import java.util.*;

public class PizzaUtilities {
    public static Set availableToppings = new HashSet();
    public static void main(String[] args) {
	availableToppings.add("pepperoni");
	availableToppings.add("sausage");
	availableToppings.add("mushrooms");
	availableToppings.add("green peppers");
	availableToppings.add("pineapple");
	availableToppings.add("anchovies");
	availableToppings.add("hamburger");
	availableToppings.add("extra cheese");
	
	Set people = new HashSet();
	people.add("Fred");
	people.add("Ben");
	people.add("Susan");
	people.add("Beth");
	
	Map map = determinePreferences(people);
	Set toppings = selectRandomToppings();
	Set eaters = determineEaters(map, toppings);
	Set possibleToppings = determineToppings(map);
    }
    
    /**
     * Generates a random set of toppings.
     * 
     * @return Set of random toppings (Strings), where each topping in
     *         availableToppings has a 50% chance of being included.
     */
    public static Set selectRandomToppings(){
    }
    
    /**
     * Given a Set of people, assigns to each person a random set of
     * "preferred" toppings.
     * 
     * @param people - a set of Strings
     * @return Map assigning to each person a random set of toppings
     */
    public static Map determinePreferences(Set people) {
    }
    
    /**
     * Given a potential pizza (a set of toppings), determines which people
     * want to eat it.
     * 
     * @param map -- maps people (Strings) to their preferences (Sets of 
     *               toppings)
     * @param toppings -- set of toppings on a pizza that being offered
     * @return Set of persons who want to eat this pizza.  (For a person to be 
     *         included, every item in "toppings" must also be on that person's
     *         set of preferences.)
     */
    public static Set determineEaters(Map map, Set toppings){
    }
    
    /**
     * Given a map of people and their toppings preferences, determines a pizza
     * (a set of toppings) such that everyone is willing to eat it.
     * 
     * @param map -- maps people (Strings) to their preferences (Sets of 
     *               toppings).
     * @return a Set of toppings that everyone can eat.  (Any topping in
     *         availableToppings will be included if EVERY person has listed it
     *         as a preference.)
     */
    public static Set determineToppings(Map map){
    }
}