Algorithms

public void AddNumber(int value, int power) // 10^3 = power1, 10^4 = power 2, 10^5 = power 3 etc.
        {
            if (power == 0)
            {
                NumberContainer[0] += value;
                while (NumberContainer[0] >= 1000)
                {
                    NumberContainer[0] -= 1000;
                    AddNumber(1, 1);
                }
            } else if(power < mPower)
            {
                NumberContainer[power] += value;
                while( NumberContainer[power] >= 10)
                {
                    NumberContainer[power] -= 10;
                    AddNumber(1, power + 1);
                }
            }else
            {
                //power too large
            }
        }

        public static NumberControl operator +(NumberControl c1, NumberControl c2)
        {
            //set new maxpower to largest of the two
            int mMaxp = c1.mPower;
            if (c2.mPower > mMaxp) mMaxp = c2.mPower;

            NumberControl nc = new NumberControl(mMaxp);

            for(int i = 0;i < c1.NumberContainer.Count;i++)
            {
                nc.AddNumber(c1.NumberContainer[i], i);
            }

            for (int i = 0; i < c2.NumberContainer.Count; i++)
            {
                nc.AddNumber(c2.NumberContainer[i], i);
            }

            return nc;
        }

Given k sets of integers A1,A2,..,Ak of total size O(n), you should determine whether exist a1A1, a2A2,...,akAk, such that a1+a2+..+ak-1 =ak. Your algorithm should run in Tk(n) time, where Tk(n) = O(n^(k/2)*log n) for even k, and O(n^((k+1)/2)) for odd values of k.