算法基础系列之一：非递归求和为数值N的所有组合

CSDN上最近常常问到这样上面的问题，例如，求所有和为10的组合(组合中的数皆为自然数，且各不相同)，则输出：

1+2+3+4

1+2+7

1+3+6

1+4+5

1+9

2+3+5

2+8

3+7

4+6

今天又有人问，回来想了想，递归的想起来头疼，写了一个非递归的方法，初步测试似乎没有错误，发上来请大家帮忙改进改进^^，也可帮忙提供一些更好的方法：

        private static int Num = 10;

 

        static void Main(string[] args)

        {

            List<int> l = new List<int>();

            l.Add(0);

            int loopCount = 0;

            int outputCount = 0;

            int lastRemove = 0;

 

            while (true)

            {

                if (Sum(l) < Num)

                {

                    if (lastRemove == 0)

                    {

                        l.Add(l[l.Count - 1] + 1);

                    }

                    else

                    {

                        l.Add(lastRemove + 1);

                        lastRemove = 0;

                    }

                }

 

                if (Sum(l) == Num)

                {

                    Console.WriteLine(Output(l));

                    outputCount++;

                    l.RemoveAt(l.Count - 1);

                    lastRemove = l[l.Count - 1];//

                    l.RemoveAt(l.Count - 1);

                }

 

                if (Sum(l) > Num)

                {

                    l.RemoveAt(l.Count - 1);

                    l.RemoveAt(l.Count - 1);

                    if (Sum(l) > 0)

                    {

                        int x = Num - Sum(l);

                        Console.WriteLine(Output(l) + "+" + x.ToString());

                        outputCount++;

                    }

                    else

                    {

                        break;

                    }

                    lastRemove = l[l.Count - 1];

                    l.RemoveAt(l.Count - 1);

                }

                loopCount++;

            }

 

            Console.WriteLine("loop count:"+loopCount);

            Console.WriteLine("output count:" + outputCount);

            Console.Read();

        }

 

        static int Sum(List<int> l)

        {

            int sum = 0;

            for (int i = 0; i < l.Count; i++)

            {

                sum += l[i];

            }

            return sum;

        }

 

        static string Output(List<int> l)

        {

            string output="";

            for (int i = 1; i < l.Count; i++)

            {

                output += l[i].ToString() + "+";

            }

            return output.Substring(0, output.Length - 1);

        }