C code to generate the largest pascal's triangle on the screen

pascal_triangle.cpp

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

#ifndef LINUX
#define LINUX
#endif

/* uncomment the following line if you get compilation errors */
//#undef LINUX

#ifdef LINUX
#include <sys/ioctl.h>
#include <fcntl.h>
#endif


int main()
{
	unsigned long t, Nth_row, total_rows, r, midx, max_num_len;
	long i;
	char spacing[20];
#ifdef LINUX
	struct winsize terminal_screen;
#endif


	printf("\n===============================================================================");
	printf("\n                               Pascal's Triangle                               ");
	printf("\n===============================================================================");
	printf("\n--------------------------------------   --------------------------------------");
	printf("\n        Number of Rows of the triangle|:|");
	scanf("%lu", &total_rows);
	printf("--------------------------------------   --------------------------------------\n");
	printf("Length of the Maximum number generated|:|");
	scanf("%lu", &max_num_len);
	printf("--------------------------------------   --------------------------------------\n");

#ifdef LINUX
	/* get the maximum size of the screen */
	if (ioctl(open("/dev/tty", O_NONBLOCK), TIOCGWINSZ, &terminal_screen) < 0)
    {
		/* If an error occurred while taking the terminal screen size
		   then read it manually from the user */
#endif
		printf("               Enter mid point of line|:|");
		scanf("%lu", &midx);
		printf("--------------------------------------   --------------------------------------\n");
#ifdef LINUX
    }
	else
		/* if successfull then set midx */
		midx = terminal_screen.ws_col / 2;
#endif


	/* setting the spacing.
	   it will actually work like "%Nlu" while displaying a number
	   where N is the part of print format of printf */
	sprintf(spacing, "%%%lulu", max_num_len + max_num_len);


	/* The main algorithm:

	   An arbitrary row can be represented as:-

	   C(n,0)   C(n, 1)   C(n,2) ...   C(n, n-1)   C(n, n)

	   where,
	   n            = Row number
	   C(n, r)      = factorial(n) / (factorial(n-r) * factorial(r))
	   factorial(n) = 1 x 2 x 3 x 4 ... x (n-1) x n

	   Now, to generate T(r) term of the row we have to know the previous term.
	   Since, we already know the first term will always be 1 by calclating
	   C(n, 0) so we need to work out on a formula to calculate the next term
	   given we already know the row number.

	   T(r)     =   C(n, r)    ,   r > 0
	   T(r-1)   =   C(n, r-1)

	   T(r)         C(n, r)
	   --------  =  -----------
	   T(r-1)       C(n, r-1)

	   Doing the necessary calculations and simplifying the equation we get,

	   T(r) = T(r-1) * (n - r + 1) / r

	   We already know 'n' which the row number and 'r' is itself dependant upon
	   'n'. T(r-1) will firstly be 1 and will change as the loop progresses.

	   Analogy of the theory and the program:
	   T(r) = t = T(r-1)
	   n    = Nth_row
	   r    = r
	*/
	for (Nth_row = 0; Nth_row < total_rows; Nth_row++)
    {
		/* Print preceding spaces of a row.
		   Number of spaces decreases as the Nth_row increases */
		for (i = midx - max_num_len * (Nth_row + 1); i > 0; --i)
			printf(" ");

		/* Every row always begins with a one */
		printf(spacing, t = 1);

		/* Print other numbers(if any) */
		for (r = 1; r <= Nth_row; r++)
			/* The formula to generate the next number */
			printf(spacing, t = t * (Nth_row - r + 1) / r);

		/* Always move to next line when a whole row is printed */
		printf("\n");
    }
	return 0;
}