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 = 1, F2 = 1),
Every other number in the sequence is the sum of the preceding two (Fn = Fn-1 + Fn-2).
You will also find a different definition of the Fibonacci sequence in the literature, starting with values 0 and 1, but it only differs...