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 that 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, as follows:

• The first two numbers in the sequence are both 1 (F1 = 1, F2 = 1)
• Every other number in...