排列组合的概念
排列：从n个不同元素中取出m（m≤n）个元素，按照一定的顺序排成一列，叫做从n个元素中取出m个元素的一个排列(Arrangement)。
组合：从m个不同的元素中，任取n（n≤m）个元素为一组，叫作从m个不同元素中取出n个元素的一个组合。
排列组合实现代码
上一个项目做的一个水路的路径规划时，用到了排列的数据结构。求任意N个点里M个点的不同顺序的组合个数。
这样求最优路径。下面贴一段不知道哪里找的排列组合的算法。
public class PermutationAndCombination<T>
{
/// <summary>
/// 交换两个变量
/// </summary>
/// <param name="a">变量1</param>
/// <param name="b">变量2</param>
public static void Swap(ref T a, ref T b)
{
T temp = a;
a = b;
b = temp;
}
/// <summary>
/// 递归算法求数组的组合(私有成员)
/// </summary>
/// <param name="list">返回的范型</param>
/// <param name="t">所求数组</param>
/// <param name="n">辅助变量</param>
/// <param name="m">辅助变量</param>
/// <param name="b">辅助数组</param>
/// <param name="M">辅助变量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 - ] = i - ;
if (m > )
{
GetCombination(ref list, t, i - , m - , b, M);
}
else
{
if (list == null)
{
list = new List<T[]>();
}
T[] temp = new T[M];
for (int j = ; j < b.Length; j++)
{
temp[j] = t[b[j]];
}
list.Add(temp);
}
}
}
/// <summary>
/// 递归算法求排列(私有成员)
/// </summary>
/// <param name="list">返回的列表</param>
/// <param name="t">所求数组</param>
/// <param name="startIndex">起始标号</param>
/// <param name="endIndex">结束标号</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, );
list.Add(temp);
}
else
{
for (int i = startIndex; i <= endIndex; i++)
{
Swap(ref t[startIndex], ref t[i]);
GetPermutation(ref list, t, startIndex + , endIndex);
Swap(ref t[startIndex], ref t[i]);
}
}
}
/// <summary>
/// 求从起始标号到结束标号的排列，其余元素不变
/// </summary>
/// <param name="t">所求数组</param>
/// <param name="startIndex">起始标号</param>
/// <param name="endIndex">结束标号</param>
/// <returns>从起始标号到结束标号排列的范型</returns>
public static List<T[]> GetPermutation(T[] t, int startIndex, int endIndex)
{
if (startIndex < || endIndex > t.Length - )
{
return null;
}
List<T[]> list = new List<T[]>();
GetPermutation(ref list, t, startIndex, endIndex);
return list;
}
/// <summary>
/// 返回数组所有元素的全排列
/// </summary>
/// <param name="t">所求数组</param>
/// <returns>全排列的范型</returns>
public static List<T[]> GetPermutation(T[] t)
{
return GetPermutation(t, , t.Length - );
}
/// <summary>
/// 求数组中n个元素的排列
/// </summary>
/// <param name="t">所求数组</param>
/// <param name="n">元素个数</param>
/// <returns>数组中n个元素的排列</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 = ; i < c.Count; i++)
{
List<T[]> l = new List<T[]>();
GetPermutation(ref l, c[i], , n - );
list.AddRange(l);
}
return list;
}
/// <summary>
/// 求数组中n个元素的组合
/// </summary>
/// <param name="t">所求数组</param>
/// <param name="n">元素个数</param>
/// <returns>数组中n个元素的组合的范型</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;
}
}
求组合：求5个数里任意3个数的组合
static void Main(string[] args)
{
int[] IntArr = new int[] { , , , , }; //整型数组
List<int[]> ListCombination = PermutationAndCombination<int>.GetCombination(IntArr, ); //求全部的3-3组合
foreach(int[] arr in ListCombination)
{
foreach(int item in arr)
{
Console.Write(item + " ");
}
Console.WriteLine("");
}
Console.ReadKey();
}
求排列：5个数取3个的任意排列
int[] IntArr = new int[] { , , , , }; //整型数组
List<int[]> ListCombination = PermutationAndCombination<int>.GetPermutation(IntArr, ); //求全部的5取3排列
foreach(int[] arr in ListCombination)
{
foreach(int item in arr)
{
Console.Write(item + " ");
}
Console.WriteLine("");
}