Algoritmica Grafurilor.doc

7/27/2019 Algoritmica Grafurilor.doc

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ALGORITMICA GRAFURILOR

Cuprins

1.LABORATOR 1....................................................................................................................................................................2

1.1.CREAREAUNUIARBOREBINARSIPARCURGEREASAPRINCELE 3 FORME: RSD, SRD,SDR .........................................2

2.LABORATOR 2....................................................................................................................................................................4

2.1.CITIREAUNUIGRAF..........................................................................................................................................................4

2.2.OBTINEREADINTR-UNGRAFAUNUIALTGRAFPRINCONTRACTIE..................................................................................4

3.LABORATOR 3....................................................................................................................................................................6

3.1.AVANDDATUNGRAF,DETERMINATIUNSUBGRAFALSAU..............................................................................................6

3.2.AVANDDATUNGRAF,DETERMINATIUNGRAFPARTIALALSAU.....................................................................................63.3.DETERMINATIVECINIIUNUIVARFALUNUIGRAF............................................................................................................8

3.4. DETERMINATIGRADELEVARFURILORUNUIGRAF,GRADULMINIMSIGRADULMAXIM..................................................8

3.5. DETERMINATIW+(A)-MULTIMEAARCELORINCIDENTECU A CATREEXTERIOR, W- (A)-MULTIMEAARCELOR

INCIDENTECU A CATREINTERIORSIVECINIILUI A, UNDE A ESTEOSUBMULTIMEDEVARFURIALEGRAFULUI...............10

3.6. VERIFICATIDACAUNGRAFESTESIMETRIC/ANTISIMETRIC...........................................................................................11

4.LABORATOR 4..................................................................................................................................................................12

4.1. DETERMINATIDACADOUAGRAFURISUNTIZOMORFE..................................................................................................12

5. LABORATOR 5.................................................................................................................................................................14

5.1. ALGORITMUL ROY-WARSHALL...................................................................................................................................14

5.2.ALGORITMUL ROY-FLOYD.............................................................................................................................................14

5.3.ALGORITMULLUI DIJKSTRA...........................................................................................................................................166.LABORATOR 6..................................................................................................................................................................18

6.1.ALGORITMUL BELLMAN-FORD......................................................................................................................................18

6.2.ALGORITMULLUI PRIM..................................................................................................................................................19

6.3.ALGORITMULLUI KRUSKAL...........................................................................................................................................20

7.LABORATOR 7..................................................................................................................................................................24

7.1.COLORARAREASECVENTIALAAUNUIGRAF..................................................................................................................24

7.2.COLORAREASECVENTIALA(ALGORITMUL LARGERFIRST)............................................................................................25

8.LABORATOR 8..................................................................................................................................................................28

8.1.ALGORITMUL FORD-FULKERSON...................................................................................................................................28

1


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1. LABORATOR 1

1.1. Crearea unui arbore binar si parcurgerea sa prin cele 3 forme:

RSD, SRD,SDR

# include # include

# include # include typedef struct arbore

{int inf;struct arbore *st,*dr;

}arbore;arbore *creare(void){arbore *aux;char ch;

printf("\n e nod NULL?[d/n]");ch=getche();ch=toupper(ch);if (ch=='N'){aux=(arbore *)malloc(sizeof(arbore));printf("\n informatia=");scanf("%d",&aux->inf);printf("\n urmeaza succesorul stang al nodului cu informatia

%d",aux->inf);aux->st=creare();printf("\n urmeaza succesorul drept al nodului cu informatia

%d",aux->inf);aux->dr=creare();return aux;

}else return NULL;

}void RSD(arbore *a){if (a!=NULL){printf("%d ",a->inf);

RSD(a->st);RSD(a->dr);}

}void SRD(arbore *a){if(a!=NULL){SRD(a->st);printf("%d ",a->inf);

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SRD(a->dr);}

}void SDR(arbore *a){if (a!=NULL){SDR(a->st);

SDR(a->dr);printf("%d ",a->inf);

}}void main(void){clrscr();arbore *a;a=creare();printf("\n parcurgerea RSD este ");RSD(a);

printf("\n parcurgerea SRD este ");SRD(a);printf("\n parcurgerea SDR este ");SDR(a);getch();

}

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2. LABORATOR 2

2.1. Citirea unui graf

# include # include void main(void)

{int n,a[50][50],i,j;FILE *f;f=fopen("graf.in","r");fscanf("f,"%d",&n);for(i=1;i


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scanf("%d",&x);scanf("%d",&y);if(a[x][y]==0) printf("\n nu se poate face contractarea!");

else{for(i=1;i


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3. LABORATOR 3

3.1. Avand dat un graf,determinati un subgraf al sau.

# include # include void main(void)

{int n,a[50][50],i,j,m,v[50],k;FILE *f;f=fopen("graf.in","r");fscanf(f,"%d",&n);for(i=1;i


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# include # include void main(void){int n,a[50][50],i,j,m,v[50],k;FILE *f;char c;f=fopen("graf.in","r");

fscanf(f,"%d",&n);for(i=1;i


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a[j][i]=0;}}*/

getch();}

3.3. Determinati vecinii unui varf al unui graf.

# include # include void main(void){int n,a[50][50],i,j,x,v[50],k;FILE *f;f=fopen("graf.in","r");fscanf(f,"%d",&n);for(i=1;i


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int exterior;}semigrad[50];

int minim(int v[50],int n){int i,min=v[1];for(i=2;i


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getch();}

3.5. Determinati w+(A)-multimea arcelor incidente cu A catre exterior,

w- (A)-multimea arcelor incidente cu A catre interior si vecinii lui

A, unde A este o submultime de varfuri ale grafului.

# include # include int in(int v[50],int n,int x){for(int i=1;i


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if (in(v,k,j)==0){k++;v[k]=j;

}for(i=1;i


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4. LABORATOR 4

4.1. Determinati daca doua grafuri sunt izomorfe.

# include # include int a[25][25],st[25],n,m,t,b[25][25];void initializare(void){int i,j;FILE *f;f=fopen("graf.txt","r");fscanf(f,"%d",&n);for(i=1;i


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}int valid(int k){for(int i=1;i


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5. LABORATOR 5

5.1. Algoritmul Roy-Warshall.

# include # include int min(int a,int b){return a


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# include int min(int a,int b){return a


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5.3. Algoritmul lui Dijkstra

#include #include #include #include typedef struct set

{

int inf;struct set *next;

}set;int d[50];int min(set *s){int i,min,t;min=d[s->inf];t=s->inf;for(set *p=s;p!=NULL;p=p->next)

if (d[p->inf]inf];t=p->inf;}

return t;}set *stergere(set *s,int inf){set *p=s,*q;if (s->inf==inf) s=s->next;

else{

while(p->next->inf!=inf && p->next!=NULL) p=p->next;if (p->next!=NULL){q=p->next;p->next=q->next;free(q);}}

return s;}void main(void){int a[25][25],m[50][50],u,i,j,n,x;FILE *f;set *s,*aux,*q;f=fopen("gr.txt","r");fscanf(f,"%d",&n);for(i=1;i


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printf("\n graful are %d varfuri,matricea de adiacenta fiind:\n",n);for(i=1;i


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6. LABORATOR 6

6.1. Algoritmul Bellman-Ford

# include # include void main(void){int a[50][50],m[50][50],d[50],i,j,n,s,k;FILE *f;clrscr();f=fopen("gr.txt","r");fscanf(f,"%d",&n);for(i=1;i


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for(j=1;jd[i]+m[i][j])

d[j]=d[i]+m[i][j];}

printf("vectorul d este:");for(i=1;i


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FILE *f;clrscr();f=fopen("graf.in","r");fscanf(f,"%d",&n);for(i=1;i


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# include # include typedef struct min

{int lin,col;}min;

int n,a[50][50],m[50][50],t[50][50],k,ok,v[50],st[50];void initializare(void)

{for(int i=1;i1 && t[st[k]][st[k-1]]==0) return 0;for(int i=2;i


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}void main(void){int i,j,k,x,y;FILE *f;clrscr();f=fopen("graf.in","r");fscanf(f,"%d",&n);

for(i=1;i


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m[x][y]=1000;m[y][x]=1000;

}printf("arborele de cost minim este:\n");afisare(t,n);getch();

}

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7. Laborator 7

7.1. Colorararea secventiala a unui graf

# include # include # include void stergere(int v[50],int n,int x){int i,j;for(i=1;i


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afisare(a,n);printf("introduceti ordinea de colorare a varfurilor:");for(i=1;i


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}}void afisare(int a[50][50],int n){int i,j;printf("\n");for(i=1;i


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t=d[i];d[i]=d[j];d[j]=t;

}for(i=1;i


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8. LABORATOR 8

8.1. Algoritmul Ford-Fulkerson

# include # include # include struct retea

{int arc,capacitate,flux;

}a[50][50];int r[50][50],st[50],n,k,min,intrare,iesire,flux,t;void initializare(void){for(int i=1;i1 && r[st[p-1]][st[p]]==0) return 0;for(int i=1;i


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{st[p]=i;if (valid(p)==1)if (p>=3 && st[p]==iesire) {k=1;tipar(p);}else bktr(p+1);

}}void main(void)

{int i,j,ok,ok1;FILE *f;clrscr();f=fopen("graf.txt","r");fscanf(f,"%d",&n);for(i=1;i


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}if (ok==0) intrare=i;if (ok1==0) iesire=i;

}do{k=0;t=0;initializare();

st[1]=intrare;bktr(2);}while(k==1);flux=0;for(i=1;i

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Algoritmica Grafurilor.doc