Fibonacci number
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The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, …
The idea is to add the two last numbers in order to produce the next value.
recursive implementation
function FibonacciNumber(const n: integer): integer;
begin
// recursive case
if n > 1 then
result := (FibonacciNumber(n-1) + FibonacciNumber(n-2))
// base case
else if n = 0 then
result := 0
else
result := 1;
end;iterative implementation
This one is preferable for its run-time behaviour.
function Fibonacci(n: Integer): Integer;
var
i,u,v,w: Integer;
begin
if n <= 0 then
exit(0);
if n = 1 then
exit(1);
u := 0;
v := 1;
for i := 2 to n do
begin
w := u + v;
u := v;
v := w;
end;
Result := v;
end;