Finding Norm of Matrix

#include<conio.h>
#include<stdio.h>
#include<math.h>

int main()
  {
    int i,j,m,n;
    int mat[10][10];
    double s,nm;
    printf("\n Enter the no. of rows and columns : ");
    scanf("%d %d",&m,&n);
    s = 0;
    for(i=0;i<m;i++)
    {
      printf("Row %d : ",i+1);    
       
      for(j=0;j<n;j++)
      {
        scanf("%d",&mat[i][j]);    
        s += pow(mat[i][j],2);                  
      }              
    }
    nm = sqrt(s);
    printf("\n\nThe Norm of this matrix : %lf",nm);  
    getch();
    return 0;
  }

Finding the Saddle Point of Matrix

#include<conio.h>
#include<stdio.h>
#include<math.h>

int main()
  {
    int i,j,m,n,min;
    int mat[10][10];
    printf("\n Enter the no. of rows and columns : ");
    scanf("%d %d",&m,&n);

    for(i=0;i<m;i++)
    {
      printf("Row %d : ",i+1);            
      for(j=0;j<n;j++)
       scanf("%d",&mat[i][j]);  
    }
   
    for(i=0;i<m;i++)
    {
      min = 0;        
      for(j=1;j<n;j++)
      {
        if(mat[i][min] > mat[i][j])
         min = j;            
      }    
      for(j=0;j<m;j++)
      {
        if(mat[j][min] > mat[i][min])
         break;                            
      }
      printf("\n Row %d : ",i+1);
      if(j == m)
       printf("Saddle point exists at Column %d",min+1);
      else
       printf("Saddle point doesn't exists");    
    }    
    getch();
    return 0;
  }

Finding Skew-Symmetric Matrix

#include<conio.h>
#include<stdio.h>
#include<math.h>

int main()
  {
    int i,j,m,n,min;
    int mat[10][10];
    do
    {
    printf("\n Enter the no. of rows and columns : ");
    scanf("%d %d",&m,&n);
    }while(m!=n);

    for(i=0;i<m;i++)
    {
      printf("Row %d : ",i+1);          
      for(j=0;j<n;j++)
       scanf("%d",&mat[i][j]);  
    }
 
    for(i=1;i<m;i++)
    {        
     for(j=0;j<i;j++)
     {
       if(mat[i][j] != -mat[j][i])
        break;            
     }  
    }  
 
    if(i == m && j+1 == i)
     printf("\n\nIt is a Skew-Symmetric Matrix");
    else
     printf("\n\nIt is not a Skew-Symmetric Matrix");
    getch();
    return 0;
  }

Finding Symmetric Matrix

#include<conio.h>
#include<stdio.h>
#include<math.h>

int main()
  {
    int i,j,m,n,min;
    int mat[10][10];
    do
    {
    printf("\n Enter the no. of rows and columns : ");
    scanf("%d %d",&m,&n);
    }while(m!=n);

    for(i=0;i<m;i++)
    {
      printf("Row %d : ",i+1);          
      for(j=0;j<n;j++)
       scanf("%d",&mat[i][j]);  
    }
 
    for(i=1;i<m;i++)
    {        
     for(j=0;j<i;j++)
     {
       if(mat[i][j] != mat[j][i])
        break;            
     }  
    }  
 
    if(i == m && j+1 == i)
     printf("\n\nIt is a Symmetric Matrix");
    else
     printf("\n\nIt is not a Symmetric Matrix");
    getch();
    return 0;
  }

Longest Common Sub-sequence 2

#include<stdio.h>

#include<conio.h>

#include<stdlib.h>

#include<string.h>

char a[10],b[10];

int count[10][10],dir[10][10];

void backtrack(int i, int j)

{

if(i!=0 && j!=0)

  {

if(dir[i][j] == 3)

    {

backtrack(i-1,j-1);

printf("%c",a[i-1]);        

    }     

else if(dir[i][j] == 2)

backtrack(i-1,j);

else

backtrack(i,j-1);

  }  

}

int main()

{

                int i,j,k,count1,count2;

                printf("\n Enter 1st string : ");

gets(a);

fflush(stdin);

printf("\n Enter 2nd string : ");

gets(b);

                count1 = strlen(a);

    count2 = strlen(b);

                for(i=1;i<=count1;i++)

                count[i][0]=0;

                for(i=1;i<=count2;i++)

                count[0][i]=0;

                for(i=1;i<=count1;i++)

                {

                                for(j=1;j<=count2;j++)

                                {

                                                if(a[i-1]==b[j-1])

                                                {

                                                                count[i][j]=count[i-1][j-1]+1;

                                                                dir[i][j]=3;

                                                }

                                                else if(count[i][j-1]>=count[i-1][j])

                                                {

                                                                count[i][j]=count[i][j-1];

                                                                dir[i][j]=1;

                                                }

                                                else

                                                {

                                                                count[i][j]=count[i-1][j];

                                                                dir[i][j]=2;

                                                }

                                }

                }

                char temp;

                i=0;

                while(i<count2)

                {

                printf("%c\t",b[i]);

                i++;

    }

                printf("\n");

for(i=1;i<=count1;i++)

                {

printf("%c",a[i-1]);

                                for(j=1;j<=count2;j++)

                                {

                                                if(dir[i][j]==1)

                                                temp='-';

                                                else if(dir[i][j]==2)

                                                temp='|';

                                                else if(dir[i][j]==3)

                                                temp='\\';

                                                printf("%c%d\t",temp,count[i][j]);

                                }

                                printf("\n");

                }             

printf("The LCS is : ");

backtrack(count2,count1);          

getch();

return(0);

}

Longest Common Sub-sequence

#include<stdio.h>
#include<conio.h>
#include<string.h>
#define max 20

int c[max+1][max+1];
char b[max+1][max+1];
char x[max],y[max];
int m,n;

void showLCS(int i,int j)
{
  if(i!=0 && j!=0)
  {
    if(b[i][j] == '\\')
    {
      showLCS(i-1,j-1);    
      printf("%c",x[i-1]);        
    }    

    else if(b[i][j] == '|')
     showLCS(i-1,j);

    else
     showLCS(i,j-1);
  }  
}

int main()
{
 int i,j;  

 printf("\n Enter 1st string : ");
 gets(x);

 printf("\n Enter 2nd string : ");
 gets(y);

 m = strlen(x);
 n = strlen(y);

 for(i=1;i<=m;i++)
 {
  c[i][0] = 0;
  b[i][0] = ' ';
 }

 for(j=0;j<=n;j++)
 {
  c[0][j] = 0;
  b[0][j] = ' ';
 }

 for(i=1;i<=m;i++)
 {
  for(j=1;j<=n;j++)
  {
    if(x[i-1] == y[j-1])
    {
      c[i][j] = c[i-1][j-1]+1;
      b[i][j] = '\\';          
    }


    else
    {
      if(c[i-1][j] >= c[i][j-1])
      {
        c[i][j] = c[i-1][j];
        b[i][j] = '|';
      }

      else
      {
        c[i][j] = c[i][j-1];
        b[i][j] = '_';
      }      
    }
  }
 }

 for(i=0;i<=m;i++)
 {
   printf("\n");
   for(j=0;j<=n;j++)
    printf(" %c%d",b[i][j],c[i][j]);              
 }

 getch();
 printf("\n\n The LCS of both strings : ");
 showLCS(m,n);
 getch();
 return 0;  
}

Strassen's Multiplication

#include<stdio.h>
#include<conio.h>

int main()
{
  int a[2][2],b[2][2],c[2][2],i,j;
  int m1,m2,m3,m4,m5,m6,m7;
  printf("Enter the 4 elements of first matrix: ");
  for(i=0;i<2;i++)
      for(j=0;j<2;j++)
           scanf("%d",&a[i][j]);

  printf("Enter the 4 elements of second matrix: ");
  for(i=0;i<2;i++)
      for(j=0;j<2;j++)
           scanf("%d",&b[i][j]);

  printf("\nThe first matrix is\n");
  for(i=0;i<2;i++){
      printf("\n");
      for(j=0;j<2;j++)
           printf("%d\t",a[i][j]);
  }
  printf("\nThe second matrix is\n");
  for(i=0;i<2;i++){
      printf("\n");
      for(j=0;j<2;j++)
           printf("%d\t",b[i][j]);
  }
  m1= (a[0][0] + a[1][1])*(b[0][0]+b[1][1]);  
  m2= (a[1][0]+a[1][1])*b[0][0];
  m3= a[0][0]*(b[0][1]-b[1][1]);
  m4= a[1][1]*(b[1][0]-b[0][0]);
  m5= (a[0][0]+a[0][1])*b[1][1];
  m6= (a[1][0]-a[0][0])*(b[0][0]+b[0][1]);
  m7= (a[0][1]-a[1][1])*(b[1][0]+b[1][1]);

  c[0][0]=m1+m4-m5+m7;
  c[0][1]=m3+m5;
  c[1][0]=m2+m4;
  c[1][1]=m1-m2+m3+m6;
   printf("\nAfter multiplication using \n");
   for(i=0;i<2;i++){
      printf("\n");
      for(j=0;j<2;j++)
           printf("%d\t",c[i][j]);
   }
   getch();
   return 0;
}

Various Matrix Operations

#include<conio.h>
#include<iostream.h>
#define max 3

class matrix
{
 private :
  int mx[max][max];
  int det;
  int tmx[max][max];
  float imx[max][max];
  int cf[max][max];
  int adj[max][max];
 public :
  void inp_dat();
  int find_mdet(int,int);
  void find_trns(int);
  void pro_dat();
};

int i,j,k;

void matrix :: inp_dat()
{
 for(i=1;i<=max;i++)
 {
  cout<<"\n Enter the elements for Row #"<<i<<" :";
  for(j=1;j<=max;j++)
   cin>>mx[i][j];
 }
 for(i=1;i<=max;i++)
 {
  cout<<"\n Row #"<<i<<" :";
  for(j=1;j<=max;j++)
   cout<<" "<<mx[i][j];
 }
}

void matrix :: find_trns(int choice)
{
 for(int i=1;i<=max;i++)
 {
  cout<<"\n Row #"<<i<<" :";
  for(int j=1;j<=max;j++)
  {
  if(choice == 1)
   {
   tmx[i][j] = mx[j][i];
   cout<<" "<<tmx[i][j];
   }
  else
   {
   adj[i][j] = cf[j][i];
   cout<<" "<<adj[i][j];
   }
  }
 }
}

int matrix :: find_mdet(int r,int c)
{
 int ar[4],res;
 k = 0;
 for(i=1;i<=max;i++)
 {
  for(j=1;j<=max;j++)
  {
   if(i != r && j != c)
   {
    ar[k] = mx[i][j];
    k++;
   }
  }
 }
 res = ar[0]*ar[3]-ar[1]*ar[2];
 return res;
}

void matrix :: pro_dat()
{
 int prod = 1;
 det = 0;
 for(i=1;i<=max;i++)
 {
  det += prod*mx[1][i]*find_mdet(1,i);
  prod *= -1;
 }
 cout<<"\n\n Its Determinant is : "<<det;
 cout<<"\n\n Its Transpose is : \n\n ";
 find_trns(1);
 cout<<"\n\n Its co-factor is : \n";
 for(i=1;i<=max;i++)
 {
  cout<<"\n Row #"<<i<<" :";
  for(j=1;j<=max;j++)
  {
  cf[i][j] = prod*find_mdet(i,j);
  cout<<" "<<cf[i][j];
  prod *= -1;
  }
 }
 cout<<"\n\n Its Adjoint is : \n ";
 find_trns(2);
 if(det == 0)
  cout<<"\n\n It's Inverse doesn't exists as its Determinant is Zero.";
 else
 {
  cout<<"\n\nIts Inverse is : \n";
  for(i=1;i<=max;i++)
  {
   cout<<"\n Row #"<<i<<" :";
   for(j=1;j<=max;j++)
   {
   imx[i][j] = (float) adj[i][j]/det;
   cout<<" "<<imx[i][j];
   }
  }
 }
}

void main()
{
clrscr();
matrix mat;
mat.inp_dat();
mat.pro_dat();
getch();
}