數學中排列組合,排列P（N，R）

其實排列實現了，組合也就實現了組合C(N,R)就是P(N,R)/P(R,R) ，比較簡單的是遞迴演算法，但考慮到遞迴的效能，下面採用了2種非遞迴的方法，程式碼如下

using System; using System.Collections.Generic; namespace Test { class Program { static void Main(string[] args) { Console.WriteLine(P1(6, 3)); Console.WriteLine(P2(6, 3)); Console.WriteLine(C(6, 2)); } /// <summary> /// 排列迴圈方法 /// </summary> /// <param name="N"></param> /// <param name="R"></param> /// <returns></returns> static long P1(int N, int R) { if (R > N || R <= 0 || N <= 0 ) throw new ArgumentException("params invalid!"); long t = 1; int i = N; while (i!=N-R) { try { checked { t *= i; } } catch { throw new OverflowException("overflow happens!"); } --i; } return t; } /// <summary> /// 排列堆疊方法 /// </summary> /// <param name="N"></param> /// <param name="R"></param> /// <returns></returns> static long P2(int N, int R) { if (R > N || R <= 0 || N <= 0 ) throw new ArgumentException("arguments invalid!"); Stack<int> s = new Stack<int>(); long iRlt = 1; int t; s.Push(N); while ((t = s.Peek()) != N - R) { try { checked { iRlt *= t; } } catch { throw new OverflowException("overflow happens!"); } s.Pop(); s.Push(t - 1); } return iRlt; } /// <summary> /// 組合 /// </summary> /// <param name="N"></param> /// <param name="R"></param> /// <returns></returns> static long C(int N, int R) { return P1(N, R) / P1(R, R); } } }