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+ +\begin{document} +\maketitle + +\section{Présentation de l’algorithme} + +Nous allons travailler sur un graphe donc chaque sommet représente une ville et les arrêtes entre les sommets représentent le temps nécéssaire pour voyager entre deux villes. + +\begin{figure}[ht] +\centering +\begin{tikzpicture} + \node[shape=circle,draw=black] (A) at (0,4) {A}; + \node[shape=circle,draw=black] (B) at (8,4) {B}; + \node[shape=circle,draw=black] (C) at (4,4) {C}; + \node[shape=circle,draw=black] (D) at (6,0) {D}; + \node[shape=circle,draw=black] (E) at (2,0) {E}; + + \path (A) edge node[above] {2} (C); + \path (A) edge node[left] {3} (E); + \path (C) edge node[above] {20} (B); + \path (B) edge node[left] {1} (D); + \path (B) edge node[left] {10} (E); + \path (E) edge node[above left] {2} (D); +\end{tikzpicture} +\caption{Un réseau de villes} \label{fig:M1} +\end{figure} + +On veut calculer le temps minimal de voyage entre la ville A et toutes les autres.\\ +On regarde chaque ville une par une, et pour chacune : +\begin{itemize} + \item Permet elle d’atteindre plus vite une autre ville ? Si oui on note la nouvelle durée. + \item Les villes qu’on ne peut pas attendre gardent leur durée précédente. + \item On choisit la ville la plus proche pour le tour suivant. + \item On note sa durée comme étant la plus courte possible. +\end{itemize} + +\section{Exercices} +\begin{figure}[ht] +\centering +\begin{tikzpicture} + \node[shape=circle,draw=black] (A) at (2,4) {A}; + \node[shape=circle,draw=black] (B) at (6,4) {B}; + \node[shape=circle,draw=black] (C) at (8,2) {C}; + \node[shape=circle,draw=black] (D) at (6,0) {D}; + \node[shape=circle,draw=black] (E) at (2,0) {E}; + + \path (A) edge node[above] {20} (B); + \path (A) edge node[left] {3} (E); + \path (C) edge node[above] {5} (B); + \path (B) edge node[left] {1} (D); + \path (B) edge node[left] {10} (E); + \path (E) edge node[above left] {2} (D); + \path (D) edge node[below right] {7} (C); +\end{tikzpicture} +\caption{Un second réseau de villes} \label{fig:M1} +\end{figure} + + +\end{document}