基於C#的排列和組合演算法
using System;
using System.Collections.Generic;
namespace Algorithms
{
public class PermutationAndCombination<T>
{
/// <summary>
/// 交換兩個變數
/// </summary>
/// <param name="a">變數1</param>
/// <param name="b">變數2</param>
public static void Swap(ref T a, ref T b)
{
T temp = a;
a = b;
b = temp;
}
/// <summary>
/// 遞迴演算法求陣列的組合(私有成員)
/// </summary>
/// <param name="list">返回的範型</param>
/// <param name="t">所求陣列</param>
/// <param name="n">輔助變數</param>
/// <param name="m">輔助變數</param>
/// <param name="b">輔助陣列</param>
/// <param name="M">輔助變數M</param>
private static void GetCombination(ref List<T[]> list, T[] t, int n, int m, int[] b, int M)
{
for (int i = n; i >= m; i--)
{
b[m - 1] = i - 1;
if (m > 1)
{
GetCombination(ref list, t, i - 1, m - 1, b, M);
}
else
{
if (list == null)
{
list = new List<T[]>();
}
T[] temp = new T[M];
for (int j = 0; j < b.Length; j++)
{
temp[j] = t[b[j]];
}
list.Add(temp);
}
}
}
/// <summary>
/// 遞迴演算法求排列(私有成員)
/// </summary>
/// <param name="list">返回的列表</param>
/// <param name="t">所求陣列</param>
/// <param name="startIndex">起始標號</param>
/// <param name="endIndex">結束標號</param>
private static void GetPermutation(ref List<T[]> list, T[] t, int startIndex, int endIndex)
{
if (startIndex == endIndex)
{
if (list == null)
{
list = new List<T[]>();
}
T[] temp = new T[t.Length];
t.CopyTo(temp, 0);
list.Add(temp);
}
else
{
for (int i = startIndex; i <= endIndex; i++)
{
Swap(ref t[startIndex], ref t[i]);
GetPermutation(ref list, t, startIndex + 1, endIndex);
Swap(ref t[startIndex], ref t[i]);
}
}
}
/// <summary>
/// 求從起始標號到結束標號的排列,其餘元素不變
/// </summary>
/// <param name="t">所求陣列</param>
/// <param name="startIndex">起始標號</param>
/// <param name="endIndex">結束標號</param>
/// <returns>從起始標號到結束標號排列的範型</returns>
public static List<T[]> GetPermutation(T[] t, int startIndex, int endIndex)
{
if (startIndex < 0 || endIndex > t.Length - 1)
{
return null;
}
List<T[]> list = new List<T[]>();
GetPermutation(ref list, t, startIndex, endIndex);
return list;
}
/// <summary>
/// 返回陣列所有元素的全排列
/// </summary>
/// <param name="t">所求陣列</param>
/// <returns>全排列的範型</returns>
public static List<T[]> GetPermutation(T[] t)
{
return GetPermutation(t, 0, t.Length - 1);
}
/// <summary>
/// 求陣列中n個元素的排列
/// </summary>
/// <param name="t">所求陣列</param>
/// <param name="n">元素個數</param>
/// <returns>陣列中n個元素的排列</returns>
public static List<T[]> GetPermutation(T[] t, int n)
{
if (n > t.Length)
{
return null;
}
List<T[]> list = new List<T[]>();
List<T[]> c = GetCombination(t, n);
for (int i = 0; i < c.Count; i++)
{
List<T[]> l = new List<T[]>();
GetPermutation(ref l, c[i], 0, n - 1);
list.AddRange(l);
}
return list;
}
/// <summary>
/// 求陣列中n個元素的組合
/// </summary>
/// <param name="t">所求陣列</param>
/// <param name="n">元素個數</param>
/// <returns>陣列中n個元素的組合的範型</returns>
public static List<T[]> GetCombination(T[] t, int n)
{
if (t.Length < n)
{
return null;
}
int[] temp = new int[n];
List<T[]> list = new List<T[]>();
GetCombination(ref list, t, t.Length, n, temp, n);
return list;
}
}
public class MainClass
{
static void Main()
{
int[] arr = new int[6];
for (int i = 0; i < arr.Length; i++)
{
arr[i] = i + 1;
}
//求排列
List<int[]> lst_Permutation = Algorithms.PermutationAndCombination<int>.GetPermutation(arr, 3);
//求組合
List<int[]> lst_Combination = Algorithms.PermutationAndCombination<int>.GetCombination(arr, 3);
Console.WriteLine(lst_Combination.Count );
for (int i = 0; i < lst_Combination.Count ; i++)
{
int[] result = lst_Combination[i];
for (int j = 0; j < result.Length ; j++)
{
Console.Write ("----" + result[j]);
}
Console.WriteLine();
}
Console.ReadKey();
}
}
}