// ----------------------------------------------------------------------
// 
//  Module:          pascal.cc
//  Description:     generates Pascal's triangle modulo 2
//                   with blanks representing 0's.
//  Contributed by:  Rene Peralta
//  Date:            2001
//  
// ----------------------------------------------------------------------

#define UNKNOWN -1
#define MAX_SIZE 512

#include <stdlib.h>
#include <stdio.h>
#include <iostream.h>

long num_rows;
long PT[MAX_SIZE][MAX_SIZE];

void init();
long c(long n, long k); // returns the corr. binomial coefficient

int
main( int argc, char *argv[ ] )
{
    cout << "how many rows?" << endl;
    cin >> num_rows;
    init();
    
    for (long n = 0; n < num_rows; n++)
    {
      for (long k = 0; k <= n; k++)
        if (c(n,k) == 1) cout << "1" ;
	 else cout << " " ;
      cout << endl;
    }
}

long c(long n, long k) // returns the corr. binomial coefficient
{
  if (PT[n][k] == UNKNOWN) PT[n][k] = (c(n-1,k-1) + c(n-1,k)) % 2;
  return(PT[n][k]);
}

void init()
{
  for (long n = 0; n < num_rows; n++)
    for (long k = 0; k <= n; k++)
      if ((k==0) || (k==n)) PT[n][k] = 1;
      else  PT[n][k] = UNKNOWN;
}