C#，相遇数（Rencontres Number）的算法与源代码

相遇数（Rencontres Number，partial derangement numbers）是指部分扰动的数量，或与独立对象的r相遇的置换数（即具有固定点的独立对象的置换数）。

看不通。懂的朋友给解释一下哈。

源程序：

using System;

namespace Legalsoft.Truffer.Algorithm
{
	public static partial class Number_Sequence
	{
		private static int Rencontres_Number_Binomial_Coeff(int n, int k)
		{
			if (k == 0 || k == n)
			{
				return 1;
			}
			return Rencontres_Number_Binomial_Coeff(n - 1, k - 1) + Rencontres_Number_Binomial_Coeff(n - 1, k);
		}
		
		public static int Rencontres_Number(int n, int m)
		{
			if (n == 0 && m == 0)
			{
				return 1;
			}
			if (n == 1 && m == 0)
			{
				return 0;
			}
			if (m == 0)
			{
				return (n - 1) * (Rencontres_Number(n - 1, 0) + Rencontres_Number(n - 2, 0));
			}
			return Rencontres_Number_Binomial_Coeff(n, m) * Rencontres_Number(n - m, 0);
		}

		private static int[,] Rencontres_Number_Binomial_Coeff_Second(int n, int k)
		{
			int[,] Coeff = new int[MAX, MAX];
			for (int i = 0; i <= n; i++)
			{
				for (int j = 0; j <= Math.Min(i, k); j++)
				{
					if (j == 0 || j == i)
					{
						Coeff[i, j] = 1;
					}
					else
					{
						Coeff[i, j] = Coeff[i - 1, j - 1] + Coeff[i - 1, j];
					}
				}
			}
			return Coeff;
		}

		public static int Rencontres_Number_Second(int n, int m)
		{
			int[,] Coeff = Rencontres_Number_Binomial_Coeff_Second(n, m);
			int[,] dp = new int[n + 1, m + 1];
			for (int i = 0; i <= n; i++)
			{
				for (int j = 0; j <= m; j++)
				{
					if (j <= i)
					{
						if (i == 0 && j == 0)
						{
							dp[i, j] = 1;
						}
						else if (i == 1 && j == 0)
						{
							dp[i, j] = 0;
						}
						else if (j == 0)
						{
							dp[i, j] = (i - 1) * (dp[i - 1, 0] + dp[i - 2, 0]);
						}
						else
						{
							dp[i, j] = Coeff[i, j] * dp[i - j, 0];
						}
					}
				}
			}
			return dp[n, m];
		}
	}
}

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