Moduli number system

A number system with moduli is defined by a vector of k moduli, [m1,m2, ···,mk].

The moduli must be pairwise co-prime, which means that, for any pair of moduli, the only common factor is 1.

In such a system each number n is represented by a string "-x1--x2-- ... --xk-" of its residues, one for each modulus. The product m1 ... mk must be greater than the given number n which is to be converted in the moduli number system.

For example, if we use the system [2, 3, 5] the number n = 11 is represented by "-1--2--1-",
the number n = 23 by "-1--2--3-". If we use the system [8, 7, 5, 3] the number n = 187 becomes "-3--5--2--1-".

You will be given a number n (n >= 0) and a system S = [m1,m2, ···,mk] and you will return a string "-x1--x2-- ...--xk-" representing the number n in the system S.

If the moduli are not pairwise co-prime or if the product m1 ... mk is not greater than n, return "Not applicable".

Examples:

fromNb2Str(11 [2,3,5]) -> "-1--2--1-"

fromNb2Str(6, [2, 3, 4]) -> "Not applicable", since 2 and 4 are not coprime

fromNb2Str(7, [2, 3]) -> "Not applicable" since 2 * 3 < 7

fromNb2Str 187 [8,7,5,3] -> "-3--5--2--1-" fromNb2Str 6 [2, 3, 4] -> "Not applicable", since 2 and 4 are not coprime fromNb2Str 7 [2, 3] -> "Not applicable", since 2 * 3 < 7

 

public static class Kata
    {
        public static String fromNb2Str(int n, int[] sys)
        {
            string str = "Not applicable";
            bool flag = CoPrimeArray(sys);
            if (flag)
            {
                IEnumerable<int> list = sys.Select(x => n % x);
                int result = sys.Aggregate(1, (sum, y) => sum * y);
                if (result > n)
                {
                    str = string.Join(string.Empty, list.Select(x => string.Format("-{0}-", x)));
                }
            }
            return str;
        }

        public static bool CoPrimeArray(int[] array)
        {
            bool coPrime = false;
            int max = array.Max();
            int sqrt = Convert.ToInt32(Math.Floor(Math.Sqrt(max)));
            bool[] tempArray = new bool[max + 1];
            tempArray = tempArray.Select(x => x = true).ToArray();
            int prime = 2;//质数，从最小的开始
            IEnumerable<int> dividePrime = array.Where(x => x % prime == 0);//获取能够被质数整除的数字的集合
            while (true)
            {
                if (dividePrime.Count() > 1)
                {
                    //这里的判断涉及到了Linq的延迟加载,随着prime的改变，每一次的dividePrime是不同的
                    break;
                }
                //被除数/除数=商
                for (int i = prime; i <= sqrt; i++)
                {
                    for (int j = i; j * i < max; j++)
                    {
                        //j*i这个位置的数据可以被i整除
                        if (tempArray[j * i])
                        {
                            tempArray[j * i] = false;
                        }
                    }
                }
                while (true)
                {
                    prime++;
                    if (prime == max)
                    {
                        //除数已经达到最大值，说明数组里面的所有数字互质
                        coPrime = true;
                        break;
                    }
                    else
                    {
                        if (tempArray[prime])
                        {
                            //说明没有被前面prime个数字整除过,
                            //假如prime是3的话,并且符合的话，说明3没有被2整除过
                            //假如prime是7的话，并且符合的话，说明7没有被2到6的数字整除过
                            break;
                        }
                    }
                }
                if (coPrime)
                {
                    break;
                }
            }
            return coPrime;
        }
    }