import java.util.ArrayList;
import java.math.BigInteger;
public class Loopy
{
    public static void main(String[] args)
    {
        //test your stuff here.
    }
    /**
     * produce a table of values for the square function starting
     * at start, ending before end, and whhich increments the x-value
     * by increment. Return this in a string.
     */
    public static String tableOfSquares(double start, double end, double increment)
    {
        return "";
    }
    /**
     * @param roster a list of email names
     * @return an ArrayList of names in the first half of the alphabet, case insensitive
     */
    public static ArrayList<String> firstHalf(ArrayList<String> roster)
    {
        return null;
    }
    /**
     * @param roster a list of email names
     * This has the side-effect of filtering in all elements in the
     * first half of the alphabet, case insensitive.
     */
    public static void firstHalfInPlace(ArrayList<String> roster)
    {
    }
    /**
     * @param n the size of the population
     * @param k the size of the sample
     * @return the number of ordered samples of size k 
     * in the population. This is n(n-1)(n-2).....  (n-k+1).
     */
    public static BigInteger permutations(int n, int k)
    {
        return null;
    }
    /**
     * @param n the size of the population
     * @param k the size of the sample
     * @return the number of ordered samples of size k 
     * in the population. This is 
     * n(n-1)(n-2).....  (n-k+1)/k!.
     * Be smart:  the product  of any k consecutive integers
     * is divisible by k.  You should be able to compute
     * choose(1000000000, 3).  hint: ZIPPER
     */
    public static BigInteger choose(int n, int k)
    {
        return null;
    }
}