本算法是教材中的全排列方法之一，本人仅做封装，在此感谢发现算法和传播算法的大牛们.

    /// <summary>
    /// 全排列算法,算法原理:Perm(n)=[n]*Pern(n-1).N的全排列等于将N个数取一个放在第N个位置后，剩下的N-1个数做全排列。
    /// 这个算法的一个用途是进行行列式的展开和计算，这也是这次封装这个算法的目的。
    /// </summary>
    public class Permulation
    {
        /// <summary>
        /// 排列结果
        /// </summary>
        private List<List<int>> _PermArray { get; set; }
        /// <summary>
        /// 去重用.
        /// </summary>
        private Dictionary<string, List<int>> _NoRepeatArray { get; set; }
        /// <summary>
        /// 要排列的整数数组
        /// </summary>
        private int[] _Numbers { get; set; }
        /// <summary>
        /// 元素个数
        /// </summary>
        private int _N { get; set; }
        /// <summary>
        /// 是否去重.
        /// </summary>
        private bool _RemoveDup { get; set; }
        
        /// <summary>
        /// 全排列计数
        /// </summary>
        public int TotalCount { get; set; }
        /// <summary>
        /// 排列结果
        /// </summary>
        public List<List<int>> PermulationArray
        {
            get
            {
                return _PermArray;
            }
        }
        /// <summary>
        /// 任意给定数字数组进行全排列
        /// </summary>
        /// <param name="Numbers">数组</param>
        /// <param name="RemoveDup">是否去重</param>
        public Permulation(int[] Numbers, bool RemoveDup = false)
        {
            _NoRepeatArray = new Dictionary<string, List<int>>();
            _PermArray = new List<List<int>>();
            TotalCount = 0;
            _Numbers = Numbers;
            _N = Numbers.Count();
            _RemoveDup = RemoveDup;
        }
        /// <summary>
        /// 自然数1-N全排列
        /// </summary>
        /// <param name="N"></param>
        public Permulation(int N)
        {
            _PermArray = new List<List<int>>();
            TotalCount = 0;
            _Numbers = new int[N];
            for (int i = 1; i <= N; i++)
            {
                _Numbers[i - 1] = i;
            }
            _N = N;
        }
        /// <summary>
        /// 交换位置.
        /// </summary>
        /// <param name="Nums"></param>
        /// <param name="i"></param>
        /// <param name="j"></param>
        private void Swap(int[] Nums, int i, int j)
        {
            int theTemp = Nums[i - 1];
            Nums[i - 1] = Nums[j - 1];
            Nums[j - 1] = theTemp;

        }
        /// <summary>
        /// 执行全排列
        /// </summary>
        public void DoCalculation()
        {
            DoArray(1);
        }
        /// <summary>
        /// 递归算法进行全排列.
        /// </summary>
        /// <param name="NextIndex"></param>
        private void DoArray(int NextIndex)
        {
            if (NextIndex > _N)
            {
                var theNums = new List<int>();
                //利用字典本身的字符串哈希算法判重。
                var theSeqStr = "";
                for (int i = 0; i < _N; i++)
                {
                    //注意这里需要分割，防止1 23和12 3之类造成的重复.
                    theSeqStr += "," + _Numbers[i];
                    theNums.Add(_Numbers[i]);
                }
                if (_RemoveDup)
                {
                    if (!_NoRepeatArray.ContainsKey(theSeqStr))
                    {
                        _NoRepeatArray.Add(theSeqStr, theNums);
                        _PermArray.Add(theNums);
                        TotalCount++;
                    }
                }
                else
                {
                    _PermArray.Add(theNums);
                    TotalCount++;
                }

            }
            else
            {
                //与后面的所有位置进行交换，但注意，每次交换完，应复原。
                for (int i = NextIndex; i <= _N; i++)
                {
                    Swap(_Numbers, NextIndex, i);
                    DoArray(NextIndex + 1);
                    //复原
                    Swap(_Numbers, NextIndex, i);
                }
            }
        }

    }

注：本算法只经过简单测试，没经过大批量测试。

算法（全排列算法封装）