Fibonacci number
From Free Pascal wiki
│
Deutsch (de) │
English (en) │
suomi (fi) │
français (fr) │
русский (ru) │
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
{**
implements Fibonacci sequence recursively
\param n the index of the Fibonacci number to retrieve
\returns the Fibonacci value at n
}
function fibonacci(const n: byte): qword;
begin
// optimization: then part gets executed most of the time
if n > 1 then
begin
fibonacci := fibonacci(n - 2) + fibonacci(n - 1);
end
else
begin
// since the domain is restricted to non-negative integers
// we can bluntly assign the result to n
fibonacci := n;
end;
end;
iterative implementation
This one is preferable for its run-time behavior.
{**
implements Fibonacci sequence iteratively
\param n the index of the Fibonacci number to calculate
\returns the Fibonacci value at n
}
function fibonacci(const n: longword): qword;
type
/// more meaningful identifiers than simple integers
relativePosition = (previous, current, next);
var
/// temporary iterator variable
i: longword;
/// holds preceding fibonacci values
f: array[relativePosition] of qword;
begin
f[previous] := 0;
f[current] := 1;
// note, in Pascal for-loop-limits are inclusive
for i := 1 to n do
begin
f[next] := f[previous] + f[current];
f[previous] := f[current];
f[current] := f[next];
end;
// assign to previous, bc f[current] = f[next] for next iteration
fibonacci := f[previous];
end;
