Stirling numbers of the second kind: Difference between revisions
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(115 digits, k = 28)
</pre>
=={{header|Visual Basic .NET}}==
{{trans|Java}}
<lang vbnet>Imports System.Numerics
Module Module1
Class Sterling
Private Shared ReadOnly COMPUTED As New Dictionary(Of String, BigInteger)
Private Shared Function CacheKey(n As Integer, k As Integer) As String
Return String.Format("{0}:{1}", n, k)
End Function
Private Shared Function Impl(n As Integer, k As Integer) As BigInteger
If n = 0 AndAlso k = 0 Then
Return 1
End If
If (n > 0 AndAlso k = 0) OrElse (n = 0 AndAlso k > 0) Then
Return 0
End If
If n = k Then
Return 1
End If
If k > n Then
Return 0
End If
Return k * Sterling2(n - 1, k) + Sterling2(n - 1, k - 1)
End Function
Public Shared Function Sterling2(n As Integer, k As Integer) As BigInteger
Dim key = CacheKey(n, k)
If COMPUTED.ContainsKey(key) Then
Return COMPUTED(key)
End If
Dim result = Impl(n, k)
COMPUTED.Add(key, result)
Return result
End Function
End Class
Sub Main()
Console.WriteLine("Stirling numbers of the second kind:")
Dim max = 12
Console.Write("n/k")
For n = 0 To max
Console.Write("{0,10}", n)
Next
Console.WriteLine()
For n = 0 To max
Console.Write("{0,3}", n)
For k = 0 To n
Console.Write("{0,10}", Sterling.Sterling2(n, k))
Next
Console.WriteLine()
Next
Console.WriteLine("The maximum value of S2(100, k) = ")
Dim previous = BigInteger.Zero
For k = 1 To 100
Dim current = Sterling.Sterling2(100, k)
If current > previous Then
previous = current
Else
Console.WriteLine(previous)
Console.WriteLine("({0} digits, k = {1})", previous.ToString().Length, k - 1)
Exit For
End If
Next
End Sub
End Module</lang>
{{out}}
<pre>Stirling numbers of the second kind:
n/k 0 1 2 3 4 5 6 7 8 9 10 11 12
0 1
1 0 1
2 0 1 1
3 0 1 3 1
4 0 1 7 6 1
5 0 1 15 25 10 1
6 0 1 31 90 65 15 1
7 0 1 63 301 350 140 21 1
8 0 1 127 966 1701 1050 266 28 1
9 0 1 255 3025 7770 6951 2646 462 36 1
10 0 1 511 9330 34105 42525 22827 5880 750 45 1
11 0 1 1023 28501 145750 246730 179487 63987 11880 1155 55 1
12 0 1 2047 86526 611501 1379400 1323652 627396 159027 22275 1705 66 1
The maximum value of S2(100, k) =
7769730053598745155212806612787584787397878128370115840974992570102386086289805848025074822404843545178960761551674
(115 digits, k = 28)</pre>
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