費氏數列就是F(N)=F(N-1)+(N-2),F(1)=1,F(2)=1,F(3)=F(2)+F(1)=1+1=2,F(4)=F(3)+F(2)=2+1=3,F(5)=F(4)+F(3)=3+2=5以此類推.....
var
N,i:Integer//i是多的
T1,T2,tt:Integer//tt是暫存用的
begin
T1:=0
T2:=1//第一次計算時會需要一隻兔子
N:=10//會有10.9.8.7.6.5.4.3.2.1
while N > 0 do//N和0覺定你會有幾個數字,只有這樣所以你可以改成N=100 0=90
begin
Dec(N)//對n作累減用,當然你把>改成<時就要改成inc(N)
Memo1.Lines.Add(IntToStr(T1+T2))//AAAAAAAAAAAA
tt:=T1;//把母兔數量存起來
T1:=T2;//把子代變成母代
T2:=tt+T2//現在n的母數量//BBBBBBBBBB
//AAAAAA跟BBBBBBBB指的其時是同一筆資料所以可以改成一起如下
//Memo1.Lines.Add(IntToStr(T2))//AAAAAAAAAAAA
end;
The Fibonacci numbers form a sequence of integers, mathematically defined by
F(0)=0; F(1)=1; F(n) = F(n - 1) + F(n - 2) for n > 1.
This results in the following sequence of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...
This simply means that by definition the first Fibonacci number is 0, the second number is 1 and the rest of the Fibonacci numbers are calculated by adding the two previous numbers in the sequence.
Translating that into Delphi code:
Hide Copy Code
function Fibonacci(aNumber: Integer): Integer;
begin
if aNumber < 0 then
raise Exception.Create('The Fibonacci sequence is not defined for negative integers.');
case aNumber of
0: Result:= 0;;
1: Result:= 1;
else
Result:= Fibonacci(aNumber - 1) + Fibonacci(aNumber - 2);
end;;
end;
The function above is the recursive implementation, which in my opinion fits naturally. Now, the iterative implementation might not be as cleaner as that:
Hide Copy Code
function Fibonacci(aNumber: Integer): Integer;
var
I,
N_1,
N_2,
N: Integer;
begin
if aNumber < 0 then
raise Exception.Create('The Fibonacci sequence is not defined for negative integers.');
case aNumber of
0: Result:= 0;
1: Result:= 1;
else
begin
N_1:= 0;
N_2:= 1;
for I:=2 to aNumber do
beginn
N:= N_1 + N_2;
N_1:= N_2;
N_2:= N;
end;
Result:= N;
end;
end;
end;
Finally, if you want to produce the first 21 Fibonacci numbers try this out:
Hide Copy Code
program Project2;
{$APPTYPE CONSOLE}
{$R *.res}
uses
System.SysUtils;
var
I: Integer;
function Fibonacci(aNumber: Integer): Integer;
begin
{Your implementation goes here}
end;
begin
for I:=0 to 20 do
Writeln(Fibonacci(I));
Readln;
end.
