Divide and conquer

1. conquer Divide and Divide and conquer

2. A.K.A. Divide et impera

3. Ce este “Divide and Conquer”? • Divide and conquer ( Divide et impera ) esteun important algoritm , in stiintacalculatorului, bazatperecursie multi-ramificata. • Cu ajutorulacestuia, problemaestesectionata in douasaumaimultesubprobleme de acelasi tip (sausimilare) panacandproblemadevinedestul de simplapentru a putea fi rezolvata direct. • In final, solutiilesubproblemelor se combinapentru a da un rezultatproblemeioriginale.

4. Pe de alta parte, abilitatea de intelegere, cat sicea de implementare a unuialgoritm de tipulDivide and conqueresteuna care ceretimppentru a putea fi perfectionata.

5. Aplicatii { divide(s,d,m); deis(s,m,x1); deis(m+1,d,x2); combinas(x1,x2,k); } } int main() { cin>>n; for(i=1;i<=n;i++) cin>>v[i]; deis(1,n,k); cout<<"\nsumaelementelor="<<k; return 0; } • #include<iostream> • intn,v[20],i,z,k; • using namespace std; • void divide(ints,intd,int &m) • { • m=(s+d)/2; • } • void combinas(int x1,int x2,int &k) • { • k=x1+x2; • } • void deis(ints,intd,int &k) • { • int m,x1,x2; • if(s==d) • k=v[s]; • else Suma elementelorunui vector

6. Aplicatii { divide(s,d,m); deis(s,m,x1); deis(m+1,d,x2); combinas(x1,x2,k); } } int main() { cin>>n; for(i=1;i<=n;i++) cin>>v[i]; deis(1,n,k); cout<<"\nprodusulelementelor="<<k; return 0; } • #include<iostream> • intn,v[20],i,z,k; • using namespace std; • void divide(ints,intd,int &m) • { • m=(s+d)/2; • } • void combinas(int x1,int x2,int &k) • { • k=x1+x2; • } • void deis(ints,intd,int &k) • { • int m,x1,x2; • if(s==d) • k=v[s]; • else k=x1*x2;

7. Determinareaelementului minim if(s==d) z=v[s]; else { divide(s,d,m); deimin(s,m,x1); deimin(m+1,d,x2); combinamin(x1,x2,z); } } int main() { cin>>n; for(i=1;i<=n;i++) cin>>v[i]; deimin(1,n,z); cout<<"minimul="<<z;} • #include<iostream> • intn,v[20],i,z,k; • using namespace std; • void divide(ints,intd,int &m) • { • m=(s+d)/2; • } • void combinamin(int x1,int x2,int &z) • { • if(x1<x2) • z=x1; • else • z=x2; • } • void deimin(ints,intd,int &z) • { • int x1,x2; • int m;

8. Determinareaelementului maxim void deimax(ints,intd,int &z) { int x1,x2; int m; if(s==d) z=v[s]; else { divide(s,d,m); deimax(s,m,x1); deimax(m+1,d,x2); combinamax(x1,x2,z); } } int main() { cin>>n; for(i=1;i<=n;i++) cin>>v[i]; deimax(1,n,z); cout<<"maximul="<<z; } • #include<iostream> • intn,v[20],i,z,k; • using namespace std; • void divide(ints,intd,int &m) • { • m=(s+d)/2; • } • void combinamax(int x1,int x2,int &z) • { • if(x1<x2) • z=x2; • else • z=x1; • }

9. CMMDC • #include<iostream.h> • int cmmdc(int a[20], int li, int ls) • { if(li==ls) return a[li]; • else • { int x,y; • x=cmmdc(a,li,(li+ls)/2); • y=cmmdc(a,(li+ls)/2+1,ls); • while(x!=y) • if(x>y) x=x-y; • else y=y-x; • return x; • } • } • void main() • { • int a[20],n,i; • cout<<"n=";cin>>n; • for(i=1;i<=n;i++) cin>>a[i]; • cout<<"cmmdc este: "<<cmmdc(a,1,n); • }

10. Turnurile din Hanoi • #include<iostream> • using namespace std; • long double nr; • int hanoi(int n, int a,int b, int c) • {if ( n ) • {hanoi(n-1,a,c,b); • cout<<a<<"->"<<b<<endl; • nr++; • hanoi(n-1,c,b,a);} • } • int main () • {int n; • cout<<"n= ";cin>>n; • //n este numarul de piese; • hanoi(n,1,2,3); • cout<<"numarul total de mutari a fost "<<nr; • }

11. MergeSort for(i=1;i<=k;i++) v[p+i-1]=a[i]; } int divide(int p,int u) {int m; if(u-p<=1) ordo(p,u); else {m=(p+u)/2; divide(p,m); divide(m+1,u); interclas(p,u,m); } } int main () {citire(); divide(1,n); afis(); } while(i<=m && j<=u) if(v[i]<v[j]) {k++; a[k]=v[i]; i++; } else {k++; a[k]=v[j]; j++; } if(i<=m) for(j=i;j<=m;j++) {k++; a[k]=v[j]; } else for(i=j;i<=u;i++) {k++; a[k]=v[i]; } • #include <iostream> • using namespace std; • int v[1000],n; • int citire() • {int i; • cin>>n; • for(i=1;i<=n;i++) • cin>>v[i]; • } • int afis() • {int i; • for(i=1;i<=n;i++) • cout<<v[i]<<" "; • cin>>i; • } • int ordo(int p,int u) • {int aux; • if(v[p]>v[u]) • {aux=v[p]; • v[p]=v[u]; • v[u]=aux; • } • } • int interclas(int p,int u,int m) • {int i,j,a[1000],k=0; • i=p; • j=m+1;

12. QuickSort • #include <iostream> • using namespace std; • int v[100],n,k; • int poz(int li,int ls,int &k,int v[100]) • { int i=li,j=ls,c,i1=0,j1=-1; • while(i<j) • { if(v[i]>v[j]) • { c=v[j]; v[j]=v[i]; v[i]=c; • c=i1; i1=-j1; j1=c; • } • i=i+i1; j=j+j1; • } • k=i; • } • int quick(int li,int ls) • { if(li<ls) • { poz(li,ls,k,v); • quick(li,k-1); • quick(k+1,ls); • } • } • int main() • { int i; • cin>>n; • for(i=1;i<=n;i++) • cin>>v[i]; • quick(1,n); • for(i=1;i<=n;i++) • cout<<v[i]<<" "; • }

13. Problemataieturilor int main() { cout<<"Numarul de gauri= "; cin>>n; for(i=1; i<=n; i++) { cout<<endl; cin>>v[i].x;cin>>v[i].y; } cin>>X>>Y; taiere(0, 0, X, Y); cout<<endl<<"Cea mai mare suprafata neperforata are coordonatele ("<<xs<<","<<ys<<");("<<xd<<","<<yd<<")"<<endl; cout<<"Are suprafata "<<S; } • #include<iostream> • using namespace std; • struct punct { • int x,y; • }; • int X, Y; • punct v[20]; • int n; • int S; • int xs, ys, xd, yd,i; • void taiere(int x1, int y1, int x2, int y2) { • //x1,y1; x2,y2 - coordonatele coltului stanga-jos,dreapta-sus; • int g=0, poz; • for(int i=1; i<=n && !g; i++) • //ma opresc cand dau peste o perforatie in interiorul suprafetei • if(v[i].x>x1 && v[i].x<x2 && v[i].y>y1 && v[i].y<y2) { • g=1; • poz=i; • } • if (g==1) { • taiere(x1, v[poz].y, x2, y2); // deasupra • taiere(x1, y1, x2, v[poz].y); // dedesubt • taiere(x1, y1, v[poz].x, y2); // stanga • taiere(v[poz].x, y1, x2, y2); // dreapta • } • else if ((x2-x1)*(y2-y1)>S) { • xs=x1; • ys=y1; • xd=x2; • yd=y2; • S=(x2-x1)*(y2-y1); • } • } OUCH! AU!

14. Un proiectrealizat de:Predescu RobertVecerdea AndreiEbinca CristianDiaconescuMircea If(bo$$) Allow(); Else Reject(); Reject(); Allow(); Gigel