//-----------------------------------------------------------------
//	triangle.cpp
//
//	This program displays some upper rows of the famous PASCAL 
//	TRIANGLE of binomial coefficients, where the array-entries
//	bin(n,k) are the values of a recursively-defined function.
//
//	  compile-and-link using: $ g++ triangle.cpp -o triangle
//
//	programmer: ALLAN CRUSE
//	written on: 18 MAR 2007
//-----------------------------------------------------------------

#include <stdio.h>

#define N_MAX	12

int bin( int n, int k )
{
	if (( n < 0 )||( k < 0 )||( k > n )) return 0;
	if (( k == 0 )||( k == n )) return 1;
	return  bin( n-1, k-1 ) + bin( n-1, k );
}


int main( void )
{
	printf( "\n\n  THE PASCAL TRIANGLE  \n" );
	for (int i = 0; i <= N_MAX; i++)
		{
		printf( "\n" );
		for (int j = 0; j <= i; j++)
			printf( " %4d", bin( i, j ) ); 
		}
	printf( "\n\n" );
}