Matrice patratica

1.Diagonala principala:

a)pe diagonala-a[i][j] , i=j , i=1,n; j=1,n;

a[i][i] , i=1,n;

b)deasupra diagonalei-a[i][j] , i=1,n; j=1,n;

a[i][j], i=1,n-1; j=i+1,n;

c)sub diagonala-a[i][j] , i>j , i=1,n; j=1,n;

a[i][j] , i=2,n; j=1,i-1;

2.Diagonala secundara:

a)pe diagonala-a[i][j] , i+j=n+1; i=1,n; j=1,n;

j=n+1-i;

b)deasupra diagonalei-a[i][j] , i+j<n+1; i=1,n; j=1,n;

j<n+1-i;

i=1,n; j=1,n-i;

c)sub diagonala-a[i][j] , i+j>n+1; i=1,n; j=1,n;

j<n+1-i;

i=2,n; j=n+2-i,n;

3. Zone

a) Zona Sudica-i>j, i+j>n+1

b) Zona Nordica-i<j, i+j<n+1

c) Zona Estica-i<j, i+j>n+1

d) Zona Vestica-i>j, i+j<n+1

4. Simetrii

a) Diagonala principală

for(i=1;i<=n-1&&OK==1;++i)

for(j=i+1;j<=n&&OK==1;++j)

if(a[i][j]!=a[j][i]) OK=0;

b) Diagonala secundara

for(i=1;i<=n-1&&OK==1;++i)

for(j=i+1;j<=n-i&&OK==1;++j)

if(a[i][j]!=a[n+1-j][n+1-i]) OK=0;

c) Axa Ox

if(a[i][j]!=a[n+1-i][j]) OK=0;

d) Axa Oy

if(a[i][j]!=a[i][n+1-j])OK=0

Matrice

Declarare

Exemplu: float b[10][20] (matrice cu 10 linii numerotate de la 0 la 9, 20 de coloane numerotate de la 0 la 19 cu elemente de tip real);

Declarare+initializare

Exemplu: int c[3][4]={{1,5,7,4},{2,8,9,13},{40,60,90,80}};

Interclasare

-2 vectori ordonati descrescator => un vector ordonat crescactor-
#include <iostream>
using namespace std;
int main()
 {
 int x[20],y[40],z[60],i,j,m,n,k=0;
 cin>>n>>m;
 for(i=1;i<=n;++i) cin>>x[i];
 for(i=1;i<=m;++i) cin>>y[i];
 i=n;j=m;k=0;
 while(i>=1&&j>=1)
 { if(x[i]<y[j]) z[++k]=x[i–-];
   else z[++k]=y[j–-];
 }
 while(i>=1) z[++k]=x[i–-];
 while(j>=1) z[++k]=y[j–-];
 for(i=k;i>1;++i) cout<<z[i]<<",";
 cout<<z[1];
 return 0;
 }

Vectori de frecventa

#include <iostream>
using namespace std;
int main()
{
 int i,v[10],c;
 long long x;
 for(i=0;i<=9;++i) v[i]=0;
 cin>>x;
 while(x){c=x%10;x=x/10;v[c]=1;}
 for(i=9;i>=0;--i) if(v[i]!=0) cout<<i;
 return 0;
}

Perechi de numere egal depărtate de margine

#include <iostream>
using namespace std;
int main()
{
 int n,i,v[100],OK;
 cin>>n;
 for(i=1;i<=n;++i) cin>>v[i];
 OK=1;
 for(i=1;i<=n && OK==1;++i)
  if(v[i]>v[i+1])OK=0;
 if(OK==1)
  {i=1;j=n;
  while(i<j)
  {v[0]=v[i];v[i]=v[j];v[j]=v[0];
  ++i;–-j;}
  }
 for(i=1;i<=n;++i) cout<<v[i]<<" ";
 return 0;
}

Sortarea prin selecție

#include <iostream>
using namespace std;
int main()
{
 int v[100],n,i,Max,p,j;
 cin>>n;
 for(i=1;i<=n;++i) cin>>v[i];
 for(i=n;i>=2;–-i)
  {Max=v[1];p=1;
  for(j=1;j<=i;++j)
   {if (v[j]>Max){Max=v[j];p=j;}
   v[0]=v[i];v[i]=v[p];v[p]=v[0];}
  }
 for(i=1;i<=n;++i) cout<<v[i]<<" ";
 return 0;
 }

Sortare(interschimbare directa)

#include <iostream>
using namespace std;
int main()
{
 int v[100],n,i,j,aux;
  cin>>n;
 for(i=1;i<=n;++i)
  cin>>v[i];
 for(i=1;i<=n-1;++i)
  for(j=i+1;j<=n;++j)
   if(v[i]>v[j]) {aux=v[i];v[i]=v[j];v[j]=aux;}
 for(i=1;i<=n;++i)
  cout<<v[i]<<" ";
 return 0;
}

Sortare (Bule)

#include <iostream>
using namespace std;
int main()
{
 int n,i,v[100],OK,aux;
 cin>>n;
 for(i=1;i<=n;++i)
  cin>>v[i];
 do{OK=0;
    for(i=1;i<=n-1;++i)
    if(v[i]>v[i+1]) {aux=v[i];v[i]=v[i+1];v[i+1]=aux;OK=1;}
   }
 while(OK==1);
 for(i=1;i<=n;++i)
  cout<<v[i]<<" ";
 return 0;
}

Cautarea binara

#include <iostream>
using namespace std;
int main()
{
 int m,n,i,j,v[100],x,OK;
 cin>>n>>x;
 for(i=1;i<=n;++i)
  cin>>v[i];
 i=1;
 j=n;
 OK=0;
 while(i<=j && OK==0)
 {
  m=(i+j)/2;
  if(x==v[m])OK=1;
  else if(x>v[m])i=m+1;
  else j=m-1;
 }
 if(OK==1) cout<<„DA”;
 else cout<<„NU”;
 return 0;
}

Cautarea secventiala

#include <iostream>
using namespace std;
int main()
{
 int n,i,x,OK;
 cin>>n>>x;
 int v[n+1];
 for(i=1;i<=n;++i)
  cin>>v[i];
 OK=0;
 for(i=1;i<=n&&OK==0;++i)
  if(v[i]==x)OK=1;
 if(OK==1) cout<<„DA”;
 else cout<<„NU”;
 return 0;
}