排列与组合

全排列

class Program
{
    private static void Perm(int[] data, int k, ref int count)
    {
        int size = data.Length;
        if (k == size - 1)
        {
            count++;
            Console.WriteLine(string.Join(',', data));
        }
        else
        {
            for (int i = k; i < size; ++i)
            {
                if (i != k)
                    Swap(ref data[i], ref data[k]);

                Perm(data, k + 1, ref count);

                if (i != k)
                    Swap(ref data[i], ref data[k]);
            }
        }
    }

    private static void Swap(ref int a, ref int b)
    {
        b = Interlocked.Exchange(ref a, b);
    }

    static void Main(string[] args)
    {
        int n;
        string nStr;
        while (true)
        {
            while (true)
            {
                Console.WriteLine("输入一个正整数：");
                nStr = Console.ReadLine();
                if (int.TryParse(nStr, out n))
                {
                    break;
                }
            }

            var data = Enumerable.Range(1, n).ToArray();
            int count = 0;
            Perm(data, 0, ref count);
            Console.WriteLine($"总计{count}种排列方式。");
        }
    }
}

组合

方法1： n个元素里取m个， 相当于先选中一个，然后从剩下的n-1个元素中取m-1个

class Program
{
    public static void Combine(int[] data, int k, int m, int[] indexArr, ref int count)
    {
        int n = data.Length;
        for (int i = (k == m ? n - 1 : indexArr[k] - 1); i >= 0; i--)
        {
            indexArr[k - 1] = i;

            if (k > 1)
            {
                Combine(data, k - 1, m, indexArr, ref count);
            }
            else
            {
                count++;
                Console.WriteLine(string.Join(",", indexArr.Select(c => data[c])));
            }
        }
    }

    static void Main(string[] args)
    {
        int n = 0, m = 0;
        string nStr, mStr;
        while (true)
        {
            while (true)
            {
                Console.WriteLine("输入n：");
                nStr = Console.ReadLine();
                Console.WriteLine("输入m：");
                mStr = Console.ReadLine();

                if (int.TryParse(nStr, out n) && int.TryParse(mStr, out m) && m > 0 && n >= m)
                {
                    break;
                }
            }

            var data = Enumerable.Range(1, n).ToArray();
            int count = 0;
            var indexArr = new int[m];
            Combine(data, m, m, indexArr, ref count);
            Console.WriteLine($"从{n}个元素中取{m}个元素，总计{count}种组合方式。");
        }
    }
}

方法2：选择第一个，选择第二个，直到选够m个

class Program
{
    public static void Combine2(int[] data, int k, int m, List<int> indexList, ref int count)
    {
        int selected = indexList.Count;
        int n = data.Length;

        if (selected == m)
        {
            count++;
            Console.WriteLine(string.Join(",", indexList.Select(c => data[c])));
        }
        else
        {
            //选一个， 剩余的元素需要足够选出m个。
            for (int i = k; i < n - m + selected + 1; i++)
            {
                indexList.Add(i);

                Combine2(data, i + 1, m, indexList, ref count);

                indexList.RemoveAt(indexList.Count - 1);
            }
        }
    }

    static void Main(string[] args)
    {
        int n = 0, m = 0;
        string nStr, mStr;
        while (true)
        {
            while (true)
            {
                Console.WriteLine("输入n：");
                nStr = Console.ReadLine();
                Console.WriteLine("输入m：");
                mStr = Console.ReadLine();

                if (int.TryParse(nStr, out n) && int.TryParse(mStr, out m) && m > 0 && n >= m)
                {
                    break;
                }
            }

            var data = new int[n];
            for (int i = 0; i < n; i++)
            {
                data[i] = i + 1;
            }
            int count = 0;
            var outList = new List<int>();
            Combine2(data, 0, m, outList, ref count);
            Console.WriteLine($"从{n}个元素中取{m}个元素，总计{count}种组合方式。");
        }
    }
}