From 5e7fc1594d15172d403847814507d6b2ed94d953 Mon Sep 17 00:00:00 2001 From: ldartois Date: Wed, 28 Feb 2024 11:53:24 +0100 Subject: [PATCH] ok --- TP/TP1.md | 122 ----------------------------- TP/TP2.md | 94 ----------------------- TP/TP3.md | 156 -------------------------------------- TP/TP4.md | 73 ------------------ TP/WelshPowell.png | Bin 99294 -> 0 bytes TP/dijkstra.png | Bin 68691 -> 0 bytes TP/fonctionsAide.c | 85 --------------------- TP/parcoursLargeur.png | Bin 106096 -> 0 bytes TP/parcoursProfondeur.png | Bin 90114 -> 0 bytes TP/prim.png | Bin 87240 -> 0 bytes td/TD1.pdf | Bin 76312 -> 0 bytes td/TD2.pdf | Bin 71495 -> 0 bytes td/TD3.pdf | Bin 90079 -> 0 bytes td/TD4.pdf | Bin 76325 -> 0 bytes td/TD5.pdf | Bin 69945 -> 0 bytes 15 files changed, 530 deletions(-) delete mode 100644 TP/TP1.md delete mode 100644 TP/TP2.md delete mode 100644 TP/TP3.md delete mode 100644 TP/TP4.md delete mode 100644 TP/WelshPowell.png delete mode 100644 TP/dijkstra.png delete mode 100644 TP/fonctionsAide.c delete mode 100644 TP/parcoursLargeur.png delete mode 100644 TP/parcoursProfondeur.png delete mode 100644 TP/prim.png delete mode 100644 td/TD1.pdf delete mode 100644 td/TD2.pdf delete mode 100644 td/TD3.pdf delete mode 100644 td/TD4.pdf delete mode 100644 td/TD5.pdf diff --git a/TP/TP1.md b/TP/TP1.md deleted file mode 100644 index 1e7a5ec..0000000 --- a/TP/TP1.md +++ /dev/null @@ -1,122 +0,0 @@ -TP Graphes 1 : Codage de graphes -============ - -- - - - - -Exercice 1 : Matrice d'adjacence ----------- -Un graphe sera représenté ici par une structure contenant un entier (son ordre), un entier booléen (orienté ou non), et son ensemble d'arêtes, représenté par sa matrice d'adjacence : - -``` -struct graphe{ - int ordre; // l'ordre du graphe - int** adj; // la matrice d'adjacence, donnée par un double tableau dynamique - int oriente; // vaut 0 si le graphe est non orienté, 1 sinon -}; - -typedef struct graphe graphe; -``` - -**Question :** -Ecrire une fonction permettant de créer un graphe vide à partir de son ordre et de son orientation : -``` -graphe creergraphe(int ord,int or); -``` -La fonction devra entre autres réserver de la mémoire pour la matrice d'adjacence. - -**Question :** -Ecrire une fonction prenant un graphe et deux sommets, et ajoutant une arête entre ces deux sommets : -``` -void ajoutArete(graphe g,int v,int w){ - ``` - -**Question :** -Si le graphe est non orienté, toute arête de v vers w ajoute également une arête de w vers v. -Modifiez la fonction précédente pour en prendre compte. - -**Question :** -Créez dans le main le graphe des frontières de la France (on ne considérera pas les micro-états). - - -- - - - - -Exercice 2 : Voisinage ----------- - -**Question :** -Ecrire une fonction permettant de d'afficher les voisins d'un sommet dans un graphe non orienté. -Testez votre fonction sur le graphe créé au premier exercice. - -**Question :** -Modifiez votre fonction pour afficher les voisins sortants et les voisins entrants si le graphe est orienté. - -**Question :** -Ecrire une fonction comptant le nombre de voisins d'un sommet dans un graphe, en gérant les cas orienté ou non orienté. - -**Question :** -Vérifiez sur le graphe créé la propriété du cours : - -La somme du nombre de voisins de tous les états est égal au nombre d'arêtes x 2. - - -- - - - - -Exercice 3 : Listes ----------- -Il est possible de coder l'ensemble des voisins d'un sommet par une liste chaînée. -Pour cela, on utilise un codage des listes chaînées : -``` -struct mail{ - int valeur; - struct mail *suivant; -}; -``` -Ainsi que des fonctions les utilisant : -``` -int tailleM(maillon *m){ //Renvoie la taille d'une liste - int res=0; - while(m!=NULL)){ - res++; - m=m->suivant; - } - return res; -} - -void affiche(maillon *m){ //Affiche le contenu d'une liste - if(m==NULL){ - printf("\n"); - }else{ - printf("%d, ",m->valeur); - affiche(m->suivant); - } -} - - -maillon* ajouterDebut(maillon* m,int val){ //Renvoie la liste enrichie de val - maillon* res=malloc(sizeof(maillon)); - res->valeur=val; - res->suivant=m; - return res; -} - -int estDans(maillon* m,int val){ //Renvoie 0 si val n'est pas dans la liste, 1 sinon - if(m==NULL){ - return 0; - } - if(m->valeur==val){ - return 1; - } - return estDans(m->suivant,val); -} -``` -A partir de ces listes, on peut donc définir un graphe comme suit : -``` -struct graphe{ - int ordre; - maillon** voisins; - int oriente; -}; -``` -Où voisins est un table de listes chaînées. - - -**Question :** -Recréez les fonctions codées dans les exercices précédents en les adaptant à cet encodage de graphes. -Normalement, vous devriez pouvoir utiliser la même fonction `main` pour tester votre code. \ No newline at end of file diff --git a/TP/TP2.md b/TP/TP2.md deleted file mode 100644 index 5c516e0..0000000 --- a/TP/TP2.md +++ /dev/null @@ -1,94 +0,0 @@ -TP Graphes 2 : Chemins et connexité -============ - -Le TP est prévu pour être fait en utilisant le codage des graphes à l'aide de matrices d'adjacence. - -- - - - - -Exercice 0 : Affichage ----------- - -***Question :*** -Ecrire une fonction permettant d'afficher une matrice carrée (la taille de la matrice sera donnée en argument) : -``` -void afficherMatrice(int **m,int taille); -``` - - -**Question :** -Ecrire une fonction permettant d'afficher la matrice d'adjacence d'un graphe donné en argument : -``` -void afficherAdjacence(graphe g); -``` - -- - - - - -Exercice 1 : Chemins de longueur fixe ----------- - -La multiplication de matrices carrées se fait grâce à la fonction de prototype : -``` -int** multiplicationMatriceCarre(int **a,int **b,int size); - ``` - -Le code de la fonction est donné ci-dessous. Si vous le souhaitez, vous pouvez ignorer le code et faire la fonction vous-même. -``` -int** multiplicationMatriceCarre(int **a,int **b,int size){ - int** res=calloc(size,sizeof(int*)); - int i,j,k; - for(i=0;idata=v; - nf->succ=*fi; - (*fi)=nf; -} - -int dequeue(fifo **fi){ - fifo *lect=*fi; - if(lect->succ==NULL){ - int res=lect->data; - *fi=NULL; - return res; - } - while(lect->succ->succ!=NULL){ - lect=lect->succ; - } - int res=lect->succ->data; - fifo *temp=lect->succ; - lect->succ=NULL; - free(temp); - return res; -} -int empty(fifo *fi){ - return fi==NULL; -} -``` -On rappelle que pour une variable `fifo *fi`, on empile 3 en faisant `enqueue(&fi,3)` et on défile (et on stocke dans une variable x) en faisant `x=dequeue(&fi)`. - -**Question :** - -Ecrire une fonction qui, étant donnés un graphe g et un sommet v de ce graphe, renvoie sous forme de file FIFO l'ensemble des voisins de v dans g : -``` -fifo* fileVoisins(graphe g,int v); -``` - -![Parcours en Largeur](parcoursLargeur.png) - -**Question :** - -Ecrire une fonction effectuant le parcours en largeur d'un graphe g à partir d'un sommet v. -On pourra se contenter d'afficher sur la sortie standard la numérotation ainsi que les distances obtenues, plutôt que de les renvoyer : -``` -void parcoursLargeur(graphe g,int v); -``` - -**Question :** - -Tester sur un graphe (au hasard celui des frontières). Cela correspond-t-il à une exécution manuelle de l'algorithme ? - - -- - - - - -Exercice 2 : Parcours en profondeur ----------- - -Pour implémenter le parcours en profondeur d'un graphe, nous aurons besoin d'une pile, dont voici la structure et les primitives : -``` -struct pile{ - int head; - struct pile* suite; -}; - -typedef struct pile pile; - - -int emptyPile(pile *p){ - return p==NULL; -} - -void push(pile **p,int v){ - pile* newpile=malloc(sizeof(pile)); - - newpile->head=v; - newpile->suite=*p; - *p=newpile; -} - -int pop(pile **p){ - int resultat=(*p)->head; - pile* temp=*p; - *p=(*p)->suite; - free(temp); - return resultat; -} - -int first(pile *p){ - return p->head; -} -``` -On rappelle que pour une variable `pile *fi`, on push 3 en faisant `push(&fi,3)` et on dépile (et on stocke dans une variable x) en faisant `x=pop(&fi)`. -La primitive `x=first(fi)` permet de récupérer le sommet de la pile sans dépiler. - -**Question :** - -Ecrire une fonction effectuant le parcours en profondeur d'un graphe g à partir d'un sommet v. -On pourra se contenter d'afficher sur la sortie standard la numérotation de premier passage plutôt que de les renvoyer : -``` -void parcoursProfondeur(graphe g,int v); -``` - -![Parcours en Profondeur](parcoursProfondeur.png) - -**Question :** - -Tester sur un graphe (au hasard celui des frontières). Cela correspond-t-il à une exécution manuelle de l'algorithme ? - -**Question :** - -Adaptez votre code pour également calculer, puis afficher, la numérotation de dernier passage. - -- - - - - -Exercice 3 : Algorithme de Welsh-Powell ----------- - -On va implémenter l'algorithme de Welsh-Powell de coloriage glouton des graphes. -Les premières questions visent à donner des fonctions aidant à l'implémentation de l'algorithme. A vous de les suivre ou non. - -**Question : Liste des sommets selon leur degré** - --Créer une fonction `int* tableauDegre(graphe g);` renvoyant un tableau où la case i contient le degré du sommet i. - --Créer une fonction `int indiceMax(int *tab,int taille);` renvoyant l'indice de la plus grande valeur du tableau tab de longueur taille. - --En utilisant les deux premières fonctions, créer une fonction `fifo* listeDegre(graphe g);` renvoyant une liste des sommets classés selon leur degré. - -**Question** - -Pour simplifier le code de Welsh-Powell, écrire une fonction -`int voisinCouleur(graphe g,int v,int c,int *color)` renvoyant 1 si le sommet v a un voisin de la couleur c dans le tableau color, et 0 sinon. - -![Algorithme de Welsh-Powell](WelshPowell.png) - -**Question** - -Enfin, implémentez l'algorithme de Welsh-Powell. - -Indice : Vous aurez besoin de la liste des sommets triés selon leur degré, mais également d'un lecteur sur cette liste, i.e. un pointeur vers le début de la liste pouvant la parcourir autrement que par des dequeues. \ No newline at end of file diff --git a/TP/TP4.md b/TP/TP4.md deleted file mode 100644 index d4714c3..0000000 --- a/TP/TP4.md +++ /dev/null @@ -1,73 +0,0 @@ -TP Graphes 4 : Plus Court Chemin et Arbre Recouvrant Minimal -============ - -Le TP est prévu pour être fait en utilisant le codage des graphes à l'aide de matrices d'adjacence. -Pour plus de clarté, vous pouvez utiliser un nouveau fichier, en copiant les structures et fonctions nécessaires depuis les TPs précédants. - - -- - - - - -Exercice 0 : Graphes valués ----------- - -Nous avons enrichi nos graphes avec une valuation des arêtes. - -**Question :** - -Comment intégrer cela à notre structure de données ? - - -Quel fonction(s) faut-il modifier pour prendre en compte cet enrichissement ? - -**Question :** - -Créez un nouveau fichier graphesvalues.c contenant la structure et les primitives nécessaires à la manipulation des graphes valués. - - -- - - - - -Exercice 1 : Algorithme de Dijkstra ----------- - - - -L'algorithme de Dijkstra renvoie deux données : la fonction d donnant la distance minimale entre la source et un sommet, et la fonction père donnant la direction à prendre pour atteindre cette distance minimale. - -**Question :** - -Une fonction des sommets vers un entier (ou un autre sommet) sera représentée par un tableau où la case i contient la valeur de la fonction pour i. - -Le C ne permettant de renvoyer qu'une structure de données, comment permettre de renvoyer les deux fonctions ? - -**Question :** - -Implémentez l'algorithme de Dijsktra, que je redonne ci-dessous : - -![Algorithme de Dijkstra](dijkstra.png) - - -**Question :** - -Testez votre algorithme en reprenant le graphes des frontières avec des valuation de votre choix. -Vérifier à la main que l'algorithme effectue les bons calculs. - - - -- - - - - -Exercice 2 : Algorithme de Prim ----------- - -Pour simplifier l'implémentation, on se contentera d'afficher sur la sortie standard les arêtes sélectionnées. On renverra tout de même la valuation totale de l'arbre couvrant. - -![Algorithme de Prim](prim.png) - - -**Question (optionnelle) :** - -Comme pour Dijkstra, l'ensemble des sommets atteint sera représenté par un tableau binaire. -Ecrivez une fonction `void selecArete(graphe g,int* atteint,int* x,int* y);` -qui trouve et dans le graphe g l'arête de poids minimale entre un sommet atteint et un sommet non atteint. 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cX=calloc(g.ordre,sizeof(int)); - int* cY=calloc(g.ordre,sizeof(int)); - for(i=0;ivaleur],cY[read->valeur]); - read=read->suivant; - } - } -*/ - Touche(); - FermerGraphique(); - -} - - - -//Aides matrices -//Creation matrice carrée vide : -int** creerMatriceId(int taille){ - int** res=calloc(taille,sizeof(int*)); - for(int i=0;if&JXF*0nC-x3r`X5&|{?6ciMai10UAD5zJeP*5*t;9$XL_EwXJzz6sr z!YVdUP{TLYfUmTGM86yZzEhiJ}T+FS9}5Ovb4SG z)YiD2Vsq4JxVU_aRKV|tZ2S)H)r((WKED0;hqxfS&AwMRtAEVFt6XJU3&b!bbRrP)Fm1kS4L-PO$yMT|)=~@uM zX;xN2q+w?MBrdN_OgpJmcJp_fx z$u?8J6-=1v5qx@Ky2(%n)M^v1sMYAqM*NgjRN|Ai_a$9*2%DczNz=n+#^`CKqy#sv3o za6$oV+h2sA!iA(#_Hg$n>d+WTf})?MO+N9^|JsRD{-dh{2amMgQEP+CX@fjT$yq@8 z$PykG)p5P-9(iAXgOWC7gh}s&U`V4G5#ly-ZQg}M;9FT)31dp~7M13O7r(GPg@{a6 z#Q13m-H+8i1z)Ko@gze0pLLZc4Ey!J9iu1>>D(kNX-%A6Mz@QKAL#B`%?gXG?5ui+ zDH4P0QC=!n+u=YpE**G^A-^)l-|XKVFqcZ@&ap>2#-0AeK@tPjTwGio_b5w@@vmj7 z*&7$@_St@=OlPH%J&|jg_!ctGLe9>nw5BU;)`C|#n%y?WM=OyV3qfsZ7XOAlQ-?4P0a`xM(>-cVH& 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