Caching

Our good friend Mr. Smith has improved his programming skills considerably. Currently, he is learning about recursive functions and he programmed his first recursive piece of code. He wrote a simple seven-liner which calculates the nth element in the Fibonacci sequence:

`function TfrmFibonacci.FibonacciRecursive(element: int64): int64;begin  if element < 3 then    Result := 1  else    Result := FibonacciRecursive(element - 1) +              FibonacciRecursive(element - 2);end;`

I will not argue with him—if you look up the definition of a Fibonacci sequence it really looks like it could be perfectly solved with a recursive function.

A sequence of Fibonacci numbers, F, is defined with two simple rules:

• First two numbers in the sequence are both 1 (F1 = ...

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