/*
         * Groups binary numbers based on 1's.
         * Stores group in a hashtable associated with a list (bucket) for each group.
         */
        private static ImplicantGroup Group(ImplicantCollection implicants)
        {
            ImplicantGroup group = new ImplicantGroup();

            foreach (Implicant m in implicants)
            {
                int count = GetOneCount(m.Mask);

                if (!group.ContainsKey(count))
                {
                    group.Add(count, new ImplicantCollection());
                }

                group[count].Add(m);
            }

            return(group);
        }
        /*
         * Simplifies a givenset of implicants.
         */
        private static bool Simplify(ref ImplicantCollection implicants)
        {
            /*
             * Group by number of 1's and determine relationships by comparing.
             */
            ImplicantGroup group = Group(implicants);
            ImplicantRelationshipCollection relationships = new ImplicantRelationshipCollection();

            for (int i = 0; i < group.Keys.Count; i++)
            {
                if (i == (group.Keys.Count - 1))
                {
                    break;
                }

                ImplicantCollection thisGroup = group[group.Keys.ElementAt(i)];
                ImplicantCollection nextGroup = group[group.Keys.ElementAt(i + 1)];

                foreach (Implicant a in thisGroup)
                {
                    foreach (Implicant b in nextGroup)
                    {
                        if (GetDifferences(a.Mask, b.Mask) == 1)
                        {
                            relationships.Add(new ImplicantRelationship(a, b));
                        }
                    }
                }
            }

            /*
             * For each relationship, find the affected minterms and remove them.
             * Then add a new implicant which simplifies the affected minterms.
             */
            foreach (ImplicantRelationship r in relationships)
            {
                ImplicantCollection rmList = new ImplicantCollection();

                foreach (Implicant m in implicants)
                {
                    if (r.a.Equals(m) || r.b.Equals(m))
                    {
                        rmList.Add(m);
                    }
                }

                foreach (Implicant m in rmList)
                {
                    implicants.Remove(m);
                }

                Implicant newImplicant = new Implicant();
                newImplicant.Mask = GetMask(r.a.Mask, r.b.Mask);
                newImplicant.Minterms.AddRange(r.a.Minterms);
                newImplicant.Minterms.AddRange(r.b.Minterms);

                bool exist = false;
                foreach (Implicant m in implicants)
                {
                    if (m.Mask == newImplicant.Mask)
                    {
                        exist = true;
                    }
                }

                if (!exist) //Why am I getting dupes?
                {
                    implicants.Add(newImplicant);
                }
            }

            //Return true if simplification occurred, false otherwise.
            return(!(relationships.Count == 0));
        }