A Simple Memoization Function Class.

Memoization is simply remembering the previous worked out answers for the value inputted for the function.

Public Class Memo(Of T0 , T1 )
  Private TheFunction As Func(Of Memo(of T0,T1),T0,T1)
  Private MemoizationValues As New Dictionary(Of T0,T1)
  Public Sub New ( TheFunction As Func(of Memo(Of T0 , T1), T0, T1 ) )
    Me.TheFunction = TheFunction
  End Sub
  Public Default  Property Fun(x As T0) As T1
    Set(Value As T1)
      If Not MemoizationValues.ContainsKey(x) Then MemoizationValues(x) = Value 
    End Set
    Get
      If MemoizationValues.ContainsKey(x) Then Return MemoizationValues(x)
      Dim Value = TheFunction(Me,x)
      MemoizationValues(x)=Value
      Return Value
    End Get
  End Property
End Class

Now let define a few functions.

Fibonacci

Dim fib As New Memo(Of BigInteger, BigInteger)(Function(f,x) f(x-2) + f(x-1))
fib(0) = 0
fib(1) = 1

Console.WriteLine("Fib(10) = ", Fib(10))

Factorial

Dib Fact As New Memo(Of BigInteger, BigInteger(Function(f,x) x * f(x-1))
f(0) = 1

Console.WriteLine("Fact(10) = ", Fact(10) )

Both are rather close to how you would write the mathematically.