public class Recursion
{
    //+sum1
    public static int sum1(int n)
    // post: compute the sum of 0..n
    {
	int result = 0;
	for (int i = 1; i <= n; i++)
	{
	    result = result + i;
	}
	return result;
    }
    //-sum1
    //+sum2
    public static int sum2(int n)
    // post: compute the sum of 0..n
    {
	if (n < 1) return 0;
	else return sum1(n-1) + n;
    }
    //-sum2
    //+sum3
    public static int sum3(int n)
    // post: compute the sum of 0..n
    {
	if (n < 1) return 0;        // base case
	else return sum3(n-1) + n;  // reduction, progress, sol'n
    }
    //-sum3
    //+sum3b
    public static int sum3(int n)
    // post: compute the sum of 0..n
    {
	if (n < 1) return 0;	    // 1
	else return                 // 2
                    sum3(           // 3
			 n-1        // 4
			    ) + n;  // 5
    }
    //-sum3b
}