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Sucesion Fibonacci El ejercicio de Fibonacci pregunta cuántas parejas de conejos habrá en una granja luego de "n" meses, si se coloca inicialmente una sola pareja y se parte de las siguientes premisas: 1. Los conejos alcanzan la madurez sexual a la edad de un mes. 2. En cuanto alcanzan la madurez sexual los conejos se aparean y siempre resulta preñada la hembra. 3. El periodo de gestación de los conejos es de un mes. 4. Los conejos no mueren. 5. La hembra siempre da a luz una pareja de conejos de sexos opuestos. 6. Los conejos tienen una moral y un instinto de variedad genética muy relajados y se aparean entre parientes. El proceso de crecimiento de la población de conejos es mejor descrito con la siguiente ilustración. Como se puede observar el número de parejas de conejos por mes está determinado por la sucesión de Fibonacci. En matemáticas, la sucesión de Fibonacci es la siguiente sucesión infinita de números naturales: 0,1,1,2,3,5,8,13,21,34,55,89,144 La sucesión inicia con 0 y 1, y a partir de ahí cada elemento es la suma de los dos anteriores. A cada elemento de esta sucesión se le llama número de Fibonacci. Esta sucesión fue descrita en Europa por Leonardo de Pisa, matemático italiano del siglo XIII también conocido como Fibonacci. Tiene numerosas aplicaciones en ciencias de la computación, matemáticas y teoría de juegos. La respuesta se da a continuación por los algoritmos en los lenguajes de programación más populares y nuevos. Ada Asp Awk Basic Boo C C++ C# Caml Cobol Eiffel Erlang F# Forth Fortran Haskell Java JavaScript Lisp Lua Oberon OCaml Oz Pascal Perl PHP Prolog Python Rebol Rexx Ruby Scala Scheme Scriptol Smalltalk Tcl {************ Ada ***********} Recursive function fib(n : integer) return integer is begin if n < 2 then return n; else return fib(n-1) + fib(n-2); end if; end fib; Iterative function fib(n : integer) return integer is first : integer := 0; second : integer := 1; tmp : integer; begin for i in 1..n loop tmp := first + second; first := second; second := tmp; end loop; return first; end fib; {*********** Asp ************} Recursive function fibo(byval i) if (i = 0 or i = 1) then fibo = i else fibo = fibo(i - 1) + fibo(i - 2) end If end function <% for num = 1 to n = fibo(num) %> Iterative <table> <% dim a = 1 dim b = 1 dim num dim d for num = 1 to 12 d = a + b a = b - 1 b = d response.Write("<tr><td> " & num & "</td><td>" & a & "</td></tr>" next %> </table> {************ Awk *********} function fib(n) { if(n < 2) return(1); return(fib(n-2) + fib(n-1)); } BEGIN { printf("%dn", fib(10)); exit; } {************ Basic**********} x = 1 y = 1 n = 100 FOR x = 1 to n z = x + y x = y y = z PRINT z + 1 NEXT x {********** Boo*********} def fibo(): a, b = 0, 1 while true: yield b a, b = b, a+b for i as int, element in zip(range(x), fibo()): print("${i + 1}: ${element}" { ********** C *********** Recursive int fib(int n) { if (n < 2) return n; else return fib(n-1) + fib(n-2); } printf("%dn", fib(10)); Iterative int fib(int n) { int first = 0, second = 1; int tmp; while (n--) { tmp = first+second; first = second; second = tmp; } return first; } *********** C++ *********** Recursive int fib(int n) { if (n < 2) return n; else return fib(n-1) + fib(n-2); } cout << fib(10) << endl; Iterative int fibonacci(int n) { int u = 0; int v = 1; int i, t; for(i = 2; i <= n; i++) { t = u + v; u = v; v = t; } return v; } {*********** C# (C Sharp) **************} Recursive using System; class App { public static int fibo(int n) { return (n Iterative public class Fibonacci { public static void Main() { int oldnum = 1; int currnum = 1; int nextNumber; System.Console.Write(currnum + " "; while (currnum < 50) { System.Console.Write(currnum + " "; nextNumber = currnum + oldnum; oldnum = currnum; currnum = nextNumber; } } } {************ Cobol **************} IDENTIFICATION DIVISION. PROGRAM-ID. FIBONACCI. ENVIRONMENT DIVISION. DATA DIVISION. WORKING-STORAGE SECTION. 77 N PIC 9(18). 77 N1 PIC Z(18). 77 M PIC 9(18) VALUE 1. 77 O PIC 9(18). 77 I PIC 9(4) VALUE 1. 77 Q PIC X. PROCEDURE DIVISION. PARA-A. DISPLAY ( 1 , 1 ) ERASE. DISPLAY ( 2 , 1 ) "FIBONACCI NUMBERS FROM 1 TO 100 ARE:". MOVE 0 TO N. DISPLAY " ". DISPLAY 0. DISPLAY 1. MOVE 0 TO O. PARA-B. COMPUTE N = O + M. MOVE N TO N1. MOVE M TO O. MOVE N TO M. DISPLAY N1. ADD 1 TO I. IF I = 21 DISPLAY "PRESS TAB KEY TO VIEW NEXT PAGE." ACCEPT Q. IF I = 41 DISPLAY "PRESS TAB KEY TO VIEW NEXT PAGE." ACCEPT Q. IF I = 61 DISPLAY "PRESS TAB KEY TO VIEW NEXT PAGE." ACCEPT Q. IF I = 81 DISPLAY "PRESS TAB KEY TO VIEW NEXT PAGE." ACCEPT Q IF I = 99 GO TO STOP-PARA ELSE GO TO PARA-B. STOP-PARA. DISPLAY " ". STOP RUN. {********* Eiffel************} Recursive class FIBONACCI feature fib (k: INTEGER): INTEGER is -- Fibonnaci numbers require pre_fib: k >= 0 do if k = 0 then Result := 0 else if k = 1 then Result := 1 else Result := fib (k-2) + fib (k-1) end end; -- fib Iterative fibiter (k: INTEGER): INTEGER is -- Fibonacci require pre_fib: k > 0 local j, p, c, n: INTEGER do from p := 0; c := 1; j := 1 until j = k loop n := p + c; p := c; c := n; j := j + 1 end; Result := c end; -- fib1 {***************** Erlang *************** -module(fibo). -export([main/1]). main() -> main(['1']). main() -> Num = list_to_integer(atom_to_list(Arg)), io:fwrite("~wn", [fib(Num)]), halt(0). fib(N) when N < 2 -> 1; fib(N) -> fib(N-2) + fib(N-1). {*************** F# (F Sharp)*****************} let rec fibonacci x = match x with 0 -> 1 | 1 -> 1 | n -> fibonacci(x - 1) + fibonacci(x - 2);; fibonacci 10;; {********** Forth************} read NUM from last command line argument 0. argc @ 1- arg >number 2drop drop constant NUM compute fibonacci numbers : fib Récursif dup 2 < if drop 1 else dup 2 - fib swap 1 - fib + then ; NUM fib 1 u.r cr bye A very short version: Nombres de Fibonacci par Bill Spight : FIBO ( n -- n1 n0) n >= 0, n0 = Fibo(n), n1 = Fibo(n-1) DUP 0= IF 1 SWAP ELSE 1- RECURSE TUCK + ENDIF ; {********* Fortran****************} PROGRAM F2A I=35; K=I CALL F(I) PRINT *,K,'th Fibonacci number is',I STOP END PROGRAM C C Subroutine F(I) calculates the I'th Fibonacci number C SUBROUTINE F(I) DIMENSION A(I+1) A(1)=1; A(2)=1 DO1J=3,I+1 A(J)=A(J-1)+A(J-2) 1 CONTINUE I=A(I+1) RETURN END SUBROUTINE {*********** Haskell*************} module Main where import System.Environment fibo = 1 : 1 : zipWith (+) fibo (tail fibo) main = do args <- getArgs print (fibo !! (read(args!!0)-1)) {***************** Java**************} public class fibo { public static void main(String args[]) { int N = Integer.parseInt(args[0]); System.out.println(fib(N)); } public static int fib(int n) { if (n < 2) return(1); return( fib(n-2) + fib(n-1) ); } } Source code {********** JavaScript****************} function fibo(n) { if (n < 2) return 1; return fibo(n-2) + fibo(n-1); } for(var i = 1; i < x ; i++) { document.write(i, " = ", fibo(i), "<br>"; } {********Lisp*********} (defun fibonacci (x) " Calcule le nombre de fibonacci pour x " (if (<= x 2) 1 (+ (fibonacci (- x 2))(fibonacci (1- x))))) (loop for i from 1 to x do (print (fibonacci i))) {*********** Lua **********} function fib(n) if (n < 2) then return(1) end return( fib(n-2) + fib(n-1) ) end N = tonumber((arg and arg)) or 1 write(fib(N), "n" {***********Oberon************} MODULE fibonacci; (* n premiers nombres de Fibonacci *) CONST n=151; VAR Fibs: ARRAY n+1 OF INTEGER; i,j : INTEGER; BEGIN j:=0; Fibs[0]:=0; Fibs:=1; i:=2; WHILE i <= n DO Fibs:= Fibs[i-2] + Fibs[i-1]; i:=i+1; END; i:=0; WHILE i <= n DO Write(Fibs); i:=i+1; END; END fibonacci. {***********Ocaml************} let rec fib n = if n < 2 then 1 else fib (n - 2) + fib (n - 1) let _ = let n = try int_of_string Sys.argv.(1) with Invalid_argument _ -> 1 in Printf.printf "%dn" (fib n) {*********** Oz**************} functor import System Application define fun {Fib N} case N of 0 then 1 [] 1 then 1 else {Fib N-2} + {Fib N-1} end end in local A in = {Application.getArgs plain} {System.printInfo {Fib {String.toInt A}}} end {Application.exit 0} end {********* Pascal***********} Recursive program fibo; var result : longint; num,i, error: integer; strnum: string; function fib(n : integer) : longint; begin if n <= 2 then fib := 1 else fib := fib(n-2) + fib(n-1); end; begin if ParamCount = 0 then begin writeln('Enter integer:'); readln(strnum); val(strnum,num,error); end else begin val (ParamStr(1), num, error); end; for i := 1 to num do begin result:= fib(i); writeln(i, ' : ', result); end; end. Source code {********** Perl**************} Iterative using bigint #! /usr/bin/perl use bigint; my ($a, $b) = (0, 1); for (; { print "$an"; ($a, $b) = ($b, $a+$b); } Recursive sub fibo; sub fibo {$_ [0] < 2 ? $_ [0] : fibo ($_ [0] - 1) + fibo ($_ [0] - 2)} Iterative sub fibo { my ($n, $a, $b) = (shift, 0, 1); ($a, $b) = ($b, $a + $b) while $n-- > 0; $a; } {************ PHP*************} Recursive <?php function fibo($n) { return(($n Iterative function fibonacci($length) { for( $l = array(1,1), $i = 2, $x = 0; $i < $length; $i++ ) { $l[] = $l[$x++] + $l[$x]; } return $l; } for{ $x=0; $x< $fibmax; $x++) echo "fib(" , $x , " ", fibonacci($x), "n" {******* Prolog*********} Recursive fibo(N, 1) :-, N<2, !. fibo(N, R) :- N1 is N-1, N2 is N-2, fibo(N1, R1),fibo(N2, R2), R is R1 + R2. {******** Python********} Recursive import sys def fib(n): if n < 2: return n else: return fib(n - 1) + fib(n - 2) def main(): limit = int(sys.argv) print fib(limit) main() With generator def fib(): a, b = 0, 1 while True: yield a a, b = b, a + b {******* Rebol*********} Fib: func [ return either N < 2 [ 1 ] [ (Fib N - 2) + (Fib N - 1) ] ] NUM: to-integer to-string system/script/args NUM: either NUM < 1 [ 1 ] [ NUM ] R: Fib NUM write %output.rebol rejoin [ R ] {********* Rexx*********} parse arg n If n < 1 Then Do n = 1 End R = fib(N) say R exit fib: PROCEDURE PARSE ARG N IF N<2 THEN RETURN 1 RETURN fib(N-2) + fib(N-1) {********** Ruby*********} Recursive parse arg n If n < 1 Then Do n = 1 End R = fib(N) say R exit fib: PROCEDURE PARSE ARG N IF N<2 THEN RETURN 1 RETURN fib(N-2) + fib(N-1) Iterative def fib(num) i, j = 0, 1 while i <= num yield i i, j = j, i + j end end fib(10) {|i| puts i} {********** Scala*********} Recursive object Fibonacci with Application { def fibo(n: Int): Int = if (n < 2) 1 else fibo(n - 1) + fibo(n - 2); Console.println("fib("+ x +" = " + fib(x)); }; Iterative object Fibonacci with Application { def fibo(n: Int): Int = if (n < 2) 1 else { def iter(x: Int, prev: Int, result: Int): Int = if (x > n) result else iter(x + 1, result, prev + result); iter(3, 1, 2) }; Console.println("fib("+ x +" = " + fib(x)); }; {********* Scheme*********} Recursive (define fibo (lambda (x) (if (< x 2) x (+ (fibo (- x 1)) (fibo (- x 2)))))) Iterative (define (fibo x) (define (fibo-iter x a b) (if (= x 0) a (fibo-iter (- x 1) b (+ a b)))) (fibo-iter x 0 1)) Display (define (fibo-run a b) (display a) (newline) (fibo-run b (+ a b))) (define fibo-run-all (fibo-run 0 1))) {********** Scriptol********} Recursive constant int fmax = 16 int z ` Récursif Fibonacci function int fib(int n) if n <= 1 z = n else z = fib(n - 1) + fib(n - 2) /if return z for int i in 0..fmax ` loop in a range print "fib($i)= " , fib(i) /for Iterative int fibonacci(int n) int u = 0 int v = 1 int t for int i in 2 .. n t = u + v u = v v = t /for return v for int x in 1..fibmax echo "fib(" , x , " ", fibonacci(x), "n" {********** Smalltalk **********} ^self <= 2 ifTrue: ifFalse: [(self - 1) fibonacci + (self - 2) fibonacci] {******** Tcl*********} proc fib {n} { if {$n < 2} { return 1 } else { return [expr {[fib [expr {$n-2}]] + [fib [expr {$n-1}]]}] } } set N [lindex $argv 0] if {$N < 1} { set N 1 } puts [fib $N] Fuente: Scriptol.com, interactiva.matem.unam.mx Nos Vemos un Abrazo