public class Manhattan {

    public static void main (String[] argv)
    {
        // Test case 1: go from (1,1) to (0,0)
	int r = 1, c = 1;
	int n = countPaths (r, c);
	System.out.println ("r=" + r + " c=" + c + " => n=" + n);

        // Test case 2: go from (2,2) to (0,0)
	r = 2;
	c = 2;
	n = countPaths (r, c);
	System.out.println ("r=" + r + " c=" + c + " => n=" + n);

        // Test case 2: go from (5,7) to (0,0)
	r = 5;
	c = 7;
	n = countPaths (r, c);
	System.out.println ("r=" + r + " c=" + c + " => n=" + n);
    }


    static int countPaths (int numRows, int numCols)
    {
	// Bottom out case: there's only one way to (0,0). 
        // Note: it's || and not &&.
	if ( (numRows == 0) || (numCols == 0) ) {
	    return 1;
	}

	// Otherwise, reduce to two sub-problems and add.
        int downCount = countPaths (numRows-1, numCols);
	int rightCount = countPaths (numRows, numCols-1);
	return (downCount + rightCount);
    }
}