数字のユニークなパーティションの検索

Question

私は与えられた番号（N）のパーティションを見つけるために以下のコードを使用しています。ユニークなパーティションだけをどうやって確保できますか？例えば、パーティション（1,1,1,7）、（1,1,7,1）、（1,7,1,1）および（7,1,1,1）は同じものとみなされ、これらを出力する必要があります。

おかげ

よろしく

Dim N = 10 

     For i As Integer = 0 To N 
      For j As Integer = 0 To N 
       For k As Integer = 0 To N 
        For l As Integer = 0 To N 
         If i + j + k + l = N Then 
          Dim St As String = String.Format("({0:d}, {1:d}, {2:d}, {3:d})", i, j, k, l) 
          Console.WriteLine(St) 
         End If 
        Next 
       Next 
      Next 
     Next 

     Console.Read() 

EDIT：以下は誰かの提案から動作しているようです。

Module Module1 

    Sub Main() 

     Console.WriteLine("Please enter an integer.") 
     Dim sReadLine As String = Console.ReadLine() 
     Dim iValue As Integer 

     If IsNumeric(sReadLine) Then 
      iValue = CInt(sReadLine) 
     Else 
      Console.WriteLine("'" & sReadLine & "' is not a numeric value. Press any key to exit.") 
      'Application.Exit() 
      Console.Read() 
      Exit Sub 
      End 
     End If 

     Console.Clear() 
     Console.WriteLine("Number is {0}", iValue) 
     Console.WriteLine("") 

     Partitions1(iValue) 

     Exit Sub 

    End Sub 

    Dim partitions As New List(Of Part) 

    Private Sub Partitions1(N As Integer) 
     For i As Integer = 0 To N 
      For j As Integer = 0 To N 
       For k As Integer = 0 To N 
        For l As Integer = 0 To N 
         If i + j + k + l = N Then 
          Dim thisPartition As New Part() 
          thisPartition.Parts = New Integer() {i, j, k, l} 
          If Not partitions.Contains(thisPartition) Then 
           partitions.Add(thisPartition) 
          End If 
         End If 
        Next 
       Next 
      Next 
     Next 

     For Each x In partitions 
      Dim St = "(" 
      For Each y In x.Parts 
       St = St & y & ", " 
      Next 
      St = Left(St, Len(St) - 2) 
      St = St & ")" 
      Console.WriteLine(St) 
     Next 

     Console.WriteLine("") 
     Console.WriteLine("{0} unique partititons found.", partitions.Count) 
     Console.Read() 

    End Sub 

    Public Class Part 'Sorted array of integer with comparer 
     Implements IEquatable(Of Part) 
     Public Property Parts As Integer() 
      Get 
       Return m_Parts 
      End Get 
      Set(value As Integer()) 
       m_Parts = value 
       Array.Sort(m_Parts) 
      End Set 
     End Property 

     Private m_Parts As Integer() 

     Public Overloads Function Equals(other As Part) As Boolean _ 
      Implements IEquatable(Of Part).Equals 
      If other Is Nothing Then 
       Return False 
      End If 
      If other.Parts.GetLength(0) <> m_Parts.GetLength(0) Then Return False 
      Dim result As Boolean = True 
      Array.Sort(other.Parts) 
      For I As Integer = 0 To other.Parts.GetLength(0) - 1 
       If other.Parts(I) <> m_Parts(I) Then 
        result = False 
        Exit For 
       End If 
      Next 
      Return result 
     End Function 
     ' Should also override == and != operators. 
    End Class 

End Module 

Answer 1

リストで見つけた解決策を収集し、リストから重複を除外してリストを印刷するalgoを書き込みます。