{3mm}\\
D'apr\`es les valeurs de $N$ et de $p$, que repr\'esente la valeur de $p$.
\end{minipage}
\begin{minipage}{0.3\textwidth}
\begin{scriptsize}
\begin{algorithmic}[1]
\State $p \leftarrow vrai$;
\State $i \leftarrow 2$;
\State Lire (N)
\Repeat
\State $r \leftarrow Reste(N, i)$;
\If{(r==0)} \textbf{alors}
\State $p \leftarrow faux$
\EndIf
\State $i\leftarrow i+1$
\Until{(($i>=N-1$) OU ($p==faux$))}
\end{algorithmic}
\end{scriptsize}
\end{minipage}
\end{definition}
\begin{definition}[]
\begin{minipage}{0.7\textwidth}
Ex\'ecuter l'algorithme ci-contre avec les entr\'ees $a$ et $b$ des lignes 1 et 2 du tableau ci-dessous et compl\'ter la ligne 3.\\[3ex]
\begin{tabular}{c|c|c|c|c|c|c}
Ex\'ecution \HandRight & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$a$ & 2 & 3 & 13 & 25 & 37 & 16 \\
\hline
$b$ & 4 & 5 & 6 & 12 & 12 & 38 \\
\hline
$q$ & ... & ... & ... & ... & ... & ... \\
\hline
\end{tabular}
\vspace{3mm}
D'apr\`es les valeurs de $a$, $b$ et de $q$, qu'indique de la valeur de $q$ ?
\begin{alphList}
\item le maximum de $a$ et $b$,
\item le PGCD de $a$ et $b$,
\item le PPCM de $a$ et $b$.
\end{alphList}
\end{minipage}
\begin{minipage}{0.3\textwidth}
\begin{scriptsize}
\begin{algorithmic}[1]
\State Lire(a,b);
\State $i \leftarrow 2$;
\If{(a<b)}\textbf{}alors
\State $temp\leftarrow a$;
\State $a\leftarrow b$;
\State $b\leftarrow temp$;
\EndIf
\State $r \leftarrow Reste(a,b)$;
\While{($r<>0$)} \textbf{faire}
\State $a \leftarrow b$;
\State $b \leftarrow r$;
\State $r \leftarrow Reste(a,b)$;
\EndWhile
\State $q \leftarrow b$;
\end{algorithmic}
\end{scriptsize}
\end{minipage}
\end{definition}
\begin{definition}[]
\begin{numList}
\item Ecrire, en utilisant une structure de contr\^ole de votre choix, un algorithme qui calcule le produit suivant
$$f = \prod_{k=1}^{k=n}k = k!= 1 \times 2 \times \dots \times (n-1) \times n $$
\item Ecrire, en utilisant une structure de contr\^ole de votre choix, un algorithme qui calcule la somme
$$s = \sum_{q=1}^{q=M}q! = 1! + 2! + \dots + M!$$
\end{numList}
\end{definition}
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%\begin{center}\SnowflakeChevronBold \SnowflakeChevronBold \SnowflakeChevronBold \end{center}
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\end{document}