Difference between revisions of "Calculate the Fibonacci sequence"

From CodeCodex

(Common Lisp)
Line 284: Line 284:
 
</pre>
 
</pre>
  
A different algorithm, based on US' NIST's Dictionary Of Algorithms description of Bill Gosper & Gene Salamin method, at [http://www.nist.gov/dads/HTML/fibonacciNumber.html] (***Much much much*** faster):
+
A different algorithm, based on US' NIST's Dictionary Of Algorithms description of Bill Gosper & Gene Salamin method, at [http://www.nist.gov/dads/HTML/fibonacciNumber.html] ('''Much much much''' faster):
 
<pre>
 
<pre>
 
;;; Helper functions:
 
;;; Helper functions:

Revision as of 03:23, 30 May 2007

Related content:

Source code for calculation of the Fibonacci sequence.

Algol 68

This version asks the user to input an integer i, and prints out the first i numbers in the Fibonacci sequence.

PROC print fibo = (INT n) VOID :
    # prints out the Fibonacci sequence up to n. #
    BEGIN
        INT a := 0, b := 1;
        FOR i TO n DO
            print((whole(i, 0), " => ", whole(b, 0), new line));
            INT c = a + b;
            a := b;
            b := c
        OD
    END;

INT i;
print("Compute Fibonacci sequence up to? ");
read((i, new line));
print fibo(i)

80386+ Assembly

MASM:

.data
fibonacci DWORD 100 dup (0)
.code
mov edx,offset fibonacci
mov eax,1
mov ebx,1
mov ecx,49
@@:
mov DWORD PTR [edx],eax
mov DWORD PTR [edx+4],ebx
add eax,ebx
add ebx,eax
add edx,8
sub ecx,1
jnz @B

BASIC

fib0=0

fib1=1

FOR cnt= 1 TO n

	fib2=fib1+fib0

	PRINT fib2

	fib0=fib1

	fib1=fib2

NEXT cnt


/* fib2 is the sum of the two preceeding terms.*/

C

<HIGHLIGHTSYNTAX language="c">

  1. include <stdio.h>

int main() {

 int i, x;
 int a = 0;
 int b = 1;
 printf("%i\n%i\n", a, b);
 for(i = 2; i < 100; i++)
 {
   x = a;
   a = b;
   b = x + b;
   printf("%i\n", b);
 }
 return 0;

} </HIGHLIGHTSYNTAX>

C++

<HIGHLIGHTSYNTAX language="cpp">

  1. include <iostream>

using namespace std; int main() {

  int number[30] = {1, 1, 0};
  int total;
  for(int i = 2; i < 30; i++)
  {
    number[i] = number[i - 1] + number[i - 2];
    cout << number[i];
  }
  return 0;

} </HIGHLIGHTSYNTAX>

Db

<HIGHLIGHTSYNTAX language="csharp"> static int Fibonacci (int x)

  {
  Console.WriteLine ("x = {0}", x);
  if (x <= 1)
     { return 1; }
  return Fibonacci (x-1) + Fibonacci (x-2);
  }

static void Main( )

  {
  Console.WriteLine ("Fibonacci no. = {0}", Fibonacci (5));
  Console.ReadKey();
  }

</HIGHLIGHTSYNTAX> This one is alot quicker than the above one <HIGHLIGHTSYNTAX language="csharp"> int a = 0; int b = 1; int c = 0; int n = 46; //to the N'th fibonacci No.

Console.WriteLine("Which Fibonacci Number do you want?");

n = Convert.ToInt16(Console.ReadLine());

if (n != 1) {

   for (int i = 1; i <= n; i++)
   {
       c = a + b;
       a = b;
       b = c;
   }
   Console.WriteLine("the {0}th Fibonacci number is {1}", n, a);

} else {

   Console.WriteLine("the {0}st Fibonacci number is 1", n);

} Console.ReadKey(); </HIGHLIGHTSYNTAX>

Haskell

<HIGHLIGHTSYNTAX language="haskell"> -- different versions, from slowest to fastest

-- recursive: O(exp(n)) fib_rec 0 = 1 fib_rec 1 = 1 fib_rec n = fib_rec (n-1) + fib_rec (n-2)

-- dynamic programming 1, imperative style: O(n) fib_dyn1 0 = 0 fib_dyn1 1 = 1 fib_dyn1 n = select $ until done step (0,0,1)

   where done (k,_,_)   = n == k

step (k,x,y) = (k+1,y,x+y) select (_,_,y) = y

-- dynamic programming 2: O(n) -- fibs is the infinite sequence of fibonacci numbers fibs = 0 : 1 : zipWith (+) fibs (tail fibs) fib_dyn2 n = fibs !! n

-- matrix multiplication: O(log n) -- uses the identity: (F_{n+1},F_{n})^T=M^n * (1,0)^T where M=((1,1),(1,0)) pow 0 _ = ((1,0),(0,1)) pow 1 m = m pow n m = let (q,r) = divMod n 2 y = pow q m z = prod y y in if r == 0 then z else prod z m

prod ((a,b),(c,d)) ((a',b'),(c',d'))

   = ( ( a*a' + b*c', a*b' + b*d' )
     , ( c*a' + d*c', c*b' + d*d' )
     )

fib_mat 0 = 1 fib_mat 1 = 1 fib_mat n = fst $ fst $ pow n ((1,1),(1,0)) </HIGHLIGHTSYNTAX>

Java

Java console application <HIGHLIGHTSYNTAX language="java122"> public class Fibonacci{

   static double sfib (double r, double k, double f){
       return(f==0)?k : (f==1)?r : sfib(r+k,r,f-1);
   }
   
   public static void main(String Args[]){
       int n=100;          // es kann selbst bestimmt werden bis zu welcher Zahl die Fibs
                              ausgegeben werden sollen
       System.out.println("Fibonacci Zahlen von 0 bis "+n+"\n******************************");
       for (int i=0; i<=n; i++){
           System.out.println(""+i+".\t Fib Zahl=\t"+(sfib(1,0,i)));
       }    
   }

} </HIGHLIGHTSYNTAX> A cleaner alternative that uses an ArrayList to cache previous Fibonacci values: <HIGHLIGHTSYNTAX language="java122"> public class Fibonacci {

   static ArrayList<Double> fibList;
   /**
    * A recursive Fibonacci calculation method.
* Note: This method considers that the * Fibonacci Sequence starts at 0. To alter the * method to start at 1 use the following code * in place of the fib() method: * double f; if(n <= 2) { f = 1.0; if(fibList.size() <= 2) fibList.add(f); return f; } f = (n < fibList.size()) ? fibList.get(n - 2) + fibList.get(n - 1) : fib(n - 2) + fib(n - 1); if(n >= fibList.size()) fibList.add(f); return f; * @param n the number to which the Fibonacci sequence * should be calculated. * @return the Fibonacci value at n. */ public static double fib(int n) { double f; if(n <= 1) { f = 1.0; if(fibList.size() <= 1) fibList.add(f); return f; } f = (n < fibList.size()) ? fibList.get(n - 2) + fibList.get(n - 1) : fib(n - 2) + fib(n - 1); if(n >= fibList.size()) fibList.add(f); return f; } public static void main(String[] args) { fibList = new ArrayList<Double>(); int n = 50; System.out.println("The first " + n + " Fibonacci numbers:"); for(int i = 0; i < n; i++) System.out.println(fib(i)); }

} </HIGHLIGHTSYNTAX>

Common Lisp

* (defun fib(n) (if (< n 2) n (+ (fib (- n 1)) (fib (- n 2)))))
FIB
* (fib 10)
55

Tail recursive version (much faster):

;;; Remember that Tail-recursion optimization isn't enabled by
;;; default in most CL compilers/interpreters.
(defun fib-optimized (n)
    (labels
        ((fib2 (num l m)
            (if (< num n)
                (fib2 (1+ num) (+ l m) l)
                l)))
        (fib2 0 0 1)))

A different algorithm, based on US' NIST's Dictionary Of Algorithms description of Bill Gosper & Gene Salamin method, at [1] (Much much much faster):

;;; Helper functions:
(defun pairwise-multiply (pair1 pair2)
    (let ((ac (* (first pair1) (first pair2)))
            (ad (* (first pair1) (second pair2)))
            (bc (* (second pair1) (first pair2)))
            (bd (* (second pair1) (second pair2))))
         (list (+ ac ad bc) (+ ac bd))))

;;; If you're going for values well above n=1000000 (and maybe some more),
;;; you might want to consider making this function tail-recursive, or make
;;; the iterative version.
(defun pairwise-pow (pair n)
    ;; It's an error having n < 1, you may want to change this to check for
    ;; that condition.
    (cond
        ((= n 1) pair)
        ((evenp n) (let ((result (pairwise-pow pair (truncate (/ n 2)))))
                        (pairwise-multiply result result)))
        (t (let ((result (pairwise-pow pair (truncate (/ n 2)))))
                (pairwise-multiply pair (pairwise-multiply result result))))))

(defun fibonacci (n)
    (if (zerop n) 0
        (first (pairwise-pow '(1 0) n))))

;; Try this one, don't worry, it won't take you a millisecond.
(fibonacci 10000)

Matlab

<HIGHLIGHTSYNTAX language="matlab5"> function f = binet(a,b,n) % vectorized version of fibonacci fibonacci O(1) using Binet formula % a and b are real seeds % n is the integer vector of the indices to be computed % if the seeds are integer the result is rounded to insure integer result

phi = (1+sqrt(5))/2; phi1 = -1/phi; n = n-1; c = [ 1 1; phi phi1]\[a;b]; f = c(1)*phi.^n+c(2)*phi1.^n; if (~rem(a,1) && ~rem(b,1)), f = round(f); end; </HIGHLIGHTSYNTAX>

MS-DOS

::print the first 'max' fibonacci numbers
::(only working under windows xp)
@echo off

set index=1
set max=46
set fibold=0
set fib=1

echo.---%max% first FIBONACCI-Numbers---

echo.%fibold%

:WHILE
echo.%fib%
set /A fibnew=fibold + fib
set fibold=%fib% 
set fib=%fibnew%
set /A index=index + 1
IF %index% LEQ %max% GOTO WHILE

OCaml

The simplest implementation as a non-tail-recursive function: <HIGHLIGHTSYNTAX language="ocaml">

  1. let rec fib n = if n<2 then n else fib(n-1) + fib(n-2);;

val fib : int -> int = <fun> </HIGHLIGHTSYNTAX> For example: <HIGHLIGHTSYNTAX language="ocaml">

  1. fib 10;;

- : int = 55 </HIGHLIGHTSYNTAX> This function can be made tail recursive by accumulating the two previous Fibonacci numbers (the two accumulators are optional arguments here, with default values): <HIGHLIGHTSYNTAX language="ocaml">

  1. let rec fib ?(r=1) ?(k=0) = function
   | 0 -> k
   | 1 -> r
   | f -> fib ~r:(r+k) ~k:r (f-1);;

val fib : ?r:int -> ?k:int -> int -> int = <fun> </HIGHLIGHTSYNTAX>

Perl

<HIGHLIGHTSYNTAX language="perl">

  1. !/bin/perl -wl
  2. Prints the sequence of Fibonacci numbers with arbitrary
  3. precision. If an argument N is given, the program stops
  4. after generating Fibonacci(N).

use strict; use bigint;

my $n = @ARGV ? shift : 1e9999;

             exit if $n < 0;

print "0: 0"; exit if $n < 1; print "1: 1"; exit if $n < 2;

my ($a, $b) = (0, 1); for my $k (2 .. $n) {

   ($a, $b) = ($b, $a+$b);
   print "$k: $b";

} </HIGHLIGHTSYNTAX>

PHP

<?php
$a=0;
$b=1;
echo "$a\n$b\n";
for($i=2;$i<100;$i++){
    $temp=$a;
    $a=$b;
    $b=$temp+$b;
    echo "$b\n";
}
?>

Python

Print the first 100 fibonnaci numbers, up to '354,224,848,179,261,915,075'. This program considers '0' to be the 0th fibonnaci number, and '1' to be the first. <HIGHLIGHTSYNTAX language="python">

  1. !/usr/bin/env python

a, b = 0, 1 print a for n in range(100):

    print b
    a, b = b, a+b

</HIGHLIGHTSYNTAX>

Ruby

#!/usr/bin/env ruby
a, b = 0, 1
puts "0: #{a}"
1.upto 100 do |n|
     puts "#{n}: #{b}"
     a, b = b, a+b
end

Scheme

<HIGHLIGHTSYNTAX language="scheme"> (define (fib n)

 (if (< n 2)
 n
 (+ (fib (- n 1)) (fib (- n 2)))))

</HIGHLIGHTSYNTAX>

Seed7

$ include "seed7_05.s7i";
  include "bigint.s7i";

const proc: main is func
  local
    var integer: i is 0;
    var bigInteger: a is 0_;
    var bigInteger: b is 1_;
    var bigInteger: c is 0_;
  begin
    writeln(a);
    for i range 1 to 100 do
      writeln(b);
      c := a;
      a := b;
      b +:= c;
    end for;
  end func;