Exercises for Computer Science
Forfatter
abfatih
Sidst opdateret
8 år siden
Licens
Other (as stated in the work)
Resumé
Exercises sheet for high school students in Skoura-Boulmane , Morocco
Exercises sheet for high school students in Skoura-Boulmane , Morocco
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%\usepackage{minibox}
%Ecriture arabe
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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}}
%=====================Algo setup
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%================================
%================================
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%================Liste definition--numList-and alphList=============
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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}
%% Macros for ``successive divisions''
%%
%\def\Division#1#2#3{ % Dividend, divisor, remainder
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% below=0pt of D-1-2.south east,
% row sep=1pt, column sep=1pt,
% every node/.append style={minimum width=12mm}] {
% #1 \pgfmatrixnextcell #2 \\
% |[marcar] (R#1)| #3 \\
% };
% \draw[shorten >=2pt, shorten <=2pt]
% (D-1-2.north west) |- (D-1-2.south east);
%}
%\def\FinDivision#1{
%\node[marcar, below=2pt of D-1-2.south] (C)(C) {#1};
%}
%\tikzset{marcar/.style={circle,draw,inner sep=2pt,minimum width=0pt,
%fill=yellow!10}}
%
%
%\begin{tikzpicture}
% \coordinate (D-1-2) at (0,0) {}; % We must start with this command.
% \Division{25}{2}{1} % First dividend, divisor, remainder
% \Division{12}{2}{0} % Dividend (previous quotient), divisor, remainder
% \Division{6}{2}{0}
% \Division{3}{2}{1}
% \FinDivision{1} % Last remainder.
%
%% We can draw an arrow jumping from one remainder
%% to the next one. Every reminder is a node called
%% Rdividend. Last remainder is node C.
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% \draw[shorten <=1mm, ->, dashed] (R6) to[out=-150,in=-65] (R12);
% \draw[shorten <=1mm, ->, dashed] (R12) to[out=-150,in=-65] (R25);
%
%% Some more information:
% \node (MSB) at ([yshift=-1.3cm]R6.south) {Most significant bit (MSB)};
% \node (LSB) at ([yshift=-2mm]MSB.south) {Less significant bit (LSB)};
%\draw[ ->] (MSB.east) to[out=30,in=-55] (C);
%\draw[ ->] (LSB.west) to[out=150,in=-95] (R25);
%\end{tikzpicture}
%\begin{center}\SnowflakeChevronBold \SnowflakeChevronBold \SnowflakeChevronBold \end{center}
%%----------------------------------------------------------------------------------------------------------------------------------------
%
%%\includepdf[doublepages=true]{serie55}
\end{document}