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...