Question

Write a program (in C or in any other language) that prints the first 64 rows of the Pascal triangle modulo 2. Specifically, the entry in row n and column k of the printout should be 0 if (_k^n) is even, and 1 otherwise. Submit both the program and the printout it produces.

Answer 1

The following C code gives you the required functionality:

#include <stdio.h>
void printPascal(int n);
int main()
{
int n = 64;
printPascal(n);
return 0;
}//end of main function

void printPascal(int n)
{
int i,j;
for(i=0;i<n;i++)
{
for(j=0;j<=i;j++)
printf("%d ",bin_coef(i,j));
printf("\n");
}
}//end of printPascal function

int bin_coef(int n, int k)
{
long long int res = 1,i;
if(k>(n-k))
k = n-k;
for(i=0;i<k;i++)
{
res = (res * (n-i))%2;
res = res / (i+1);
}
return res%2;
}//end of bin_coef function

Output:

Hope it helps, feels free to comment in case of any query.