//  The first nine rows of Pascal's Triangle
//
//  row 0:                             1
//  row 1:                           1   1
//  row 2:                         1   2   1
//  row 3:                      1   3   3   1
//  row 4:                    1   4   6   4   1
//  row 5:                  1   5  10   10  5   1
//  row 6:                1   6  15  20   15  6   1
//  row 7:              1   7  21  35   35  21  7   1
//  row 8:            1   8  28  56  70  56  28   8   1  


//  Alternative way to visualize it
//
//  row 0:  1
//  row 1:  1   1
//  row 2:  1   2   1
//  row 3:  1   3   3   1
//  row 4:  1   4   6   4   1
//  row 5:  1   5  10  10   5   1
//  row 6:  1   6  15  20  15   6   1
//  row 7:  1   7  21  35  35  21   7   1
//  row 8:  1   8  28  56  70  56  28   8   1  


public class PascalsTriangle
{
	public static void main(String[] args)
	{
		final int DEPTH=9;
		
		// Initialize the Memory for the Triangle
		int[][] P = new int[DEPTH][];
		
		for(int row=0; row < DEPTH; row++)
			P[row] = new int[row+1];
		
		// Fill in the 0-th row
		P[0][0]= 1;
		
		// Fill in the values of the Triangle
		for(int row=1; row<DEPTH; row++)
		{
			P[row][0]=1;   // First entry is always 1
			
			for(int col=1; col<row; col++)
				P[row][col]= P[row-1][col-1] + P[row-1][col];
				 
			P[row][row]=1; // Last  entry is always 1 
		}
			
			
		// Print the Triangle
		for(int row=0; row < DEPTH; row++)
		{
			for(int s=0; s< DEPTH-row; s++)
				System.out.print("  ");

			for(int col=0; col<=row; col++)
				System.out.printf("%2d  ", P[row][col]);

			System.out.println();
		}
	}
}