diff options
Diffstat (limited to 'sem_5/HLIN501_Graphes/TP-DEVOIRTP')
21 files changed, 74037 insertions, 0 deletions
diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP1/tp1 b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP1/tp1 Binary files differnew file mode 100644 index 0000000..d5c434d --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP1/tp1 diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP1/tp1.cc b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP1/tp1.cc new file mode 100644 index 0000000..c73ad89 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP1/tp1.cc @@ -0,0 +1,101 @@ +#include <cstdlib> +#include <iostream> +#include <vector> +#include <stack> +using namespace std; + +void ecritureTailles(int n, int m, int comp[]); +void composantes(int n, int m, int edge[][2], int comp[]); +void grapheRandom(int,int, int[][2]); +void printgraphe (int, int, int[][2]); +void ecritureTaillesbis(int n, int m, int comp[]); + +int main(int argc, char ** argv) +{ + int n; // Nombre de sommets. + int m; // Nombre d'aretes. + cout << "Entrer le nombre de sommets:"; + cin >> n; + cout << "Entrer le nombre d'aretes:"; + cin >> m; + int edge[m][2]; // Tableau des aretes. + int comp[n]; // comp[i] est le numero de la composante contenant i. + grapheRandom(n,m,edge); + //printgraphe(n,m,edge); + composantes(n,m,edge,comp); + cout<<endl<<endl; + ecritureTailles(n,m,comp); + ecritureTaillesbis(n,m,comp); + + return EXIT_SUCCESS; +} +void ecritureTaillesbis(int n, int m, int comp[]){ + for (int i = 0 ; i < n; i ++){ + cout << "Le sommet : " << i << " est dans la composante : "<<comp[i]<<endl; + } +} +void ecritureTailles(int n, int m, int comp[]){ + int comptemp[n]; + int compteur = 0; + int tab[n];//n sera le nombre de cellule dans la composante, t[n] sera le nombre de composantes de tant de cellules + for(int i =0 ; i <n; i ++){ + comptemp[i]=0; + tab[i]=0; + } + for (int i = 0 ; i < n; i ++){ + if (comptemp[comp[i]]==0) compteur ++; + comptemp[comp[i]] ++; //comptemp est a present un tableau qui pour n numero d'une composante associe le nombre de cellule incluses + } + for (int i =0; i < n; i ++){ + tab[comptemp[i]-1]++; + } + + cout<<"Il y a "<<compteur<<" composantes connexes"<<endl; + cout<<"Lesquelles sont : "<< endl; + for (int i = 0 ; i<n; i ++){ + if (tab[i]>=1){ + cout<<"Il y a "<< tab[i] << " composantes de taille "<< i+1 << " Sommets, le num de cette comp est : "<< comp[i]<<endl; + } + } +} +void composantes(int n, int m, int edge[][2], int comp[]){ + int taille[n]; + vector<int> L[n]; + for (int i = 0 ; i < n; i ++) { + comp[i]=i; + taille[i]=1; + L[i].push_back(i); + } + for ( int i = 0 ; i < m; i ++){ + int * x = &comp[edge[i][0]]; + int * y = &comp[edge[i][1]]; + if (*x != *y){ + if (*x>*y){ + int aux = *x; + taille[*y]+=taille[aux]; + for(int j = 0; j < taille[aux]; j ++){ + int tmp = L[aux].back(); + comp[tmp]=*y; + L[*y].push_back(tmp); + L[aux].pop_back(); + } + } + } + } +} + +void printgraphe (int n, int m, int edge[][2]){ + cout<<n<<" Sommets et "<<m<<" aretes"<<endl; + for (int i = 0 ; i < m; i ++){ + cout << "Arete "<< i << ":[" <<edge[i][0]<< ";"<<edge[i][1]<<"]"; + } + cout<<endl; +} + +void grapheRandom(int n,int m, int edge[][2]){ + srand(time(NULL)); + for (int i = 0; i < m;i ++){ + edge[i][0]=rand()%n; + edge[i][1]=rand()%n; + } +} diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/a.out b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/a.out Binary files differnew file mode 100644 index 0000000..6742753 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/a.out diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/ex2arbre.ps b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/ex2arbre.ps new file mode 100644 index 0000000..bc47c2d --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/ex2arbre.ps @@ -0,0 +1,541 @@ +%!PS-Adobe-3.0 +%%BoundingBox: 0 0 612 792 + +500 250 3 0 360 arc +0 setgray +fill +stroke + +408 445 3 0 360 arc +0 setgray +fill +stroke + +216 598 3 0 360 arc +0 setgray +fill +stroke + +102 569 3 0 360 arc +0 setgray +fill +stroke + +169 384 3 0 360 arc +0 setgray +fill +stroke + +356 213 3 0 360 arc +0 setgray +fill 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776 lineto +stroke + +591 113 moveto +69 775 lineto +stroke + +509 30 moveto +69 775 lineto +stroke + +591 113 moveto +52 762 lineto +stroke + +591 113 moveto +66 776 lineto +stroke + +509 30 moveto +52 762 lineto +stroke + +509 30 moveto +66 776 lineto +stroke + +41 731 moveto +556 54 lineto +stroke + +556 54 moveto +69 775 lineto +stroke + +556 54 moveto +52 762 lineto +stroke + +556 54 moveto +66 776 lineto +stroke + +41 731 moveto +544 22 lineto +stroke + +544 22 moveto +69 775 lineto +stroke + +544 22 moveto +52 762 lineto +stroke + +544 22 moveto +66 776 lineto +stroke + +showpage diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tp2 b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tp2 Binary files differnew file mode 100644 index 0000000..0742932 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tp2 diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tp2.cc b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tp2.cc new file mode 100644 index 0000000..e598127 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tp2.cc @@ -0,0 +1,189 @@ +#include <cstdlib> +#include <iostream> +#include <vector> +#include <fstream> +#include <cmath> + +typedef struct coord{int abs; int ord;} coord; +void pointRandom(int n, coord point[]); +void distances(int n, int m, coord point[], int edge[][3]); +void tri(int m, int edge[][3]); +void affichageGraphique(int n, int m, coord point[], int arbre[][2], const char * filename); +void kruskal (int n, int edge[][3], int arbre[][2]); +void fusion(int tableau[][3],int deb1,int fin1,int fin2); +void tri_fusion(int tableau[][3],int longueur); +void tri_fusion_bis(int tableau[][3],int deb,int fin); +using namespace std; + +int +main() +{ + int n; //Le nombre de points. + cout << "Entrer le nombre de points: "; + cin >> n; + int m=n*(n-1)/2; // Le nombre de paires de points. + coord point[n]; // Les coordonnees des points dans le plan. + int edge[m][3]; // Les paires de points et le carre de leur longueur. + int arbre[n-1][2]; // Les aretes de l'arbre de Kruskal. + pointRandom(n,point); + distances(n,m,point,edge); + tri_fusion(edge,m); + // for (int i =0; i < m; i ++){ + // cout << "point "<< edge[i][0]<<":"<<edge[i][1]<<" coords : ("<< point[edge[i][0]].abs<<";"<<point[edge[i][0]].ord <<") ; ("<<point[edge[i][1]].abs<<" ; "<<point[edge[i][1]].ord<<") norme : "<<edge[i][2]<< endl; + // } + int edge2[m][2]; + for(int i =0; i < m; i ++){ + edge2[i][0]=edge[i][0]; + edge2[i][1]=edge[i][1]; + } + affichageGraphique(n,m, point,edge2, "graphe.ps"); + kruskal(n,edge,arbre); + cout<<"Kruskal OK"<<endl; + affichageGraphique(n,n-1,point,arbre, "arbre.ps"); + // system("evince graphe.ps"); + return EXIT_SUCCESS; +} + +void pointRandom(int n, coord point[]){ + srand(time(NULL)); + for (int i =0; i < n; i ++){ + point[i].abs = rand()%612; + point[i].ord =rand()%792; + //cout << "Created point "<<i<<" coords : "<< point[i].abs <<" : "<<point[i].ord<<endl; + } +} + +void distances(int n, int m, coord point[], int edge[][3]){ + int k = 0; + for (int i =0; i < n; i ++){ + for(int j = i+1; j < n; j ++){ + edge[k][0]=i; + edge[k][1]=j; + edge[k][2]=pow((point[i].abs - point[i].ord)-(point[j].abs - point[j].ord),2); + k++; + } + } + cout<<"calcul des distance : OK"<<endl; +} + +void fusion(int tableau[][3],int deb1,int fin1,int fin2) + { + int table1[fin1-deb1+1][3]; + int deb2=fin1+1; + int compt1=deb1; + int compt2=deb2; + int i; + for(i=deb1;i<=fin1;i++) + { + swap(table1[i-deb1],tableau[i]); + } + + for(i=deb1;i<=fin2;i++) + { + if (compt1==deb2) + { + break; + } + else if (compt2==(fin2+1)) + { + swap(tableau[i],table1[compt1-deb1]); + compt1++; + } + else if (table1[compt1-deb1][2]<tableau[compt2][2]) + { + swap(tableau[i],table1[compt1-deb1]); + compt1++; + } + else + { + swap(tableau[i],tableau[compt2]); + compt2++; + } + } + } + +void tri_fusion_bis(int tableau[][3],int deb,int fin) + { + if (deb!=fin) + { + int milieu=(fin+deb)/2; + tri_fusion_bis(tableau,deb,milieu); + tri_fusion_bis(tableau,milieu+1,fin); + fusion(tableau,deb,milieu,fin); + } + } + +void tri_fusion(int tableau[][3],int longueur) + { + if (longueur>0) + { + tri_fusion_bis(tableau,0,longueur-1); + } + } +void tri(int m, int edge[][3]){ + for (int i = 0 ; i < m ; i ++){ + for(int j=i+1; j < m; j ++){ + if ( edge[i][2]>edge[j][2]){ + swap(edge[i][0],edge[j][0]); + swap(edge[i][1],edge[j][1]); + swap(edge[i][2],edge[j][2]); + } + } + } +} + +void affichageGraphique(int n, int m, coord point[], int arbre[][2], const char * filename) +// Cree le fichier Exemple.ps qui affiche +// les points et l'arbre de Kruskal. +{ + ofstream output; + output.open(filename,ios::out); + output << "%!PS-Adobe-3.0" << endl; + output << "%%BoundingBox: 0 0 612 792" << endl; + output << endl; + for(int i=0;i<n;i++) + { + output << point[i].abs << " " << point[i].ord << " 3 0 360 arc" <<endl; + output << "0 setgray" <<endl; + output << "fill" <<endl; + output << "stroke"<<endl; + output << endl; + } + output << endl; + for(int i=0;i<m;i++) + { + output << point[arbre[i][0]].abs << " " << point[arbre[i][0]].ord + << " moveto" << endl; + output << point[arbre[i][1]].abs << " " << point[arbre[i][1]].ord + << " lineto" << endl; + output << "stroke" << endl; + output << endl; + } + output << "showpage"; + output << endl; +} + +void kruskal (int n, int edge[][3], int arbre[][2]){ + int comp[n]; + int indicea=0; + for(int i =0; i < n-1; i ++){ + arbre[i][0]=0; + arbre[i][1]=0; + } + for (int i = 0; i < n; i ++){ + comp[i]=i; + } + for(int i = 0 ; i < n*(n-1)/2;i++ ){ + if ( comp[edge[i][0]]!=comp[edge[i][1]]){ + int aux = comp[edge[i][0]]; + arbre[indicea][0]=edge[i][0]; + arbre[indicea][1]=edge[i][1]; + for(int j = 0; j < n; j ++){ + if (comp[j]==aux){ + comp[j]=comp[edge[i][1]]; + } + } + indicea++; + } + } +} diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tribulle.cc b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tribulle.cc new file mode 100644 index 0000000..0266596 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP2/tribulle.cc @@ -0,0 +1,189 @@ +#include <cstdlib>
+#include <iostream>
+#include <vector>
+#include <fstream>
+#include <cmath>
+
+typedef struct coord{int abs; int ord;} coord;
+void pointRandom(int n, coord point[]);
+void distances(int n, int m, coord point[], int edge[][3]);
+void tri(int m, int edge[][3]);
+void affichageGraphique(int n, int m, coord point[], int arbre[][2], const char * filename);
+void kruskal (int n, int edge[][3], int arbre[][2]);
+void fusion(int tableau[][3],int deb1,int fin1,int fin2);
+void tri_fusion(int tableau[][3],int longueur);
+void tri_fusion_bis(int tableau[][3],int deb,int fin);
+using namespace std;
+
+int
+main()
+{
+ int n; //Le nombre de points.
+ cout << "Entrer le nombre de points: ";
+ cin >> n;
+ int m=n*(n-1)/2; // Le nombre de paires de points.
+ coord point[n]; // Les coordonnees des points dans le plan.
+ int edge[m][3]; // Les paires de points et le carre de leur longueur.
+ int arbre[n-1][2]; // Les aretes de l'arbre de Kruskal.
+ pointRandom(n,point);
+ distances(n,m,point,edge);
+ tri(m,edge);
+ for (int i =0; i < m; i ++){
+ cout << "point "<< edge[i][0]<<":"<<edge[i][1]<<" coords : ("<< point[edge[i][0]].abs<<";"<<point[edge[i][0]].ord <<") ; ("<<point[edge[i][1]].abs<<" ; "<<point[edge[i][1]].ord<<") norme : "<<edge[i][2]<< endl;
+ }
+ int edge2[m][2];
+ for(int i =0; i < m; i ++){
+ edge2[i][0]=edge[i][0];
+ edge2[i][1]=edge[i][1];
+ }
+ affichageGraphique(n,m, point,edge2, "graphe.ps");
+ kruskal(n,edge,arbre);
+ affichageGraphique(n,n-1,point,arbre, "arbre.ps");
+ // system("evince graphe.ps");
+ return EXIT_SUCCESS;
+}
+
+void pointRandom(int n, coord point[]){
+ srand(time(NULL));
+ for (int i =0; i < n; i ++){
+ point[i].abs = rand()%612;
+ point[i].ord =rand()%792;
+ cout << "Created point "<<i<<" coords : "<< point[i].abs <<" : "<<point[i].ord<<endl;
+ }
+}
+
+void distances(int n, int m, coord point[], int edge[][3]){
+ int k = 0;
+ for (int i =0; i < n; i ++){
+ for(int j = i+1; j < n; j ++){
+ edge[k][0]=i;
+ edge[k][1]=j;
+ edge[k][2]=(pow(point[j].abs-point[i].abs,2)+pow(point[j].ord-point[i].ord,2));
+ k++;
+ }
+ }
+ cout<<"calcul des distance : OK"<<endl;
+}
+
+void fusion(int tableau[][3],int deb1,int fin1,int fin2)
+ {
+ int table1[fin1-deb1+1][3];
+ int deb2=fin1+1;
+ int compt1=deb1;
+ int compt2=deb2;
+ int i;
+ //on recopie les éléments du début du tableau
+ for(i=deb1;i<=fin1;i++)
+ {
+ swap(table1[i-deb1],tableau[i]);
+ }
+
+ for(i=deb1;i<=fin2;i++)
+ {
+ if (compt1==deb2) //c'est que tous les éléments du premier tableau ont été utilisés
+ {
+ break; //tous les éléments ont donc été classés
+ }
+ else if (compt2==(fin2+1)) //c'est que tous les éléments du second tableau ont été utilisés
+ {
+ swap(tableau[i],table1[compt1-deb1]); //on ajoute les éléments restants du premier tableau
+ compt1++;
+ }
+ else if (table1[compt1-deb1][2]<tableau[compt2][2])
+ {
+ swap(tableau[i],table1[compt1-deb1]); //on ajoute un élément du premier tableau
+ compt1++;
+ }
+ else
+ {
+ swap(tableau[i],tableau[compt2]); //on ajoute un élément du second tableau
+ compt2++;
+ }
+ }
+ }
+
+void tri_fusion_bis(int tableau[][3],int deb,int fin)
+ {
+ if (deb!=fin)
+ {
+ int milieu=(fin+deb)/2;
+ tri_fusion_bis(tableau,deb,milieu);
+ tri_fusion_bis(tableau,milieu+1,fin);
+ fusion(tableau,deb,milieu,fin);
+ }
+ }
+
+void tri_fusion(int tableau[][3],int longueur)
+ {
+ if (longueur>0)
+ {
+ tri_fusion_bis(tableau,0,longueur-1);
+ }
+ }
+void tri(int m, int edge[][3]){
+ for (int i = 0 ; i < m ; i ++){
+ for(int j=i+1; j < m; j ++){
+ if ( edge[i][2]>edge[j][2]){
+ swap(edge[i][0],edge[j][0]);
+ swap(edge[i][1],edge[j][1]);
+ swap(edge[i][2],edge[j][2]);
+ }
+ }
+ }
+}
+
+void affichageGraphique(int n, int m, coord point[], int arbre[][2], const char * filename)
+// Cree le fichier Exemple.ps qui affiche
+// les points et l'arbre de Kruskal.
+{
+ ofstream output;
+ output.open(filename,ios::out);
+ output << "%!PS-Adobe-3.0" << endl;
+ output << "%%BoundingBox: 0 0 612 792" << endl;
+ output << endl;
+ for(int i=0;i<n;i++)
+ {
+ output << point[i].abs << " " << point[i].ord << " 3 0 360 arc" <<endl;
+ output << "0 setgray" <<endl;
+ output << "fill" <<endl;
+ output << "stroke"<<endl;
+ output << endl;
+ }
+ output << endl;
+ for(int i=0;i<m;i++)
+ {
+ output << point[arbre[i][0]].abs << " " << point[arbre[i][0]].ord
+ << " moveto" << endl;
+ output << point[arbre[i][1]].abs << " " << point[arbre[i][1]].ord
+ << " lineto" << endl;
+ output << "stroke" << endl;
+ output << endl;
+ }
+ output << "showpage";
+ output << endl;
+}
+
+void kruskal (int n, int edge[][3], int arbre[][2]){
+ int comp[n];
+ int indicea=0;
+ for(int i =0; i < n-1; i ++){
+ arbre[i][0]=0;
+ arbre[i][1]=0;
+ }
+ for (int i = 0; i < n; i ++){
+ comp[i]=i;
+ }
+ for(int i = 0 ; i < n*(n-1)/2;i++ ){
+ if ( comp[edge[i][0]]!=comp[edge[i][1]]){
+ int aux = comp[edge[i][0]];
+ arbre[indicea][0]=edge[i][0];
+ arbre[indicea][1]=edge[i][1];
+ for(int j = 0; j < n; j ++){
+ if (comp[j]==aux){
+ comp[j]=comp[edge[i][1]];
+ }
+ }
+ indicea++;
+ }
+ }
+}
diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP3/tp3 b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP3/tp3 Binary files differnew file mode 100644 index 0000000..31f4a09 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP3/tp3 diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP3/tp3.cc b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP3/tp3.cc new file mode 100644 index 0000000..67644a4 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP3/tp3.cc @@ -0,0 +1,223 @@ +#include <cstdlib> +#include <iostream> +#include <vector> +#include <fstream> +#include <cmath> +#include<vector> +#include<queue> +#include<stack> + +typedef struct coord{int abs; int ord;} coord; +bool search (std::vector<int> vec, int x); +void ecritureNiveaux(int n, int niveau[]); +void voisinsRandom(int n, int m, std::vector<int>voisins[]); +void afficheGraph (int n, std::vector<int>voisins[]); +void parcoursLargeur(int n, std::vector<int>voisins[],int niveau[], int ordre[], int pere[]); +void afficheArbre(int n, int pere[], int ordre[]); +void pacoursProf(int n, int r, std::vector<std::stack<int>*> voisins, int debut[],int fin[], int pere[], int niveau[]); +void vectortostack(int n,std::vector<int> arch[], std::vector<std::stack <int>* > young); +void afficheArbrebis(int n, int pere[]); +int sommeniveau(int n, int niveau[]); +using namespace std; + +void voisinsRandom(int n, int m, vector<int>voisins[]){ + srand(time(NULL)); + int x=1; int y=0; + for (int i = 0; i < m; i ++){ + do { + x = rand()%n; + y = rand()%n; + while (x==y){ + y = rand()%n; + } + } while (search(voisins[x],y)); + voisins[x].push_back(y); + voisins[y].push_back(x); + } +} +bool search (vector<int> vec, int x){ + int i = 0; + if (vec.size()==0){ + return false; + } + while (vec[i]!=x){ + i ++; + if (i>vec.size()){ + return false; + } + } + return true; +} +int main() { + int n; //Le nombre de points. + int m; // nb aretes + cout << "Entrer le nombre de points: "; + cin >> n; + cout << "Entrer le nombre d'aretes: "; + cin>>m; + if (m > n*(n-1)/2){ + cout<<"Nombre d'aretes trop grand, cap à : "<< n*(n-1)/2<<endl; + m=n*(n-1)/2; + } + vector<int> voisins[n]; + int pere[n]; + int pere2[n]; + int ordre[n]; + int niveau[n]; + int niveau2[n]; + int debut[n]; + int fin[n]; + vector<stack < int >* > piledevoisins = vector< stack < int > * >(n); + for (int i =0; i < n; i ++){ + piledevoisins[i]=new stack<int>; + } + // for (int i = 0; i < n ; i ++){ + // piledevoisins[i]=new stack<int>; + // } + voisinsRandom(n,m,voisins); + //afficheGraph(n,voisins); + parcoursLargeur(n,voisins,niveau,ordre,pere); + //afficheArbre(n, pere, ordre); + //ecritureNiveaux(n,niveau); + cout<<"Parcours en largeur OK"<<endl; + vectortostack(n, voisins, piledevoisins); + pacoursProf(n,0,piledevoisins, debut, fin, pere2, niveau2); + //afficheArbrebis(n,pere); + //ecritureNiveaux(n,niveau2); + cout<<"Parcours Prof OK"<<endl; + cout<<"Smax larg vaut : "<< sommeniveau(n,niveau)<<endl; + cout<<"Smax prof vaut : "<< sommeniveau(n,niveau2)<<endl; + return EXIT_SUCCESS; +} + +int sommeniveau(int n, int niveau[]){ + int ret = 0; + for (int i =0; i < n; i ++){ + ret+=niveau[i]; + // cout << niveau[i]<<" + "; + } + cout<<endl; + return ret; +} +void afficheGraph (int n, vector<int>voisins[]){ + for (int i =0; i < n; i ++){ + int j = 0; + cout<<"Sommet "<<i<< " Voisins : "; + while (voisins[i].size()>j){ + cout<< " "<<voisins[i][j]; + j ++; + } + cout<<endl; + } +} +void afficheArbre(int n, int pere[], int ordre[]){ + for (int i =0; i < n; i ++ ){ + cout << "Pere de "<<i<<" : "<<pere[i]<<endl; + cout << "Ordre de "<<i<<" : "<<ordre[i]<<endl; + + } +} +void afficheArbrebis(int n, int pere[]){ + for (int i =0; i < n; i ++ ){ + cout << "Pere de "<<i<<" : "<<pere[i]<<endl; + } +} +void parcoursLargeur(int n, vector<int>voisins[],int niveau[], int ordre[], int pere[]){ + int dejavu[n]; + for (int i =0; i < n; i ++ ){ + dejavu[i]=0; + niveau[i]=0; + } + int r=0; + dejavu[r]=1; + ordre[r]=1; + pere[r]=r; + niveau[r]=0; + queue<int> AT; + AT.push(r); + int t = 2; + while (!AT.empty()){ + int v = AT.front(); + AT.pop(); + for (int i =0; i < voisins[v].size();i ++){ + int x = voisins[v][i]; + if (!dejavu[x]){ + dejavu[x]=1; + AT.push(x); + ordre[x]=t; + t ++; + pere[x]=v; + niveau[x]=niveau[v]+1; + } + } + } +} +void pacoursProf(int n, int r, vector<stack<int>* > voisins, int debut[],int fin[], int pere[] ,int niveau[]){ + bool dejavu[n]; + for (int i =0; i < n; i ++ ){ + dejavu[i]=false; + niveau[i]=0; + } + dejavu[r]=1; + debut[r]=1; + pere[r]=r; + niveau[r]=0; + stack<int> AT; + AT.push(r); + int t = 2; + while (!AT.empty()){ + int x = AT.top(); + if (voisins[x]->empty()){ + AT.pop(); + fin[x]=t; + t ++; + } + else { + int y = voisins[x]->top(); + voisins[x]->pop(); + if (!dejavu[y]){ + dejavu[y]=true; + AT.push(y); + debut[y]=t; + t++; + pere[y]=x; + niveau[y]=niveau[x]+1; + cout << "Niveau de "<<y << " = "<<niveau[x]+1<<endl; + } + } + } +} +void vectortostack(int n,vector<int> arch[], vector<stack <int>* > young){ + for (int i = 0; i < n; i ++ ){ + for (int j =0; j < arch[i].size(); j++){ + young[i]->push(arch[i][j]); + } + } +} +void ecritureNiveaux(int n, int niveau[]){ + int tmp[n]; + for (int i =0; i < n; i ++){ + tmp[i]=0; + } + for (int i = 0 ; i < n; i ++ ){ + tmp[niveau[i]]++; + } + for (int i = 0; i < n; i ++){ + if (tmp[i]==0){ + return; + } + // cout<< "Il y a "<< tmp[i]<< " sommets de niveau " <<i<<endl; + } +} +void distances(int n, int m, coord point[], int edge[][3]){ + int k = 0; + for (int i =0; i < n; i ++){ + for(int j = i+1; j < n; j ++){ + edge[k][0]=i; + edge[k][1]=j; + edge[k][2]=(pow(point[j].abs-point[i].abs,2)+pow(point[j].ord-point[i].ord,2)); + k++; + } + } + cout<<"calcul des distance : OK"<<endl; +} diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP4/affichage.ps b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP4/affichage.ps new file mode 100644 index 0000000..29ce1df --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP4/affichage.ps @@ -0,0 +1,34569 @@ +%!PS-Adobe-3.0 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0000000..3889cf0 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP4/tp4 diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP4/tp4.cc b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP4/tp4.cc new file mode 100644 index 0000000..73cdc4f --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP4/tp4.cc @@ -0,0 +1,182 @@ +#include <cstdlib> +#include <iostream> +#include <vector> +#include <fstream> +#include <cmath> + +using namespace std; + +const int N=10; +const int M=(N*(N-1))/2; + +typedef struct coord{int abs; int ord;} coord; +typedef struct point{int x; int y;} point; + +void pointRandom(int n,coord point[][]); +float distancexy(coord p1,coord p2); +void voisins(int n,int dmax,coord point[][],vector<point> voisin[][],int &m); +void voisins2arete(int n,vector<int>voisins[],int arete[][2]); +void affichageGraphique(int n,int m,coord point[][],vector<int> voisins[][],const char * name); +bool existe(int n,int dis[],bool traite[]); +int searchsmallest(int n, int dist[],bool traite[]); +void dijkstra(int n,vector<int> voisin[][],coord point[][],int pere[], int m); +int construireArbre(int n,vector<int> voisin[],int pere[]); + +int main(){ + int n; // Le nombre de points. + cout << "Entrer le nombre de points: "; + cin >> n; + int dmax=50; // La distance jusqu'a laquelle on relie deux points. + coord point[N][N]; // Les coordonnees des points. + vector<point> voisin[N][N]; + vector<int> voisinbis[N]; // Les listes de voisins. + int arbre[N-1][2]; // Les aretes de l'arbre de Dijkstra. + int pere[N]; // La relation de filiation de l'arbre de Dijkstra. + int m; // Le nombre d'aretes + int arete[M][2]; // Les aretes du graphe + pointRandom(n,point); + voisins(n,dmax, point, voisin, m); + const char * filename = "affichage.ps"; + affichageGraphique(n,m,point,voisin,filename); + // cout<<"Graphe de base créé et exporté vers "<<filename<<endl; + // dijkstra(n,voisin,point,pere,m); + // construireArbre(n,voisinbis,pere); + // const char * filename2 = "affichagefin.ps"; + // affichageGraphique(n,m,point,voisinbis,filename2); + + return EXIT_SUCCESS; +} + +void pointRandom(int n, coord point[][]){ + srand(time(NULL)); + for (int i =0; i < 10; i ++){ + for (int j = 0; j < 10; j ++){ + point[i][j].abs = 60*i; + point[i][j].ord = 60*j; + cout << "Created point "<<i<<","<<j<<" coords : "<< point[i][j].abs <<" : "<<point[i][j].ord<<endl; + k++; + } + } + } +float distancexy(point p1, point p2){ + return pow((abs(p2.x-p1.x)+abs(p2.y-p1.y)),2); +} +void voisins (int n, int dmax, coord point[][], vector<point> voisins[][], int &m){ + int arrete = 0; + for (int i = 0; i < 10; i ++){ + for (int j = 0; j < 10; j ++){ + for (int o = 0; o < 10 ; o ++){ + for (int k = 0; k < 10; k ++){ + if (((o==i+1) && (j==k))|| ((k==j+1) && (i==o)) || ((o==i+1) && (k==j+1))){ + point tmp; + tmp.x=o; + tmp.y=k; + voisins[i][j].push_back(tmp); + tmp.x=i; + tmp.y=j; + voisins[o][k].push_back(tmp); + } + } + } + } + } + } +void affichageGraphique(int n, int m, coord point[], vector<int> voisins[], const char * filename) +// Cree le fichier Exemple.ps qui affiche +// les points et l'arbre de Kruskal. +{ + ofstream output; + output.open(filename,ios::out); + output << "%!PS-Adobe-3.0" << endl; + output << "%%BoundingBox: 0 0 612 792" << endl; + output << endl; + for(int i=0;i<10;i++) + for (int j = 0 ; j < 10; j ++){ + { + output << point[i][j].abs << " " << point[i][j].ord << " 3 0 360 arc" <<endl; + output << "0 setgray" <<endl; + output << "fill" <<endl; + output << "stroke"<<endl; + output << endl; + } + } + output << endl; + for(int i=0;i<10;i++) + { + for (int k =0; k < 10; k ++){ + for (int j =0; j < voisins[i][k].size(); j ++){ + + output << point[voisin[i][k][j].x][voisin[i][k][j].y].abs<<" "<<point[voisin[i][k][j].x][voisin[i][k][j].y].ord << " moveto"<<endl; + output<<point[voisins[i][j]].abs << " " << point[voisins[i][j]].ord << " lineto"<<endl; + output<< "stroke"<<endl; + output << endl; + } + } + } + } + output<<"showpage"; + output<<endl; +} +bool existe(int n,int dis[],bool traite[]){ + bool test = true; + bool ret = false; + int i = 0; + while (test && i < n){ + if (!traite[i] && (dis[i]!=-1)){ + test = false; + ret = true; + } + i++; + } + return ret; +} +int searchsmallest(int n, int dist[],bool traite[]){ + int ret=-1; + int retdist = 10000; + for (int i = 0 ; i < n; i ++){ + // cout<<"i :"<< i << " Dist de i "<< dist[i]<<" traite de i "<<traite[i]<<endl; + if (traite[i]==false){ + if (dist[i]!= -1){ + if (dist[i]<=retdist){ + retdist=dist[i]; + ret =i; + } + } + } + } + // cout<<"Lancment du traitement de :" << ret<<endl; + return ret; +} +void dijkstra(int n, vector<int> voisin[], coord point[], int pere[], int m){ + int d[n]; + bool traite[n]; + for (int i =0; i < n; i ++){ + d[i]= -1; + traite[i]=false; + } + pere[0]=0; + d[0]=0; + while (existe(n,d,traite)){ + int current = searchsmallest(n,d,traite); + //cout<<"C'est ti-par avec current = "<< current <<endl; + traite[current]=true; + // cout<<"traite current : " << traite[current]<<endl; + for (int i =0; i < voisin[current].size();i ++){ + int x = current; + int y = voisin[current][i]; + //cout<<"Traitement de l'arete "<<x<<";"<<y<<endl; + //cout << d[y] << "versus " << d[x]<< " + " <<distancexy(point[x],point[y])<<endl; + if (!traite[y] && ((d[y]==-1) || (d[y]>(d[x]+distancexy(point[x],point[y]))))){ + d[y]=d[x]+distancexy(point[x],point[y]); + pere[y]=x; + } + } + } +} +int construireArbre(int n,vector<int> voisin[],int pere[]){ + for ( int i = 0; i < n; i ++){ + voisin[i].push_back(pere[i]); + voisin[pere[i]].push_back(i); + } + return n; +} diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp5 b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp5 Binary files differnew file mode 100644 index 0000000..b201576 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp5 diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp5.cc b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp5.cc new file mode 100644 index 0000000..d864773 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp5.cc @@ -0,0 +1,243 @@ +#include <iostream> +#include <vector> + +using namespace std; + +const int N=41; +const int INF=9999; //La valeur infinie. +char villes[41][20]={"Amiens", "Angouleme", "Avignon", "Bayonne", "Bilbao", "Bordeaux", "Bourges", "Brest", "Brive", "Bruxelles", "Caen", "Cahors", "Clermont-Ferrand", "Dijon", "Geneve", "Grenoble", "Lille", "Limoges", "Luxembourg", "Lyon", "Marseille", "Millau", "Montpellier", "Mulhouse", "Nancy", "Nantes", "Nice", "Orleans", "Paris", "Perpignan", "Poitiers", "Reims", "Rennes", "Rodez", "Rouen", "Saint-Etienne", "Strasbourg", "Toulouse", "Tours", "Troyes", "Valence"}; + +void floydWarshall(int longueur[][N],int dist[][N],int P[][N]); +void affichage(int dist[][N],int chemin[][N]); +void itineraire(int i,int j,int chemin[][N]); +void itineraireville(int i,int j,int chemin[][N]); +void fermeturetrans(int longueur[][N], int dist[][N], int P[][N], bool fermeture[][N]); +void affichagematrice(int n, bool mat[][N]); + +int main(){ + + int position[41][2]={{282,84},{180,334},{412,443},{140,455},{80,480},{165,389},{304,253},{14,150},{249,365},{380,15},{182,117},{258,412},{322,322},{408,231},{470,287},{464,359},{324,32},{242,332},{470,60},{405,306},{433,480},{339,440},{365,461},{497,208},{453,148},{116,233},{515,460},{277,194},{296,146},{329,505},{208,271},{369,119},{120,175},{330,410},{228,101},{383,339},{508,152},{227,466},{220,230},{363,179},{408,377}}; + + int longueur[41][41]; + for(int i=0;i<41;i++){ + for(int j=0;j<41;j++){ + longueur[i][j]=INF; + } + longueur[i][i]=0; + } + + + longueur[0][34]=120; longueur[0][28]=130; + longueur[0][31]=180; longueur[0][16]=140; + + longueur[1][30]=130; longueur[1][17]=110; + longueur[1][8]=170; longueur[1][5]=120; + + longueur[2][40]=140; longueur[2][22]=90; + longueur[2][20]=90; + + longueur[3][5]=180; longueur[3][37]=300; + longueur[3][4]=70; + + longueur[4][3]=70; + + longueur[5][1]=120; longueur[5][8]=200; longueur[5][11]=230; + longueur[5][37]=241; longueur[5][3]=180; + + longueur[6][27]=121; longueur[6][39]=240; longueur[6][13]=250; + longueur[6][12]=190; longueur[6][38]=230; + + longueur[7][32]=240; + + longueur[8][11]=101; longueur[8][17]=100; longueur[8][1]=170; + longueur[8][5]=200; longueur[8][33]=140; + + longueur[9][16]=110; longueur[9][31]=230; longueur[9][18]=210; + + longueur[10][34]=130; longueur[10][38]=260; longueur[10][32]=180; + + longueur[11][21]=180; longueur[11][8]=101; longueur[11][5]=230; + longueur[11][37]=110; longueur[11][33]=105; + + longueur[12][6]=190; longueur[12][19]=210; longueur[12][35]=150; + longueur[12][17]=230; longueur[12][33]=270; + + longueur[13][19]=200; longueur[13][23]=221; longueur[13][24]=220; + longueur[13][39]=180; longueur[13][6]=250; longueur[13][14]=200; + + longueur[14][15]=145; longueur[14][19]=150; longueur[14][13]=200; + + longueur[15][26]=340; longueur[15][20]=270; longueur[15][40]=90; + longueur[15][19]=150; longueur[15][14]=145; + + longueur[16][0]=140; longueur[16][31]=196; longueur[16][9]=110; + + longueur[17][30]=120; longueur[17][1]=110; longueur[17][8]=100; + longueur[17][12]=230; + + longueur[18][31]=218; longueur[18][36]=220; longueur[18][9]=210; + longueur[18][24]=200; + + longueur[19][40]=150; longueur[19][35]=80; longueur[19][12]=210; + longueur[19][13]=200; longueur[19][14]=150; longueur[19][15]=150; + + longueur[20][22]=170; longueur[20][2]=90; longueur[20][26]=200; + longueur[20][15]=270; + + longueur[21][37]=190; longueur[21][11]=180; longueur[21][22]=110; + longueur[21][33]=60; + + longueur[22][29]=150; longueur[22][37]=240; longueur[22][21]=110; + longueur[22][2]=90; longueur[22][20]=170; longueur[22][40]=200; + + longueur[23][13]=221; longueur[23][24]=170; longueur[23][36]=120; + + longueur[24][36]=160; longueur[24][23]=170; longueur[24][13]=220; + longueur[24][31]=240; longueur[24][18]=200; + + longueur[25][32]=110; longueur[25][38]=210; longueur[25][30]=220; + + longueur[26][20]=200; longueur[26][15]=340; + + longueur[27][6]=121; longueur[27][39]=200; longueur[27][28]=132; + longueur[27][38]=120; + + longueur[28][0]=130; longueur[28][34]=131; longueur[28][27]=132; + longueur[28][39]=181; longueur[28][31]=140; + + longueur[29][37]=210; longueur[29][22]=150; + + longueur[30][25]=220; longueur[30][38]=100; longueur[30][17]=120; + longueur[30][1]=130; + + longueur[31][24]=240; longueur[31][28]=140; longueur[31][39]=130; + longueur[31][0]=180; longueur[31][16]=196; longueur[31][9]=230; + longueur[31][18]=218; + + longueur[32][10]=180; longueur[32][38]=250; longueur[32][7]=240; + longueur[32][25]=110; + + longueur[33][35]=200; longueur[33][40]=225; longueur[33][21]=60; + longueur[33][8]=140; longueur[33][11]=105; longueur[33][12]=270; + + longueur[34][0]=120; longueur[34][28]=131; longueur[34][10]=130; + + longueur[35][12]=150; longueur[35][19]=80; longueur[35][40]=120; + longueur[35][33]=200; + + longueur[36][23]=120; longueur[36][24]=160; longueur[36][18]=220; + + longueur[37][3]=300; longueur[37][5]=241; longueur[37][11]=110; + longueur[37][21]=190; longueur[37][22]=240; longueur[37][29]=210; + + longueur[38][10]=260; longueur[38][32]=250; longueur[38][25]=210; + longueur[38][30]=100; longueur[38][27]=120; longueur[38][6]=230; + + longueur[39][31]=130; longueur[39][28]=181; longueur[39][27]=200; + longueur[39][6]=240; longueur[39][13]=180; + + longueur[40][2]=140; longueur[40][15]=90; longueur[40][35]=120; + longueur[40][19]=150; longueur[40][33]=225; longueur[40][22]=200; + + + + // int longueur[N][N]={{0,2,INF,4,INF}, //Les longueurs des arcs. + // {INF,0,2,INF,INF}, //longueur[i][j]=INF si l'arc ij n'existe pas + // {INF,INF,0,2,INF}, + // {INF,-3,INF,0,2}, + // {2,INF,INF,INF,0}}; + int dist[N][N]; //Le tableau des distances. + int chemin[N][N]; //Le tableau de la premiere etape du chemin de i a j. + floydWarshall(longueur,dist,chemin); + affichage(dist,chemin); + itineraireville(0,5,chemin); + return 0; +} + +void floydWarshall (int longueur[][N],int dist[][N], int P[][N]){ + for (int i =0; i < N; i ++){ + dist[i][i]=0; + P[i][i]=i; + for (int j = 0 ; j < N; j ++){ + if (longueur[i][j]!=INF){ + dist[i][j]=longueur[i][j]; + P[i][j]=j; + } + else { + dist[i][j]=INF; + P[i][j]=-1; + } + } + } + for (int k = 0; k < N; k++){ + for(int i =0; i < N; i ++ ){ + for (int j = 0 ; j < N; j ++){ + if (dist[i][j]>dist[i][k]+dist[k][j]){ + dist[i][j]=dist[i][k]+dist[k][j]; + P[i][j]=P[i][k]; + } + } + } + } + for (int i =0; i < N; i ++){ + if (dist[i][i]<0){ + std::cout<<"Il existe un cycle orienté de poids <0"<<endl; + } + } + } + + +void affichage(int dist[][N],int chemin[][N]){ + for (int i = 0 ; i < N; i ++){ + for (int j = 0; j < N; j ++){ + cout<<dist[i][j]<<","; + } + cout<<endl; + } + cout<<endl; + cout<<endl; + for (int i =0; i < N; i ++){ + for (int j = 0; j < N; j ++){ + cout << "chemin de " << i << " à " <<j<< " : "<< chemin[i][j]<<endl; + } + } +} +void itineraire(int i,int j,int chemin[][N]){ + int retchemin[N]; + int working = i; + for (int k = 0 ; k < N; k ++){ + retchemin[k]=-1; + } + retchemin[0]=i; + int cpt = 1; + while (working != j){ + retchemin[cpt]=chemin[working][j]; + working = retchemin[cpt]; + cpt ++; + } + for (int k = 0 ; k < N; k ++){ + if (retchemin[k]!=-1){ + cout<<retchemin[k]<<" "; + } + } +} +void itineraireville(int i,int j,int chemin[][N]){ + int retchemin[N]; + int working = i; + for (int k = 0 ; k < N; k ++){ + retchemin[k]=-1; + } + retchemin[0]=i; + int cpt = 1; + while (working != j){ + retchemin[cpt]=chemin[working][j]; + working = retchemin[cpt]; + cpt ++; + } + for (int k = 0 ; k < N; k ++){ + if (retchemin[k]!=-1){ + cout<<villes[retchemin[k]]<<" "; + } + } + cout<<endl; +} diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp50 b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp50 Binary files differnew file mode 100644 index 0000000..81974d3 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp50 diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp50.cc b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp50.cc new file mode 100644 index 0000000..a4566d0 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/tp50.cc @@ -0,0 +1,74 @@ +#include <iostream> +#include <vector> + +using namespace std; + +const int N=6; +const int INF=9999; //La valeur infinie. + +void floydWarshall(int longueur[][N],int dist[][N],int P[][N]); +void affichage(int dist[][N],int chemin[][N]); +void itineraire(int i,int j,int chemin[][N]); +void itineraireville(int i,int j,int chemin[][N]); +void fermeturetrans(int longueur[][N], int dist[][N], int P[][N], bool fermeture[][N]); +void affichagematrice(int n, bool mat[][N]); + +int main(){ + int longueur[N][N]={{INF,INF,INF,2,INF,2}, //Les longueurs des arcs. + {2,INF,2,2,INF,INF}, //longueur[i][j]=INF si l'arc ij n'existe pas + {INF,INF,INF,2,INF,INF}, + {INF,INF,INF,INF,2,2}, + {INF,INF,2,INF,INF,2}, + {INF,INF,2,INF,INF,INF}}; + int dist[N][N]; //Le tableau des distances. + int chemin[N][N]; //Le tableau de la premiere etape du chemin de i a j. + bool ferm[N][N]; + fermeturetrans(longueur,dist,chemin,ferm); + affichagematrice(N,ferm); + return 0; +} + +void affichagematrice(int n, bool mat[][N]){ + for (int i = 0; i < n; i ++) { + cout<<"[ "; + for (int j = 0 ; j < n; j ++){ + cout<<mat[i][j]<<" , "; + } + cout << " ]"<<endl; + } +} + +void fermeturetrans(int longueur[][N], int dist[][N], int P[][N], bool fermeture[][N]){ + for (int i =0; i < N; i ++){ + dist[i][i]=0; + P[i][i]=i; + for (int j = 0 ; j < N; j ++){ + if (longueur[i][j]!=INF){ + dist[i][j]=longueur[i][j]; + P[i][j]=j; + fermeture[i][j]=true; + } + else { + dist[i][j]=INF; + P[i][j]=-1; + fermeture[i][j]=false; + } + } + } + for (int k = 0; k < N; k++){ + for(int i =0; i < N; i ++ ){ + for (int j = 0 ; j < N; j ++){ + if (dist[i][j]>dist[i][k]+dist[k][j]){ + dist[i][j]=dist[i][k]+dist[k][j]; + P[i][j]=P[i][k]; + fermeture[i][j]=true; + } + } + } + } + for (int i =0; i < N; i ++){ + if (dist[i][i]<0){ + std::cout<<"Il existe un cycle orienté de poids <0"<<endl; + } + } + } diff --git a/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/villes.cc b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/villes.cc new file mode 100644 index 0000000..1e499c9 --- /dev/null +++ b/sem_5/HLIN501_Graphes/TP-DEVOIRTP/TP5/villes.cc @@ -0,0 +1,126 @@ +char villes[41][20]={"Amiens", "Angouleme", "Avignon", "Bayonne", "Bilbao", "Bordeaux", "Bourges", "Brest", "Brive", "Bruxelles", "Caen", "Cahors", "Clermont-Ferrand", "Dijon", "Geneve", "Grenoble", "Lille", "Limoges", "Luxembourg", "Lyon", "Marseille", "Millau", "Montpellier", "Mulhouse", "Nancy", "Nantes", "Nice", "Orleans", "Paris", "Perpignan", "Poitiers", "Reims", "Rennes", "Rodez", "Rouen", "Saint-Etienne", "Strasbourg", "Toulouse", "Tours", "Troyes", "Valence"}; + +int position[41][2]={{282,84},{180,334},{412,443},{140,455},{80,480},{165,389},{304,253},{14,150},{249,365},{380,15},{182,117},{258,412},{322,322},{408,231},{470,287},{464,359},{324,32},{242,332},{470,60},{405,306},{433,480},{339,440},{365,461},{497,208},{453,148},{116,233},{515,460},{277,194},{296,146},{329,505},{208,271},{369,119},{120,175},{330,410},{228,101},{383,339},{508,152},{227,466},{220,230},{363,179},{408,377}}; + +int longueur[41][41]; +for(int i=0;i<41;i++){ + for(int j=0;j<41;j++){ + longueur[i][j]=inf; + } + longueur[i][i]=0; + } + + +longueur[0][34]=120; longueur[0][28]=130; +longueur[0][31]=180; longueur[0][16]=140; + +longueur[1][30]=130; longueur[1][17]=110; +longueur[1][8]=170; longueur[1][5]=120; + +longueur[2][40]=140; longueur[2][22]=90; +longueur[2][20]=90; + +longueur[3][5]=180; longueur[3][37]=300; +longueur[3][4]=70; + +longueur[4][3]=70; + +longueur[5][1]=120; longueur[5][8]=200; longueur[5][11]=230; +longueur[5][37]=241; longueur[5][3]=180; + +longueur[6][27]=121; longueur[6][39]=240; longueur[6][13]=250; +longueur[6][12]=190; longueur[6][38]=230; + +longueur[7][32]=240; + +longueur[8][11]=101; longueur[8][17]=100; longueur[8][1]=170; +longueur[8][5]=200; longueur[8][33]=140; + +longueur[9][16]=110; longueur[9][31]=230; longueur[9][18]=210; + +longueur[10][34]=130; longueur[10][38]=260; longueur[10][32]=180; + +longueur[11][21]=180; longueur[11][8]=101; longueur[11][5]=230; +longueur[11][37]=110; longueur[11][33]=105; + +longueur[12][6]=190; longueur[12][19]=210; longueur[12][35]=150; +longueur[12][17]=230; longueur[12][33]=270; + +longueur[13][19]=200; longueur[13][23]=221; longueur[13][24]=220; +longueur[13][39]=180; longueur[13][6]=250; longueur[13][14]=200; + +longueur[14][15]=145; longueur[14][19]=150; longueur[14][13]=200; + +longueur[15][26]=340; longueur[15][20]=270; longueur[15][40]=90; +longueur[15][19]=150; longueur[15][14]=145; + +longueur[16][0]=140; longueur[16][31]=196; longueur[16][9]=110; + +longueur[17][30]=120; longueur[17][1]=110; longueur[17][8]=100; +longueur[17][12]=230; + +longueur[18][31]=218; longueur[18][36]=220; longueur[18][9]=210; +longueur[18][24]=200; + +longueur[19][40]=150; longueur[19][35]=80; longueur[19][12]=210; +longueur[19][13]=200; longueur[19][14]=150; longueur[19][15]=150; + +longueur[20][22]=170; longueur[20][2]=90; longueur[20][26]=200; +longueur[20][15]=270; + +longueur[21][37]=190; longueur[21][11]=180; longueur[21][22]=110; +longueur[21][33]=60; + +longueur[22][29]=150; longueur[22][37]=240; longueur[22][21]=110; +longueur[22][2]=90; longueur[22][20]=170; longueur[22][40]=200; + +longueur[23][13]=221; longueur[23][24]=170; longueur[23][36]=120; + +longueur[24][36]=160; longueur[24][23]=170; longueur[24][13]=220; +longueur[24][31]=240; longueur[24][18]=200; + +longueur[25][32]=110; longueur[25][38]=210; longueur[25][30]=220; + +longueur[26][20]=200; longueur[26][15]=340; + +longueur[27][6]=121; longueur[27][39]=200; longueur[27][28]=132; +longueur[27][38]=120; + +longueur[28][0]=130; longueur[28][34]=131; longueur[28][27]=132; +longueur[28][39]=181; longueur[28][31]=140; + +longueur[29][37]=210; longueur[29][22]=150; + +longueur[30][25]=220; longueur[30][38]=100; longueur[30][17]=120; +longueur[30][1]=130; + +longueur[31][24]=240; longueur[31][28]=140; longueur[31][39]=130; +longueur[31][0]=180; longueur[31][16]=196; longueur[31][9]=230; +longueur[31][18]=218; + +longueur[32][10]=180; longueur[32][38]=250; longueur[32][7]=240; +longueur[32][25]=110; + +longueur[33][35]=200; longueur[33][40]=225; longueur[33][21]=60; +longueur[33][8]=140; longueur[33][11]=105; longueur[33][12]=270; + +longueur[34][0]=120; longueur[34][28]=131; longueur[34][10]=130; + +longueur[35][12]=150; longueur[35][19]=80; longueur[35][40]=120; +longueur[35][33]=200; + +longueur[36][23]=120; longueur[36][24]=160; longueur[36][18]=220; + +longueur[37][3]=300; longueur[37][5]=241; longueur[37][11]=110; +longueur[37][21]=190; longueur[37][22]=240; longueur[37][29]=210; + +longueur[38][10]=260; longueur[38][32]=250; longueur[38][25]=210; +longueur[38][30]=100; longueur[38][27]=120; longueur[38][6]=230; + +longueur[39][31]=130; longueur[39][28]=181; longueur[39][27]=200; +longueur[39][6]=240; longueur[39][13]=180; + +longueur[40][2]=140; longueur[40][15]=90; longueur[40][35]=120; +longueur[40][19]=150; longueur[40][33]=225; longueur[40][22]=200; + + |