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    \title{Chapitre 5 : Fonctions avec valeurs de retour - TD}
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    \begin{document}
    
    
    \maketitle
    \vspace*{-1.2cm}

    \hypertarget{exercice-1-traces-de-programme}{%
\subsection*{Exercice 1 : Traces de
programme*}\label{exercice-1-traces-de-programme}}


\paragraph{Question 1.} Combien de fois est appelÃ©e \texttt{f}~? Combien de fois est affichÃ© hello ?

    \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]

\begin{Verbatim}[commandchars=\\\{\}]
\PY{k}{def} \PY{n+nf}{f}\PY{p}{(}\PY{n}{a}\PY{p}{)} \PY{p}{:}
    \PY{k}{if} \PY{n}{a} \PY{o}{\PYZlt{}} \PY{l+m+mi}{0} \PY{p}{:} 
        \PY{k}{return}
    \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{hello}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}

\PY{n}{f}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}
\PY{n}{f}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{2}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}

\paragraph{Question 2.} Quel est l'affichage produit ? Quelles sont les valeurs des variables Ã&nbsp; la fin ?

    \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]

\begin{Verbatim}[commandchars=\\\{\}]
\PY{k}{def} \PY{n+nf}{f}\PY{p}{(}\PY{n}{x}\PY{p}{)} \PY{p}{:}
    \PY{k}{return} \PY{l+m+mi}{2} \PY{o}{*} \PY{n}{x} \PY{o}{+} \PY{l+m+mi}{3}

\PY{n}{res} \PY{o}{=} \PY{n}{f}\PY{p}{(}\PY{l+m+mi}{3}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{res}\PY{p}{)}
\PY{n}{z} \PY{o}{=} \PY{l+m+mi}{2}
\PY{n}{res} \PY{o}{=} \PY{n}{f}\PY{p}{(}\PY{n}{z}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{res}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{f}\PY{p}{(}\PY{n}{res}\PY{p}{)}\PY{p}{)}
\PY{n}{res} \PY{o}{=} \PY{n}{f}\PY{p}{(}\PY{n}{res}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{res}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{f}\PY{p}{(}\PY{n}{res}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\end{tcolorbox}

\paragraph{Question 3.} On considÃ¨re les fonctions \texttt{somme1} et \texttt{somme2} dÃ©finies
par :

    \begin{tcolorbox}[breakable, size=fbox, boxrule=1pt, pad at break*=1mm,colback=cellbackground, colframe=cellborder]

\begin{Verbatim}[commandchars=\\\{\}]
\PY{k}{def} \PY{n+nf}{somme1}\PY{p}{(}\PY{n}{a}\PY{p}{,} \PY{n}{b}\PY{p}{)}\PY{p}{:}
    \PY{n+nb}{print}\PY{p}{(}\PY{n}{a} \PY{o}{+} \PY{n}{b}\PY{p}{)}

\PY{k}{def} \PY{n+nf}{somme2}\PY{p}{(}\PY{n}{a}\PY{p}{,} \PY{n}{b}\PY{p}{)}\PY{p}{:}
    \PY{k}{return} \PY{n}{a} \PY{o}{+} \PY{n}{b}
\end{Verbatim}
\end{tcolorbox}

    \begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  Quelle est la diffÃ©rence entre \texttt{somme1} et \texttt{somme2} ?
\item
  Utiliser la fonction \texttt{somme1} pour afficher le rÃ©sultat de 2 +
  7 (sans utiliser l'opÃ©rateur \texttt{+}). MÃªme question avec la
  fonction \texttt{somme2}.
\item
  Utiliser la fonction \texttt{somme1} pour afficher le rÃ©sultat de 2 +
  7 + 18 (sans utiliser l'opÃ©rateur \texttt{+}). MÃªme question avec la
  fonction somme2. Quelle est alors la fonction la mieux programmÃ©e~?
\end{enumerate}

    \hypertarget{exercice-2-test-de-parituxe9}{%
\subsection*{Exercice 2 : Test de
paritÃ©*}\label{exercice-2-test-de-parituxe9}}

\paragraph{Question 1.} Ã‰crire la fonction \texttt{estPair} qui retourne \texttt{True} si le
nombre passÃ© en paramÃ¨tre est pair et \texttt{False} sinon.

\paragraph{Question 2.} DÃ©finir une fonction de tests unitaires pour la fonction
\texttt{estPair}.

    \hypertarget{exercice-3-heure-valide}{%
\subsection*{Exercice 3 : Heure valide*}\label{exercice-3-heure-valide}}

\paragraph{Question 1.} DÃ©finir la fonction \texttt{estHeureValide} prenant en paramÃ¨tre une
heure (donnÃ©e par 3 entiers : le nombre d'heures, le nombre de minutes
et le nombre de secondes) et retournant \texttt{True} si l'heure est
correcte, et \texttt{False} sinon.

\noindent\textbf{Remarque :} Une heure est considÃ©rÃ©e comme valide si le nombre
d'heures et compris entre 0 et 23 et le nombre de minutes et secondes
sont compris entre 0 et 59.

\paragraph{Question 2.} DÃ©finir une fonction de tests unitaires pour la fonction
\texttt{estHeureValide}.

    \hypertarget{exercice-4-nombre-de-secondes-depuis-minuit}{%
\subsection*{Exercice 4 : Nombre de secondes depuis
minuit*}\label{exercice-4-nombre-de-secondes-depuis-minuit}}

\paragraph{Question 1.} DÃ©finir la fonction \texttt{nbs} qui Ã©tant donnÃ© une heure (donnÃ©e par 3
entiers : le nombre d'heures, le nombre de minutes et le nombre de
secondes) passÃ©e en paramÃ¨tre, retourne le nombre de secondes passÃ©es
depuis minuit. Ã€ titre d'exemple, \texttt{nbs(1,1,1)} doit retourner
3661 (car une heure contient 3600 secondes et une minute 60 secondes).

\noindent\textbf{Remarque :} pour tester si l'heure passÃ©e en paramÃ¨tre est
valide, vous utiliserez la fonction \texttt{estHeureValide} de
l'exercice prÃ©cÃ©dent.

\paragraph{Question 2.} DÃ©finir une fonction \texttt{test\_nbs} qui correspond au test unitaire
de la fonction \texttt{nbs}. VÃ©rifier que votre fonction satisfait tous
les tests.


\subsection*{Exercice 5 : SÃ©rie harmonique**}
La sÃ©rie harmonique est la sÃ©rie dÃ©finie pour tout \(n &gt;\) 0 par:

\[H_n= 1 + \frac12 + \frac13 + \frac14 + \cdots + \frac1n\]

\paragraph{Question 1.} DÃ©finir la fonction \texttt{harmonique} prenant en paramÃ¨tre un entier n
et retournant la valeur \(H_n\) (la fonction retournera \texttt{-1} si
\(H_n\) n'est pas dÃ©fini).

\paragraph{Question 2.} DÃ©finir une fonction de tests unitaire de la fonction
\texttt{harmonique} sachant que  \(H_5 = 2.283333333333333\) et
\(H_{20} = 3.597739657143682\).

    \hypertarget{pour-aller-plus-loin}{%
\section*{Pour aller plus loin}\label{pour-aller-plus-loin}}

Pour les exercices suivants, des tests unitaires de chaque fonction Ã&nbsp; dÃ©finir existent dans la version notebook de ce TD pour que vous puissiez tester vos fonctions.

    \hypertarget{exercice-6-annuxe9e-bissextile}{%
\subsection*{Exercice 6 : AnnÃ©e
bissextile**}\label{exercice-6-annuxe9e-bissextile}}



DÃ©finir la fonction \texttt{estBissextile} qui retourne \texttt{True} si
l'annÃ©e passÃ©e en paramÃ¨tre correspond Ã&nbsp; une annÃ©e bissextile, et
\texttt{False} sinon.

\paragraph{Remarque :} une annÃ©e est bissextile si elle est divisible
par 4, mais pas par 100, sauf si elle est aussi divisible par 400.
Ainsi 2008 Ã©tait bissextile, 1900 n'Ã©tait pas bissextile et 2000 Ã©tait
bissextile.


    \hypertarget{exercice-7-nombre-de-jours-dans-un-mois}{%
\subsection*{Exercice 7 : Nombre de jours dans un
mois**}\label{exercice-7-nombre-de-jours-dans-un-mois}}

DÃ©finir la fonction \texttt{nbjours} prenant en paramÃ¨tre un numÃ©ro de
mois (entre 1 et 12), ainsi qu'une annÃ©e et retournant le nombre de
jours dans le mois.

\paragraph{Rappel :} 
\begin{itemize}
    \item Janvier, mars, mai, juillet, aoÃ»t, octobre et
    dÃ©cembre contiennent 31 jours. 
    \item FÃ©vrier contient 29 jours pour les
    annÃ©es bissextiles et 28 jours sinon. 
    \item Avril, juin, septembre et
    novembre contiennent 30 jours.    
\end{itemize}


\noindent\textbf{Remarques :} 
\begin{itemize}
    \item La fonction retournera 0 si le mois n'est pas
valide.
    \item On utilisera la fonction \texttt{estBissextile} pour
dÃ©terminer si l'annÃ©e passÃ©e en paramÃ¨tre est bissextile.
\end{itemize}

    \hypertarget{exercice-8-date-valide}{%
\subsection*{Exercice 8 : Date valide*}\label{exercice-8-date-valide}}

DÃ©finir la fonction \texttt{estDateValide} prenant en paramÃ¨tre une date
(dÃ©finie par 3 entiers : jours, mois, annÃ©es) et retournant
\texttt{True} si la date est valide, et \texttt{False} sinon.

\paragraph{Remarque :} on utilisera la fonction \texttt{nbjours} de
l'exercice prÃ©cÃ©dent pour vÃ©rifier si le mois passÃ© en paramÃ¨tre est
correct.



    \hypertarget{exercice-9-nombre-de-jours-depuis-le-1er-janvier-1970}{%
\subsection*{Exercice 9 : Nombre de jours depuis le 1er janvier
1970***}\label{exercice-9-nombre-de-jours-depuis-le-1er-janvier-1970}}

DÃ©finir la fonction \texttt{jours1970} qui prend en paramÃ¨tre une date
et retourne le nombre de jours passÃ©s depuis le 1er janvier 1970. Si la
date passÃ©e en paramÃ¨tre n'est pas valide, la fonction retourne 0. Si la
date est avant le 1er janvier 1970, alors la fonction renvoie un nombre
nÃ©gatif dont la valeur absolue est le nombre de jours depuis la date
jusqu'au 01/01/1970.



    \hypertarget{exercice-10-timestamp}{%
\subsection*{Exercice 10 : Timestamp*}\label{exercice-10-timestamp}}

En informatique, pour comparer des dates, on utilise le
\emph{timestamp}. Un timestamp correspond au temps Ã©coulÃ© depuis un
Ã©vÃ©nement prÃ©cis (qui sert alors de rÃ©fÃ©rence). Sur les systÃ¨mes UNIX,
le timestamp correspond au nombre de secondes Ã©coulÃ©es depuis le 1er
janvier 1970 Ã&nbsp; minuit.


DÃ©finir la fonction \texttt{timestamp} qui prend en paramÃ¨tre une date
et une heure, et retourne le nombre de secondes Ã©coulÃ©es par rapport au
1er janvier 1970.



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