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const int N = 2000;
int M[N][N];
// gets matrix values from user
void get_matrix (int M[][N],int m, int n)
{
int i;
int j;
i=0;
while (i<m)
{
j=0;
while (j<n) {
M[i][j] = getint();
j=j+1;
}
i=i+1;
}
}
// prints matrix of mXn
void print_matrix (int M[][N],int m, int n)
{
int i;
int j;
int temp;
i=0;
while (i<m) //go over columns
{
j=0;
while (j<n) //go over rows
{
putint(M[i][j]);
putch(32);
j=j+1;
}
putch(10);
i=i+1;
}
}
// swaps 2 rows of the matrix
void swap_rows (int M[][N],int x,int y,int n)
{
int temp[N];
int i;
i=0;
while (i<n) {
temp[i] = M[x][i];
i=i+1;
}
i=0;
while (i<n) {
M[x][i] = M[y][i];
i=i+1;
}
i=0;
while (i<n) {
M[y][i] = temp[i];
i=i+1;
}
}
// 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 (int M[][N],int Srow,int Scol,int m,int n)
{
int initial;
int flag;
int alpha;
alpha=0;
flag=0;
initial = Srow;
while (flag==0 && Srow<=(m-1))
{
if (M[Srow][Scol]!=0)
{
// divide row by alpha
alpha=M[Srow][Scol];
while (Scol<=(n-1))
{
M[Srow][Scol] = (M[Srow][Scol] / alpha);
Scol = Scol+1;
}
swap_rows (M,Srow,initial,n);
flag=1;
}
Srow = Srow+1;
}
return flag;
}
// adds and subtracts values from nearby rows
// in order to create a zero column under lead row.
void zero_col (int M[][N],int LeadRow,int Scol,int m,int n)
{
int i;
int j;
int alpha;
alpha=0;
i=0;
while (i<=(m-1))
{
if (i==LeadRow) {
i=i+1;
continue;
}
alpha = (0 - M[i][Scol]);
j=Scol;
while (j<=(n-1))
{
M[i][j]= (M[i][j] + (alpha * M[LeadRow][j]));
j=j+1;
}
i=i+1;
}
}
// 判断第x行是否全部是0
int allZero(int M[][N],int n,int m,int x)
{
int i;
i=0;
while(i<n)
{
if((M[x][i])!=0)
{
return 0;
}
i=i+1;
}
return 1;
}
int rank(int M[][N],int m,int n)
{
int ans;
int i;
ans=0;
i=0;
while(i<m)
{
if(!allZero(M,m,n,i)){
ans = ans+1;
}
i=i+1;
}
return ans;
}
int main()
{
int i;
int j;
int n;
int m;
int no_zero_col;
m=getint();
n=getint();
get_matrix (M,m,n); //get matrix from user
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=j+1;
}
}
if (no_zero_col==0) {
break;
}
zero_col (M,i,j,m,n);
j=j+1;
i=i+1;
}
print_matrix (M,m,n);
putint(rank(M,m,n));
return 0;
}
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