!!!アルゴリズム C# 漸化式
{{category アルゴリズム}}
{{amazon 4774193739}}

!!コード
 class Combination
 {
     /// <summary>
     /// 漸化式　(nCr) の計算
     /// </summary>
     /// <param name="n"></param>
     /// <param name="r"></param>
     /// <returns></returns>
     public static long Combi(int n, int r)
     {
         long p = 1;
 
         for (int i = 1; i <= r; i++)
         {
             p = p * (n - i + 1) / i;
         }
         return p;
     }
     public static void SampleCombi()
     {
         for (int n = 0; n <= 5; n++)
         {
             for (int r = 0; r <= n; r++)
             {
                 Console.Write($"{n}C{r} = {Combi(n, r)}  ");
             }
             Console.Write("\n");
         }
     }
 
     /// <summary>
     /// Hornerの方法
     /// </summary>
     /// <param name="x"></param>
     /// <param name="a"></param>
     /// <param name="n"></param>
     /// <returns></returns>
     public static double Horner(double x, double[] a, int n)
     {
         double p = a[n];
         for (int i=n-1; i>=0; i--)
         {
             p = p * x + a[i];
         }
         return p;
     }
     public static void SampleHorner()
     {
         double[] a = { 1, 2, 3, 4, 5 };
         for(double x=1; x<=5; x++)
         {
             Console.WriteLine($"fn({x:#0.000}) = {Horner(x,a,4):#0.000}");
         }
     }
 }
!!結果
 0C0 = 1
 1C0 = 1  1C1 = 1
 2C0 = 1  2C1 = 2  2C2 = 1
 3C0 = 1  3C1 = 3  3C2 = 3  3C3 = 1
 4C0 = 1  4C1 = 4  4C2 = 6  4C3 = 4  4C4 = 1
 5C0 = 1  5C1 = 5  5C2 = 10  5C3 = 10  5C4 = 5  5C5 = 1
 
 fn(1.000) = 15.000
 fn(2.000) = 129.000
 fn(3.000) = 547.000
 fn(4.000) = 1593.000
 fn(5.000) = 3711.000