Çó¾ØÕóµÄÖÈ

#include <stdio.h>

/*  Matrix Ranker V1.2
 *
 *  This c program will get a matrix of mXn from user as input
 *  and will output the ranked version of the matrix.
 *
 * Created by Eithan Shavit, Nov 2007                            */


void get_matrix (double **M,int m, int n);
void print_matrix (double **M,int m, int n);
int make_lead (double **M,int Srow,int Scol,int m,int n);
void swap_rows (double **M,int x,int y);
void zero_col (double **M,int LeadRow,int Scol,int m,int n);


// gets matrix values from user
void get_matrix (double **M,int m, int n)
{
 int i,j;
 for (i=0;i<m;i++)
 {
  printf ("Enter Values for row no. %d (divided by enter):\n",i+1);
  for (j=0;j<n;j++) scanf ("%lf",&M[i][j]);
 }
}


//


const double eps=0.00001;

// prints matrix of mXn
void print_matrix (double **M,int m, int n)
{
 int i,j,temp;
 for (i=0;i<m;i++) //go over columns
 {
  for (j=0;j<n;j++)  //go over rows
  {
   temp = (int) M[i][j];
   if (((M[i][j]-temp)<eps) && ((M[i][j]-temp)>-eps)) printf 

("%8d",temp); //zeros workaround
   else printf ("%8.2lf",M[i][j]);
  }
  printf ("\n");
 }
}

// makes Srow to be a lead row. if not suitable because of zeros,
// row will be swapped with another.
// returns 0 if starting column is all 0, 1 o.w.
int make_lead (double **M,int Srow,int Scol,int m,int n)
{
 int initial,flag=0;
 double alpha=0;
 initial = Srow;
 while ( (flag==0) && (Srow<=(m-1)))
 {
  if (M[Srow][Scol]<-eps || M[Srow][Scol]>eps) // if cell not zero (using zero 

div workaround)
  {
   // divide row by alpha
   alpha=M[Srow][Scol];
   for (Scol;Scol<=(n-1);Scol++)
   {
    M[Srow][Scol] = (M[Srow][Scol] / alpha);
   }
   swap_rows (M,Srow,initial); //if there was row starting with zeros, it 

will be swapped here eventually
   flag=1;

  }
  Srow++;
 }
 return flag;
}

// swaps 2 rows of the matrix
void swap_rows (double **M,int x,int y)
{
 double *temp;
 temp=M[x];
 M[x]=M[y];
 M[y]=temp;
}



// adds and subtracts values from nearby rows
// in order to create a zero column under lead row.
void zero_col (double **M,int LeadRow,int Scol,int m,int n)
{
 int i,j;
 double alpha=0;
 for (i=0;i<=(m-1);i++)
 {
  if (i==LeadRow) continue;
  alpha = (0 - M[i][Scol]);
  for (j=Scol;j<=(n-1);j++)
  {
   M[i][j]= (M[i][j] + (alpha * M[LeadRow][j]));
  }
 }

}

// ÅжϵÚxÐÐÊÇ·ñÈ«²¿ÊÇ0

int dcmp(double x)
{
    return (x>eps)-(x<-eps);
}


bool  allZero(double **M,int n,int m,int x)
{
    for(int i=0;i<n;i++)
    {
        if(dcmp(M[x][i])!=0)
        {
              return 0;
        }
    }

    return 1;
}

int  rank(double **M,int m,int n)
{
    int ans=0;
    for(int i=0;i<m;i++)
    {
      if(!allZero(M,m,n,i))
       ans++;
    }

    return ans;
}

int main()
{
 int i,j,n,m,no_zero_col;


 printf ("<< Matrix Ranker >>\n");
 printf ("Enter Matrix's dimensions (m,n), divided by enter:\n");
 scanf("%d\n%d",&m,&n);

 double **M=new double *[m];

 for (i=0;i<m;i++)
 {
       M[i]=new double[n];
 }

 get_matrix (M,m,n); //get matrix from user
 printf ("\nMatrix is :\n");
 print_matrix(M,m,n); //print matrix

 // initiate indexs
 i=0;
 j=0;

 // fire algorithm
 while ((j<=(n-1)) && (i<=(m-1)))
 {
  no_zero_col=0;
  while ((no_zero_col==0) && (j<=(n-1)))
  {
   no_zero_col=make_lead (M,i,j,m,n);
   if (no_zero_col==0) j++;
  }
  if (no_zero_col==0) break;
  zero_col (M,i,j,m,n);
  j++;
  i++;
 }
 printf ("\nRanked Matrix is :\n");
 print_matrix (M,m,n);


    printf("Rank is %d",rank(M,m,n));

 return 0;

}