C# 给定池中元素的所有n个分区
我正在尝试编写一个C#算法，该算法给出包含x元素的池中可能的n个分区的列表 为了更清楚，假设我有6个元素：1,2,3,4,5,6（x=6） 我应该给出3个数字的所有分区，即：C# 给定池中元素的所有n个分区,c#,algorithm,linq,list,partitioning,C#,Algorithm,Linq,List,Partitioning,我正在尝试编写一个C#算法，该算法给出包含x元素的池中可能的n个分区的列表 为了更清楚，假设我有6个元素：1,2,3,4,5,6（x=6） 我应该给出3个数字的所有分区，即： 1,2,3 and 4,5,6 1,3,4 and 2,5,6 1,2,5 and 3,4,6 1,2,6 and 3,4,5 etc. 我的目标函数如下所示： List<List<List<int>>> GetAllPartitions(int x, int n) 列出GetAll
1,2,3 and 4,5,6
1,3,4 and 2,5,6
1,2,5 and 3,4,6
1,2,6 and 3,4,5
etc.
List<List<List<int>>> GetAllPartitions(int x, int n)
列出GetAllPartitions（intx，intn）
公共静态IEnumerable组合（此IEnumerable元素，int k）
{
返回k==0
？新建[]{new T[0]}
：elements.SelectMany（（e，i）=>
元素.跳过（i+1）.组合（k-1）.选择（c=>（new[]{e}）.Concat（c））；
}
var result = from allResults select result where result.length = n || result.length = x-n
/// <summary>
/// A enumeration of all possible partitions of a set of items.
/// </summary>
/// <typeparam name="T">The type of the items in the set being partitioned.</typeparam>
public sealed class AllPartitionsEnumerable<T> : IEnumerable<IEnumerable<IEnumerable<T>>>
{
/// <summary></summary>
[DebuggerBrowsable(DebuggerBrowsableState.Collapsed)]
private IEnumerable<T> items;
/// <summary>
/// Creates and initializes an instance of the <see cref="AllPartitionsEnumerable{T}"/> type.
/// </summary>
/// <param name="items">The set of items to be partitioned.</param>
public AllPartitionsEnumerable(IEnumerable<T> items)
: base ()
{
this.items = items;
}
/// <summary>
/// Gets an enumerator to iterate over the partitions in this enumeration.
/// </summary>
/// <returns>An instance of <see cref="IEnumerator{T}"/>.</returns>
public IEnumerator<IEnumerable<IEnumerable<T>>> GetEnumerator()
{
return new AllPartitionsEnumerator<T>(this.items);
}
/// <summary>
/// Gets an enumerator to iterate over the partitions in this enumeration.
/// </summary>
/// <returns>An instance of <see cref="IEnumerator{T}"/>.</returns>
IEnumerator IEnumerable.GetEnumerator()
{
return this.GetEnumerator();
}
}
/// <summary>
/// An enumerator to iterate over the items in an instance of <see cref="AllPartitionsEnumerable{T}"/>.
/// </summary>
/// <typeparam name="T">The type of the items in the set being partitioned.</typeparam>
public sealed class AllPartitionsEnumerator<T> : IEnumerator<IEnumerable<IEnumerable<T>>>
{
/// <summary>The original set of items over which partitions are created.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private T[] items;
/// <summary>Flag to indicate if this enumerator has been disposed of.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private bool isDisposed;
/// <summary>Flag to indicate if this enumerator is in its initial state.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private bool isFirst;
/// <summary>The number of partitions in the current selection.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private int nc;
/// <summary>An array of values indicating the number of values in the partition at the specified index.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private int[] p;
/// <summary>An array of indices indicating to which partition the item at the specified index belongs.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private int[] q;
/// <summary>The current partition.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private T[][] current;
/// <summary>
/// Creates and initializes an instance of the <see cref="AllPartitionsEnumerator{T}"/> type.
/// </summary>
/// <param name="items">The original set of items over which partitions are enumerated.</param>
public AllPartitionsEnumerator(IEnumerable<T> items)
: base()
{
if (null == items)
{
throw new ArgumentNullException("items");
}
this.isFirst = true;
this.items = items.ToArray();
this.nc = 0;
this.p = new int[this.items.Length];
this.q = new int[this.items.Length];
this.current = null;
}
/// <summary>
/// Gets the current partition.
/// </summary>
public IEnumerable<IEnumerable<T>> Current
{
get
{
this.CheckIfDisposed();
return this.current;
}
}
/// <summary>
/// Disposes of this enumerator and releases all resources held by it.
/// </summary>
public void Dispose()
{
if (this.isDisposed)
{
return;
}
this.isDisposed = true;
this.items = null;
this.p = null;
this.q = null;
this.nc = 0;
this.current = null;
this.isFirst = true;
}
/// <summary>
/// Gets the current partition.
/// </summary>
object IEnumerator.Current
{
get
{
return this.Current;
}
}
/// <summary>
/// Selects the next item in the set of all partitions.
/// </summary>
/// <returns><c>true</c> if an item was selected; <c>false</c> if we are past the last element.</returns>
public bool MoveNext()
{
this.CheckIfDisposed();
if (this.isFirst)
{
this.isFirst = false;
this.nc = 1;
this.p[0] = this.items.Length;
for (int i = 0; i < this.items.Length; ++i)
{
this.q[i] = this.nc;
}
this.Select();
return true;
}
if (this.nc == this.items.Length )
{
return false;
}
int n = this.items.Length;
int m = n;
int l = this.q[m-1];
while (this.p[l - 1] == 1)
{
this.q[m - 1] = 1;
--m;
l = this.q[m - 1];
}
this.nc += m - n;
this.p[0] = this.p[0] + n - m;
if (l == this.nc)
{
++this.nc;
this.p[this.nc - 1] = 0;
}
this.q[m - 1] = l + 1;
this.p[l - 1] = this.p[l - 1] - 1;
this.p[l] = this.p[l] + 1;
this.Select();
return true;
}
/// <summary>
/// Resets this enumerator to its initial state.
/// </summary>
public void Reset()
{
this.CheckIfDisposed();
this.current = null;
this.isFirst = true;
this.isDisposed = false;
this.p = new int[this.items.Length];
this.q = new int[this.items.Length];
this.nc = 0;
}
/// <summary>
/// Selects the items for the current partition.
/// </summary>
private void Select()
{
this.current = new T[this.nc][];
for (int i = 0; i < this.nc; ++i)
{
int k = 0;
this.current[i] = new T[this.p[i]];
for (int j = 0; j < this.items.Length; ++j)
{
if (this.q[j] == i + 1)
{
this.current[i][k] = this.items[j];
++k;
}
}
}
}
/// <summary>
/// Checks and throws an exception if this enumerator has been disposed.
/// </summary>
private void CheckIfDisposed()
{
if (this.isDisposed)
{
throw new ObjectDisposedException(this.GetType().FullName);
}
}
}
/// <summary>
/// Retrieves all possible partitions of a set of items.
/// </summary>
/// <typeparam name="T">The type of the items in the original set.</typeparam>
/// <param name="items">The original set of items over which partitions are created.</param>
/// <returns>All possible partitions of the items in <paramref name="items"/>.</returns>
public static IEnumerable<IEnumerable<IEnumerable<T>>> AllPartitions<T>(this IEnumerable<T> items)
{
return new AllPartitionsEnumerable<T>(items);
}
//
///一组项目的所有可能分区的枚举。
///
///正在分区的集合中的项的类型。
公共密封类AllPartitionsEnumerable:IEnumerable
{
///
[DebuggerBrowsable（DebuggerBrowsableState.Collapsed）]
私人物品；
///
///创建并初始化类型的实例。
///
///要分区的项集。
public AllPartitionsEnumerable（IEnumerable项）
：base（）
{
这个项目=项目；
}
///
///获取枚举数以在此枚举中的分区上迭代。
///
///一个例子。
公共IEnumerator GetEnumerator（）
{
返回新的AllPartitionsEnumerator（this.items）；
}
///
///获取枚举数以在此枚举中的分区上迭代。
///
///一个例子。
IEnumerator IEnumerable.GetEnumerator（）
{
返回此.GetEnumerator（）；
}
}
///
///在的实例中迭代项的枚举数。
///
///正在分区的集合中的项的类型。
公共密封类AllPartitionsEnumerator:IEnumerator
{
///在其上创建分区的原始项集。
[DebuggerBrowsable（DebuggerBrowsableState.Never）]
私人物品；
///指示此枚举数是否已被释放的标志。
[DebuggerBrowsable（DebuggerBrowsableState.Never）]
私人住宅被出售；
///指示此枚举数是否处于其初始状态的标志。
[DebuggerBrowsable（DebuggerBrowsableState.Never）]
私有布尔是第一位的；
///当前选择中的分区数。
[DebuggerBrowsable（DebuggerBrowsableState.Never）]
私人内特北卡罗来纳州；
///一个值数组，指示分区中指定索引处的值数。
[DebuggerBrowsable（DebuggerBrowsableState.Never）]
私有int[]p；
///索引数组，指示指定索引处的项属于哪个分区。
[DebuggerBrowsable（DebuggerBrowsableState.Never）]
私有int[]q；
///当前分区。
[DebuggerBrowsable（DebuggerBrowsableState.Never）]
私人T[][]电流；
///
///创建并初始化类型的实例。
///
///枚举分区的原始项集。
public AllPartitionsEnumerator（IEnumerable项）
：base（）
{
if（null==项）
{
抛出新的异常（“项目”）；
}
this.isFirst=true；
this.items=items.ToArray（）；
这是0.nc=0；
this.p=newint[this.items.Length]；
this.q=newint[this.items.Length]；
this.current=null；
}
///
///获取当前分区。
///
公共可数电流
{
得到
{
这个。CheckIfDisposed（）；
返回此.current；
}
}
///
///处置此枚举数并释放其持有的所有资源。
///
公共空间处置（）
{
如果（此.isDisposed）
{
返回；
}
this.isDisposed=true；
this.items=null；
这个.p=null；
这个。q=null；
这是0.nc=0；
this.current=null；
this.isFirst=true；
}
///
///获取当前分区。
///
对象IEnumerator.Current
{
得到
{
返回此.Current；
}
}
///
///选择所有分区集中的下一项。
///
///如果选择了项目，则为true；如果超过最后一个元素，则为false。
公共图书馆
{
这个。CheckIfDisposed（）；
if（this.isFirst）
{
this.isFirst=false；
这1.nc=1；
this.p[0]=this.items.Length；
对于（int i=0；i/// <summary>
/// A enumeration of all possible partitions of a set of items.
/// </summary>
/// <typeparam name="T">The type of the items in the set being partitioned.</typeparam>
public sealed class AllPartitionsEnumerable<T> : IEnumerable<IEnumerable<IEnumerable<T>>>
{
/// <summary></summary>
[DebuggerBrowsable(DebuggerBrowsableState.Collapsed)]
private IEnumerable<T> items;
/// <summary>
/// Creates and initializes an instance of the <see cref="AllPartitionsEnumerable{T}"/> type.
/// </summary>
/// <param name="items">The set of items to be partitioned.</param>
public AllPartitionsEnumerable(IEnumerable<T> items)
: base ()
{
this.items = items;
}
/// <summary>
/// Gets an enumerator to iterate over the partitions in this enumeration.
/// </summary>
/// <returns>An instance of <see cref="IEnumerator{T}"/>.</returns>
public IEnumerator<IEnumerable<IEnumerable<T>>> GetEnumerator()
{
return new AllPartitionsEnumerator<T>(this.items);
}
/// <summary>
/// Gets an enumerator to iterate over the partitions in this enumeration.
/// </summary>
/// <returns>An instance of <see cref="IEnumerator{T}"/>.</returns>
IEnumerator IEnumerable.GetEnumerator()
{
return this.GetEnumerator();
}
}
/// <summary>
/// An enumerator to iterate over the items in an instance of <see cref="AllPartitionsEnumerable{T}"/>.
/// </summary>
/// <typeparam name="T">The type of the items in the set being partitioned.</typeparam>
public sealed class AllPartitionsEnumerator<T> : IEnumerator<IEnumerable<IEnumerable<T>>>
{
/// <summary>The original set of items over which partitions are created.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private T[] items;
/// <summary>Flag to indicate if this enumerator has been disposed of.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private bool isDisposed;
/// <summary>Flag to indicate if this enumerator is in its initial state.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private bool isFirst;
/// <summary>The number of partitions in the current selection.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private int nc;
/// <summary>An array of values indicating the number of values in the partition at the specified index.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private int[] p;
/// <summary>An array of indices indicating to which partition the item at the specified index belongs.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private int[] q;
/// <summary>The current partition.</summary>
[DebuggerBrowsable(DebuggerBrowsableState.Never)]
private T[][] current;
/// <summary>
/// Creates and initializes an instance of the <see cref="AllPartitionsEnumerator{T}"/> type.
/// </summary>
/// <param name="items">The original set of items over which partitions are enumerated.</param>
public AllPartitionsEnumerator(IEnumerable<T> items)
: base()
{
if (null == items)
{
throw new ArgumentNullException("items");
}
this.isFirst = true;
this.items = items.ToArray();
this.nc = 0;
this.p = new int[this.items.Length];
this.q = new int[this.items.Length];
this.current = null;
}
/// <summary>
/// Gets the current partition.
/// </summary>
public IEnumerable<IEnumerable<T>> Current
{
get
{
this.CheckIfDisposed();
return this.current;
}
}
/// <summary>
/// Disposes of this enumerator and releases all resources held by it.
/// </summary>
public void Dispose()
{
if (this.isDisposed)
{
return;
}
this.isDisposed = true;
this.items = null;
this.p = null;
this.q = null;
this.nc = 0;
this.current = null;
this.isFirst = true;
}
/// <summary>
/// Gets the current partition.
/// </summary>
object IEnumerator.Current
{
get
{
return this.Current;
}
}
/// <summary>
/// Selects the next item in the set of all partitions.
/// </summary>
/// <returns><c>true</c> if an item was selected; <c>false</c> if we are past the last element.</returns>
public bool MoveNext()
{
this.CheckIfDisposed();
if (this.isFirst)
{
this.isFirst = false;
this.nc = 1;
this.p[0] = this.items.Length;
for (int i = 0; i < this.items.Length; ++i)
{
this.q[i] = this.nc;
}
this.Select();
return true;
}
if (this.nc == this.items.Length )
{
return false;
}
int n = this.items.Length;
int m = n;
int l = this.q[m-1];
while (this.p[l - 1] == 1)
{
this.q[m - 1] = 1;
--m;
l = this.q[m - 1];
}
this.nc += m - n;
this.p[0] = this.p[0] + n - m;
if (l == this.nc)
{
++this.nc;
this.p[this.nc - 1] = 0;
}
this.q[m - 1] = l + 1;
this.p[l - 1] = this.p[l - 1] - 1;
this.p[l] = this.p[l] + 1;
this.Select();
return true;
}
/// <summary>
/// Resets this enumerator to its initial state.
/// </summary>
public void Reset()
{
this.CheckIfDisposed();
this.current = null;
this.isFirst = true;
this.isDisposed = false;
this.p = new int[this.items.Length];
this.q = new int[this.items.Length];
this.nc = 0;
}
/// <summary>
/// Selects the items for the current partition.
/// </summary>
private void Select()
{
this.current = new T[this.nc][];
for (int i = 0; i < this.nc; ++i)
{
int k = 0;
this.current[i] = new T[this.p[i]];
for (int j = 0; j < this.items.Length; ++j)
{
if (this.q[j] == i + 1)
{
this.current[i][k] = this.items[j];
++k;
}
}
}
}
/// <summary>
/// Checks and throws an exception if this enumerator has been disposed.
/// </summary>
private void CheckIfDisposed()
{
if (this.isDisposed)
{
throw new ObjectDisposedException(this.GetType().FullName);
}
}
}
/// <summary>
/// Retrieves all possible partitions of a set of items.
/// </summary>
/// <typeparam name="T">The type of the items in the original set.</typeparam>
/// <param name="items">The original set of items over which partitions are created.</param>
/// <returns>All possible partitions of the items in <paramref name="items"/>.</returns>
public static IEnumerable<IEnumerable<IEnumerable<T>>> AllPartitions<T>(this IEnumerable<T> items)
{
return new AllPartitionsEnumerable<T>(items);
}