算法有关问题

算法问题
任给1<=n<=20个不同等非零正整数，每个正整数最多使用一次，请问这n个正整数能够加和的结果共有多少种？
这个是我们学校软件技能大赛的题目，大家讨论下啊
用C#写下啊、。。呵呵


[解决办法]

C# code

    static void Main(string[] args)    {        int i = GetCombinationCount(new int[] { 1, 2, 3 });   //i=6    }    static int GetCombinationCount(int[] nums)    {        Dictionary<int, int> sums = new Dictionary<int, int>();        int combinations = 1 << nums.Length;        for (int i = 1; i < combinations; i++)        {            string masks = Convert.ToString(i, 2).PadLeft(nums.Length, '0');            int sum = 0;            for (int j = 0; j < masks.Length; j++)            {                if (masks[j] == '1') sum += nums[j];            }            sums[sum] = 1;        }        return sums.Count;    }}
[解决办法]
这样写可能更能对一些算法派的胃口：
原理简单的说就是n个灯(或n bits)，用或者不用，总的组合等于2^n
C# code
static int GetCombinationCount(int[] nums){    Dictionary<int, int> sums = new Dictionary<int, int>();    int combinations = 1 << nums.Length;    for (int i = 1; i < combinations; i++)    {        int sum = 0, mask = i;        foreach (int n in nums)        {            if (mask == 0) break;            if (mask % 2 == 1) sum += n;            mask >>= 1;        }        sums[sum] = 1;    }    return sums.Count;}
[解决办法]
应该有2的n次方-1种：
C# code
        static void Main(string[] args)        {            int[] a = { 24, 4, 31, 14, 59 };            GetCombination(a);        }        static string GetBinaryString(int n, int length)        {            string result = string.Empty;            int mod = 0;            while (n != 0)            {                mod = n % 2;                n = n / 2;                result = mod.ToString() + result;            }            if (result.Length < length)                result = result.PadLeft(length, '0');            return result;        }        static void GetCombination(int[] nums)        {            double count = Math.Pow(2, nums.Length);            for (int i = 1; i <= count - 1; i++)            {                Console.Write("可能的组合有:");                string str = GetBinaryString(i, nums.Length);                int sum = 0;                for (int j = 0; j < str.Length; j++)                {                    if (str[j] == '1')                    {                        Console.Write(nums[j] + " ");                        sum += nums[j];                    }                }                Console.WriteLine("和为:" + sum);            }        }