Mutual recursion
You are encouraged to solve this task according to the task description, using any language you may know.
Two functions are said to be mutually recursive if the first calls the second, and in turn the second calls the first.
Write two mutually recursive functions that compute members of the Hofstadter Female and Male sequences defined as:
(If a language does not allow for a solution using mutually recursive functions
then state this rather than give a solution by other means).
ACL2
<lang lisp>(mutual-recursion
(defun f (n) (declare (xargs :mode :program)) (if (zp n) 1 (- n (m (f (1- n))))))
(defun m (n) (declare (xargs :mode :program)) (if (zp n) 0 (- n (f (m (1- n)))))))</lang>
Ada
<lang Ada>with Ada.Text_Io; use Ada.Text_Io; procedure Mutual_Recursion is
function M(N : Integer) return Integer; function F(N : Integer) return Integer is begin if N = 0 then return 1; else return N - M(F(N - 1)); end if; end F; function M(N : Integer) return Integer is begin if N = 0 then return 0; else return N - F(M(N-1)); end if; end M;
begin
for I in 0..19 loop Put_Line(Integer'Image(F(I))); end loop; New_Line; for I in 0..19 loop Put_Line(Integer'Image(M(I))); end loop;
end Mutual_recursion;</lang>
<lang ada>with Ada.Text_Io; use Ada.Text_Io; procedure Mutual_Recursion is
function M(N: Natural) return Natural; function F(N: Natural) return Natural; function M(N: Natural) return Natural is (if N = 0 then 0 else N – F(M(N–1))); function F(N: Natural) return Natural is (if N =0 then 1 else N – M(F(N–1)));
begin
for I in 0..19 loop Put_Line(Integer'Image(F(I))); end loop; New_Line; for I in 0..19 loop Put_Line(Integer'Image(M(I))); end loop;
end Mutual_recursion;</lang>
Aime
<lang aime>integer F(integer n); integer M(integer n);
integer F(integer n) {
integer r; if (n) {
r = n - M(F(n - 1));
} else {
r = 1;
} return r;
}
integer M(integer n) {
integer r; if (n) {
r = n - F(M(n - 1));
} else {
r = 0;
} return r;
}
integer main(void) {
integer i; i = 0; while (i < 20) {
o_winteger(3, F(i)); i += 1;
} o_byte('\n'); i = 0; while (i < 20) {
o_winteger(3, M(i)); i += 1;
} o_byte('\n'); return 0;
}</lang>
ALGOL 68
<lang algol68>PROC (INT)INT m; # ONLY required for ELLA ALGOL 68RS - an official subset OF full ALGOL 68 #
PROC f = (INT n)INT:
IF n = 0 THEN 1 ELSE n - m(f(n-1)) FI;
m := (INT n)INT:
IF n = 0 THEN 0 ELSE n - f(m(n-1)) FI;
main: (
FOR i FROM 0 TO 19 DO print(whole(f(i),-3)) OD; new line(stand out); FOR i FROM 0 TO 19 DO print(whole(m(i),-3)) OD; new line(stand out)
)</lang>
- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
ALGOL W
<lang algolw>begin
% define mutually recursive funtions F and M that compute the elements % % of the Hofstadter Female and Male sequences %
integer procedure F ( integer value n ) ; if n = 0 then 1 else n - M( F( n - 1 ) );
integer procedure M ( integer value n ) ; if n = 0 then 0 else n - F( M( n - 1 ) );
% print the first few elements of the sequences % i_w := 2; s_w := 1; % set I/O formatting % write( "F: " ); for i := 0 until 20 do writeon( F( i ) ); write( "M: " ); for i := 0 until 20 do writeon( M( i ) );
end.</lang>
AppleScript
<lang AppleScript>-- f :: Int -> Int on f(x)
if x = 0 then 1 else x - m(f(x - 1)) end if
end f
-- m :: Int -> Int on m(x)
if x = 0 then 0 else x - f(m(x - 1)) end if
end m
-- TEST
on run
set xs to range(0, 19) {map(f, xs), map(m, xs)}
end run
-- GENERIC FUNCTIONS
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f) set lng to length of xs set lst to {} repeat with i from 1 to lng set end of lst to lambda(item i of xs, i, xs) end repeat return lst end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then f else script property lambda : f end script end if
end mReturn
-- range :: Int -> Int -> [Int] on range(m, n)
if n < m then set d to -1 else set d to 1 end if set lst to {} repeat with i from m to n by d set end of lst to i end repeat return lst
end range</lang>
- Output:
<lang AppleScript>{{1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12},
{0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12}}</lang>
AutoHotkey
<lang AutoHotkey>Loop 20
i := A_Index-1, t .= "`n" i "`t " M(i) "`t " F(i)
MsgBox x`tmale`tfemale`n%t%
F(n) {
Return n ? n - M(F(n-1)) : 1
}
M(n) {
Return n ? n - F(M(n-1)) : 0
}</lang>
This one is an alternative to the above.
<lang AutoHotkey>main() Return
F(n) {
If (n == 0) Return 1 Else Return n - M(F(n-1))
}
M(n) {
If (n == 0) Return 0 Else Return n - F(M(n-1)) ;
}
main() {
i = 0 While, i < 20 { male .= M(i) . "`n" female .= F(i) . "`n" i++ } MsgBox % "male:`n" . male MsgBox % "female:`n" . female
}</lang>
AWK
In AWK it is enough that both functions are defined somewhere. It matters not whether the BEGIN block is before or after the function definitions.
<lang awk>cat mutual_recursion.awk:
- !/usr/local/bin/gawk -f
- User defined functions
function F(n) { return n == 0 ? 1 : n - M(F(n-1)) }
function M(n) { return n == 0 ? 0 : n - F(M(n-1)) }
BEGIN {
for(i=0; i <= 20; i++) { printf "%3d ", F(i) } print "" for(i=0; i <= 20; i++) { printf "%3d ", M(i) } print ""
}</lang>
- Output:
$ awk -f mutual_recursion.awk 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12
BaCon
<lang freebasic>' Mutually recursive FUNCTION F(int n) TYPE int
RETURN IIF(n = 0, 1, n - M(F(n -1)))
END FUNCTION
FUNCTION M(int n) TYPE int
RETURN IIF(n = 0, 0, n - F(M(n - 1)))
END FUNCTION
' Get iteration limit, default 20 SPLIT ARGUMENT$ BY " " TO arg$ SIZE args limit = IIF(args > 1, VAL(arg$[1]), 20)
FOR i = 0 TO limit
PRINT F(i) FORMAT "%2d "
NEXT PRINT FOR i = 0 TO limit
PRINT M(i) FORMAT "%2d "
NEXT PRINT</lang>
- Output:
prompt$ ./mutually-recursive 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12
BASIC
<lang qbasic>DECLARE FUNCTION f! (n!) DECLARE FUNCTION m! (n!)
FUNCTION f! (n!)
IF n = 0 THEN f = 1 ELSE f = m(f(n - 1)) END IF
END FUNCTION
FUNCTION m! (n!)
IF n = 0 THEN m = 0 ELSE m = f(m(n - 1)) END IF
END FUNCTION</lang>
BBC BASIC
<lang bbcbasic> @% = 3 : REM Column width
PRINT "F sequence:" FOR i% = 0 TO 20 PRINT FNf(i%) ; NEXT PRINT PRINT "M sequence:" FOR i% = 0 TO 20 PRINT FNm(i%) ; NEXT PRINT END DEF FNf(n%) IF n% = 0 THEN = 1 ELSE = n% - FNm(FNf(n% - 1)) DEF FNm(n%) IF n% = 0 THEN = 0 ELSE = n% - FNf(FNm(n% - 1))</lang>
- Output:
F sequence: 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 M sequence: 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12
Bc
<lang bc>cat mutual_recursion.bc: define f(n) {
if ( n == 0 ) return(1); return(n - m(f(n-1)));
}
define m(n) {
if ( n == 0 ) return(0); return(n - f(m(n-1)));
}</lang>
POSIX bc doesn't have the print statement.
<lang bc>/* GNU bc */ for(i=0; i < 19; i++) {
print f(i); print " ";
} print "\n"; for(i=0; i < 19; i++) {
print m(i); print " ";
} print "\n"; quit</lang>
- Output:
GNU bc mutual_recursion.bc bc 1.06.95 Copyright 1991-1994, 1997, 1998, 2000, 2004, 2006 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12
Bracmat
<lang bracmat> (F=.!arg:0&1|!arg+-1*M$(F$(!arg+-1)));
(M=.!arg:0&0|!arg+-1*F$(M$(!arg+-1)));
-1:?n&whl'(!n+1:~>20:?n&put$(F$!n " "))&put$\n 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13
-1:?n&whl'(!n+1:~>20:?n&put$(M$!n " "))&put$\n 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12</lang>
Brat
<lang brat>female = null #yes, this is necessary
male = { n |
true? n == 0 { 0 } { n - female male(n - 1) }
}
female = { n |
true? n == 0 { 1 } { n - male female(n - 1 ) }
}
p 0.to(20).map! { n | female n } p 0.to(20).map! { n | male n }</lang>
C
To let C see functions that will be used, it is enough to declare them. Normally this is done in a header file; in this example we do it directly in the code. If we do not declare them explicitly, they get an implicit declaration (if implicit declaration matches the use, everything's fine; but it is better however to write an explicit declaration)
<lang c>#include <stdio.h>
- include <stdlib.h>
/* let us declare our functions; indeed here we need
really only M declaration, so that F can "see" it and the compiler won't complain with a warning */
int F(const int n); int M(const int n);
int F(const int n) {
return (n == 0) ? 1 : n - M(F(n - 1));
}
int M(const int n) {
return (n == 0) ? 0 : n - F(M(n - 1));
}
int main(void) {
int i; for (i = 0; i < 20; i++) printf("%2d ", F(i)); printf("\n"); for (i = 0; i < 20; i++) printf("%2d ", M(i)); printf("\n"); return EXIT_SUCCESS;
}</lang>
C++
C++ has prior declaration rules similar to those stated above for C, if we would use two functions. Instead here we define M and F as static (class) methods of a class, and specify the bodies inline in the declaration of the class. Inlined methods in the class can still call other methods or access fields in the class, no matter what order they are declared in, without any additional pre-declaration. This is possible because all the possible methods and fields are declared somewhere in the class declaration, which is known the first time the class declaration is parsed. <lang cpp>#include <iostream>
- include <vector>
- include <iterator>
class Hofstadter { public:
static int F(int n) { if ( n == 0 ) return 1; return n - M(F(n-1)); } static int M(int n) { if ( n == 0 ) return 0; return n - F(M(n-1)); }
};
using namespace std;
int main() {
int i; vector<int> ra, rb;
for(i=0; i < 20; i++) { ra.push_back(Hofstadter::F(i)); rb.push_back(Hofstadter::M(i)); } copy(ra.begin(), ra.end(), ostream_iterator<int>(cout, " ")); cout << endl; copy(rb.begin(), rb.end(), ostream_iterator<int>(cout, " ")); cout << endl; return 0;
}</lang>
The following version shows better what's going on and why we seemingly didn't need pre-declaration (like C) when "encapsulating" the functions as static (class) methods.
This version is equivalent to the above but does not inline the definition of the methods into the definition of the class. Here the method declarations in the class definition serves as the "pre-declaration" for the methods, as in C.
<lang cpp>class Hofstadter { public:
static int F(int n); static int M(int n);
};
int Hofstadter::F(int n) {
if ( n == 0 ) return 1; return n - M(F(n-1));
}
int Hofstadter::M(int n) {
if ( n == 0 ) return 0; return n - F(M(n-1));
}</lang>
C#
<lang csharp>namespace RosettaCode {
class Hofstadter { static public int F(int n) { int result = 1; if (n > 0) { result = n - M(F(n-1)); }
return result; }
static public int M(int n) { int result = 0; if (n > 0) { result = n - F(M(n - 1)); }
return result; } }
}</lang>
Ceylon
<lang ceylon>Integer f(Integer n)
=> if (n > 0) then n - m(f(n-1)) else 1;
Integer m(Integer n)
=> if (n > 0) then n - f(m(n-1)) else 0;
shared void run() {
printAll((0:20).map(f)); printAll((0:20).map(m));
}</lang>
- Output:
1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12
Clojure
<lang lisp>(declare F) ; forward reference
(defn M [n]
(if (zero? n) 0 (- n (F (M (dec n))))))
(defn F [n]
(if (zero? n) 1 (- n (M (F (dec n))))))</lang>
CoffeeScript
<lang coffeescript> F = (n) ->
if n is 0 then 1 else n - M F n - 1
M = (n) ->
if n is 0 then 0 else n - F M n - 1
console.log [0...20].map F console.log [0...20].map M </lang>
- Output:
<lang> > coffee mutual_recurse.coffee [ 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12 ] [ 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12 ] </lang>
Common Lisp
<lang lisp>(defun m (n)
(if (zerop n) 0 (- n (f (m (- n 1))))))
(defun f (n)
(if (zerop n) 1 (- n (m (f (- n 1))))))</lang>
D
<lang d>import std.stdio, std.algorithm, std.range;
int male(in int n) pure nothrow {
return n ? n - male(n - 1).female : 0;
}
int female(in int n) pure nothrow {
return n ? n - female(n - 1).male : 1;
}
void main() {
20.iota.map!female.writeln; 20.iota.map!male.writeln;
}</lang>
- Output:
[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12] [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12]
Déjà Vu
<lang dejavu>F n: if n: - n M F -- n else: 1
M n: if n: - n F M -- n else: 0
for i range 0 10: !.( M i F i )</lang>
- Output:
0 1 0 1 1 2 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 6
Dart
<lang dart>int M(int n) => n==0?1:n-F(M(n-1)); int F(int n) => n==0?0:n-M(F(n-1));
main() {
String f="",m=""; for(int i=0;i<20;i++) { m+="${M(i)} "; f+="${F(i)} "; } print("M: $m"); print("F: $f");
}</lang>
Delphi
<lang Delphi> unit Hofstadter;
interface
type
THofstadterFemaleMaleSequences = class public class function F(n: Integer): Integer; class function M(n: Integer): Integer; end;
implementation
class function THofstadterFemaleMaleSequences.F(n: Integer): Integer; begin
Result:= 1; if (n > 0) then Result:= n - M(F(n-1));
end;
class function THofstadterFemaleMaleSequences.M(n: Integer): Integer; begin
Result:= 0; if (n > 0) then Result:= n - F(M(n - 1));
end;
end. </lang>
E
In E, nouns (variable names) always refer to preceding definitions, so to have mutual recursion, either one must be forward-declared or we must use a recursive def construct. Either one of these is syntactic sugar for first binding the noun to an E promise (a reference with an undetermined target), then resolving the promise to the value.
Recursive def:
<lang e>def [F, M] := [
fn n { if (n <=> 0) { 1 } else { n - M(F(n - 1)) } }, fn n { if (n <=> 0) { 0 } else { n - F(M(n - 1)) } },
]</lang>
Forward declaration:
<lang e>def M def F(n) { return if (n <=> 0) { 1 } else { n - M(F(n - 1)) } } bind M(n) { return if (n <=> 0) { 0 } else { n - F(M(n - 1)) } }</lang>
def M
binds M to a promise, and stashes the resolver for that promise where bind
can get to it. When def F...
is executed, the function F closes over the promise which is the value of M. bind M...
uses the resolver to resolve M to the provided definition. The recursive def operates similarly, except that it constructs promises for every variable on the left side ([F, M]
), executes the right side ([fn ..., fn ...]
) and collects the values, then resolves each promise to its corresponding value.
But you don't have to worry about that to use it.
Eiffel
<lang Eiffel> class APPLICATION
create make
feature
make -- Test of the mutually recursive functions Female and Male. do across 0 |..| 19 as c loop io.put_string (Female (c.item).out + " ") end io.new_line across 0 |..| 19 as c loop io.put_string (Male (c.item).out + " ") end end
Female (n: INTEGER): INTEGER -- Female sequence of the Hofstadter Female and Male sequences. require n_not_negative: n >= 0 do Result := 1 if n /= 0 then Result := n - Male (Female (n - 1)) end end
Male (n: INTEGER): INTEGER -- Male sequence of the Hofstadter Female and Male sequences. require n_not_negative: n >= 0 do Result := 0 if n /= 0 then Result := n - Female (Male (n - 1)) end end
end </lang>
- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
Elixir
<lang elixir>defmodule MutualRecursion do
def f(0), do: 1 def f(n), do: n - m(f(n - 1)) def m(0), do: 0 def m(n), do: n - f(m(n - 1))
end
IO.inspect Enum.map(0..19, fn n -> MutualRecursion.f(n) end) IO.inspect Enum.map(0..19, fn n -> MutualRecursion.m(n) end)</lang>
- Output:
[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12] [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12]
Erlang
<lang erlang>-module(mutrec). -export([mutrec/0, f/1, m/1]).
f(0) -> 1; f(N) -> N - m(f(N-1)).
m(0) -> 0; m(N) -> N - f(m(N-1)).
mutrec() -> lists:map(fun(X) -> io:format("~w ", [f(X)]) end, lists:seq(0,19)), io:format("~n", []), lists:map(fun(X) -> io:format("~w ", [m(X)]) end, lists:seq(0,19)), io:format("~n", []).</lang>
Euphoria
<lang Euphoria>integer idM, idF
function F(integer n)
if n = 0 then return 1 else return n - call_func(idM,{F(n-1)}) end if
end function
idF = routine_id("F")
function M(integer n)
if n = 0 then return 0 else return n - call_func(idF,{M(n-1)}) end if
end function
idM = routine_id("M")</lang>
F#
<lang fsharp>let rec f n =
match n with | 0 -> 1 | _ -> n - (m (f (n-1)))
and m n =
match n with | 0 -> 0 | _ -> n - (f (m (n-1)))</lang>
Like OCaml, the let rec f .. and m ...
construct indicates that the functions call themselves (rec
) and each other (and
).
Factor
In Factor, if you need a word before it's defined, you have to DEFER:
it.
<lang>DEFER: F
- M ( n -- n' ) dup 0 = [ dup 1 - M F - ] unless ;
- F ( n -- n' ) dup 0 = [ drop 1 ] [ dup 1 - F M - ] if ;</lang>
FALSE
<lang false>[$[$1-f;!m;!-1-]?1+]f: [$[$1-m;!f;!- ]? ]m: [0[$20\>][\$@$@!." "1+]#%%]t:
f; t;!"
"m; t;!</lang>
Fantom
<lang fantom> class Main {
static Int f (Int n) { if (n <= 0) // ensure n > 0 return 1 else return n - m(f(n-1)) }
static Int m (Int n) { if (n <= 0) // ensure n > 0 return 0 else return n - f(m(n-1)) }
public static Void main () { 50.times |Int n| { echo (f(n)) } }
} </lang>
Forth
Forward references required for mutual recursion may be set up using DEFER. <lang forth>defer m
- f ( n -- n )
dup 0= if 1+ exit then dup 1- recurse m - ;
- noname ( n -- n )
dup 0= if exit then dup 1- recurse f - ;
is m
- test ( xt n -- ) cr 0 do i over execute . loop drop ;
' m defer@ 20 test \ 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 ' f 20 test \ 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12</lang>
Fortran
As long as the code of the two functions is inside the same "block" (module or program) we don't need special care. Otherwise, we should "load" at least the interface of the other function (each module will load mutually the other; of course the compiler won't enter in a infinite loop), e.g. by using a "use" (we do that if M and F function are inside different modules)
<lang fortran>module MutualRec
implicit none
contains
pure recursive function m(n) result(r) integer :: r integer, intent(in) :: n if ( n == 0 ) then r = 0 return end if r = n - f(m(n-1)) end function m pure recursive function f(n) result(r) integer :: r integer, intent(in) :: n if ( n == 0 ) then r = 1 return end if r = n - m(f(n-1)) end function f
end module</lang>
I've added the attribute pure so that we can use them in a forall statement.
<lang fortran>program testmutrec
use MutualRec implicit none
integer :: i integer, dimension(20) :: a = (/ (i, i=0,19) /), b = (/ (i, i=0,19) /) integer, dimension(20) :: ra, rb forall(i=1:20) ra(i) = m(a(i)) rb(i) = f(b(i)) end forall
write(*,'(20I3)') rb write(*,'(20I3)') ra
end program testmutrec</lang>
FreeBASIC
<lang freebasic>' FB 1.05.0 Win64
' Need forward declaration of M as it's used ' by F before its defined Declare Function M(n As Integer) As Integer
Function F(n As Integer) As Integer
If n = 0 Then Return 1 End If Return n - M(F(n - 1))
End Function
Function M(n As Integer) As Integer
If n = 0 Then Return 0 End If Return n - F(M(n - 1))
End Function
Dim As Integer n = 24 Print "n :"; For i As Integer = 0 to n : Print Using "###"; i; : Next Print Print String(78, "-") Print "F :"; For i As Integer = 0 To n : Print Using "###"; F(i); : Next Print Print "M :"; For i As Integer = 0 To n : Print Using "###"; M(i); : Next Print Print "Press any key to quit" Sleep</lang>
- Output:
n : 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ------------------------------------------------------------------------------ F : 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 13 14 14 15 M : 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12 13 14 14 15
Go
It just works. No special pre-declaration is necessary. <lang go>package main import "fmt"
func F(n int) int {
if n == 0 { return 1 } return n - M(F(n-1))
}
func M(n int) int {
if n == 0 { return 0 } return n - F(M(n-1))
}
func main() {
for i := 0; i < 20; i++ { fmt.Printf("%2d ", F(i)) } fmt.Println() for i := 0; i < 20; i++ { fmt.Printf("%2d ", M(i)) } fmt.Println()
}</lang>
Groovy
Solution: <lang groovy>def f, m // recursive closures must be declared before they are defined f = { n -> n == 0 ? 1 : n - m(f(n-1)) } m = { n -> n == 0 ? 0 : n - f(m(n-1)) }</lang>
Test program: <lang groovy>println 'f(0..20): ' + (0..20).collect { f(it) } println 'm(0..20): ' + (0..20).collect { m(it) }</lang>
- Output:
f(0..20): [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 13] m(0..20): [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12]
Haskell
Haskell's definitions constructs (at the top level, or inside a let
or where
construct) are always mutually-recursive:
<lang haskell>f 0 = 1
f n | n > 0 = n - m (f $ n-1)
m 0 = 0 m n | n > 0 = n - f (m $ n-1)
main = do
print $ map f [0..19] print $ map m [0..19]</lang>
Icon and Unicon
<lang Icon>procedure main(arglist) every write(F(!arglist)) # F of all arguments end
procedure F(n) if integer(n) >= 0 then
return (n = 0, 1) | n - M(F(n-1))
end
procedure M(n) if integer(n) >= 0 then
return (0 = n) | n - F(M(n-1))
end</lang>
Idris
<lang idris>mutual {
F : Nat -> Nat F Z = (S Z) F (S n) = (S n) `minus` M(F(n))
M : Nat -> Nat M Z = Z M (S n) = (S n) `minus` F(M(n))
}</lang>
Io
<lang Io>f := method(n, if( n == 0, 1, n - m(f(n-1)))) m := method(n, if( n == 0, 0, n - f(m(n-1))))
Range 0 to(19) map(n,f(n)) println 0 to(19) map(n,m(n)) println</lang>
- Output:
list(1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12) list(0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12)
J
<lang j>F =: 1:`(- M @ $: @ <:) @.* M."0 M =: 0:`(- F @ $: @ <:) @.* M."0</lang>
Example use:
<lang j> F i. 20 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12</lang>
That said, note that numbers are defined recursively, so other some approaches using numbers which give equivalent results should be acceptable.
Java
<lang java5>public static int f(final int n) {
return n == 0 ? 1 : n - m(f(n - 1));
}
public static int m(final int n) {
return n == 0 ? 0 : n - f(m(n - 1));
}
public static void main(final String args[]) {
for (int i = 0; i < 20; i++) System.out.println(f(i)); System.out.println(); for (i = 0; i < 20; i++) System.out.println(m(i));
}</lang>
JavaScript
<lang JavaScript>function f(num) {
return (num === 0) ? 1 : num - m(f(num - 1));
}
function m(num) {
return (num === 0) ? 0 : num - f(m(num - 1));
}
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map( function (x, i) { return m + i; } );
}
var a = range(0, 19);
//return a new array of the results and join with commas to print console.log(a.map(function (n) { return f(n); }).join(', ')); console.log(a.map(function (n) { return m(n); }).join(', '));</lang>
- Output:
1,1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12 0,0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12
ES6 implementation <lang JavaScript>var f = num => (num === 0) ? 1 : num - m(f(num - 1)); var m = num => (num === 0) ? 0 : num - f(m(num - 1));
function range(m, n) {
return Array.apply(null, Array(n - m + 1)).map( function (x, i) { return m + i; } );
}
var a = range(0, 19);
//return a new array of the results and join with commas to print console.log(a.map(n => f(n)).join(', ')); console.log(a.map(n => m(n)).join(', '));</lang>
More ES6 implementation
<lang JavaScript>var range = (m, n) => Array(... Array(n - m + 1)).map((x, i) => m + i)</lang>
jq
jq supports mutual recursion but requires functions to be defined before they are used. In the present case, this can be accomplished by defining an inner function.
He we define F and M as arity-0 filters: <lang jq> def M:
def F: if . == 0 then 1 else . - ((. - 1) | F | M) end; if . == 0 then 0 else . - ((. - 1) | M | F) end;
def F:
if . == 0 then 1 else . - ((. - 1) | F | M) end;</lang>Example:<lang jq>
[range(0;20) | F], [range(0;20) | M]</lang><lang sh>$ jq -n -c -f Mutual_recursion.jq
[1,1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12] [0,0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12]</lang>
Julia
<lang julia>F(n) = n < 1 ? one(n) : n - M(F(n - 1)) M(n) = n < 1 ? zero(n) : n - F(M(n - 1))</lang>
- Output:
julia> [F(i) for i = 0:19], [M(i) for i = 0:19] ([1,1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12],[0,0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12])
Kotlin
<lang scala>// version 1.0.6
fun f(n: Int): Int =
when { n == 0 -> 1 else -> n - m(f(n - 1)) }
fun m(n: Int): Int =
when { n == 0 -> 0 else -> n - f(m(n - 1)) }
fun main(args: Array<String>) {
val n = 24 print("n :") for (i in 0..n) print("%3d".format(i)) println() println("-".repeat(78)) print("F :") for (i in 0..24) print("%3d".format(f(i))) println() print("M :") for (i in 0..24) print("%3d".format(m(i))) println()
}</lang>
- Output:
n : 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ------------------------------------------------------------------------------ F : 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 13 14 14 15 M : 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12 13 14 14 15
Liberty BASIC
<lang lb> print "F sequence." for i = 0 to 20 print f(i);" "; next print print "M sequence." for i = 0 to 20 print m(i);" "; next
end
function f(n)
if n = 0 then f = 1 else f = n - m(f(n - 1)) end if end function
function m(n)
if n = 0 then m = 0 else m = n - f(m(n - 1)) end if end function
</lang>
- Output:
F sequence. 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 M sequence. 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12
LibreOffice Basic
<lang LibreOffice Basic>'// LibreOffice Basic Implementation of Hofstadter Female-Male sequences
'// Utility functions sub setfont(strfont) ThisComponent.getCurrentController.getViewCursor.charFontName = strfont end sub
sub newline oVC = thisComponent.getCurrentController.getViewCursor oText = oVC.text oText.insertControlCharacter(oVC, com.sun.star.text.ControlCharacter.PARAGRAPH_BREAK, False) end sub
sub out(sString) oVC = ThisComponent.getCurrentController.getViewCursor oText = oVC.text oText.insertString(oVC, sString, false) end sub
sub outln(optional sString) if not ismissing (sString) then out(sString) newline end sub
function intformat(n as integer,nlen as integer) as string dim nstr as string nstr = CStr(n) while len(nstr) < nlen nstr = " " & nstr wend intformat = nstr end function
'// Hofstadter Female-Male function definitions function F(n as long) as long if n = 0 Then F = 1 elseif n > 0 Then F = n - M(F(n - 1)) endif end function
function M(n) if n = 0 Then M = 0 elseif n > 0 Then M = n - F(M(n - 1)) endif end function
'// Hofstadter Female Male sequence demo routine sub Hofstadter_Female_Male_Demo '// Introductory Text setfont("LM Roman 10") outln("Rosetta Code Hofstadter Female and Male Sequence Challenge") outln out("Two functions are said to be mutually recursive if the first calls the second,") outln(" and in turn the second calls the first.") out("Write two mutually recursive functions that compute members of the Hofstadter") outln(" Female and Male sequences defined as:") outln setfont("LM Mono Slanted 10") outln(chr(9)+"F(0) = 1 ; M(0)=0") outln(chr(9)+"F(n) = n - M(F(n-1)), n > 0") outln(chr(9)+"M(n) = n - F(M(n-1)), n > 0") outln '// Sequence Generation const nmax as long = 20 dim n as long setfont("LM Mono 10") out("n = " for n = 0 to nmax out(" " + intformat(n, 2)) next n outln out("F(n) = " for n = 0 to nmax out(" " + intformat(F(n),2)) next n outln out("M(n) = " for n = 0 to nmax out(" " + intformat(M(n), 2)) next n outln
end sub
Output
n = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 F(n) = 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 M(n) = 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12 </lang>
Logo
Like Lisp, symbols in Logo are late-bound so no special syntax is required for forward references.
<lang logo>to m :n
if 0 = :n [output 0] output :n - f m :n-1
end to f :n
if 0 = :n [output 1] output :n - m f :n-1
end
show cascade 20 [lput m #-1 ?] [] [1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12] show cascade 20 [lput f #-1 ?] [] [0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12]</lang>
LSL
To test it yourself; rez a box on the ground, and add the following as a New Script. <lang LSL>integer iDEPTH = 100; integer f(integer n) { if(n==0) { return 1; } else { return n-m(f(n - 1)); } } integer m(integer n) { if(n==0) { return 0; } else { return n-f(m(n - 1)); } } default { state_entry() { integer x = 0; string s = ""; for(x=0 ; x<iDEPTH ; x++) { s += (string)(f(x))+" "; } llOwnerSay(llList2CSV(llParseString2List(s, [" "], []))); s = ""; for(x=0 ; x<iDEPTH ; x++) { s += (string)(m(x))+" "; } llOwnerSay(llList2CSV(llParseString2List(s, [" "], []))); } }</lang>
- Output:
1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45, 46, 46, 47, 48, 48, 49, 50, 50, 51, 51, 52, 53, 53, 54, 55, 55, 56, 56, 57, 58, 58, 59, 59, 60, 61, 61 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45, 46, 46, 47, 48, 48, 49, 50, 50, 51, 51, 52, 53, 53, 54, 54, 55, 56, 56, 57, 58, 58, 59, 59, 60, 61, 61
Lua
<lang lua> function m(n) return n > 0 and n - f(m(n-1)) or 0 end function f(n) return n > 0 and n - m(f(n-1)) or 1 end</lang>
It is important to note, that if m and f are to be locally scoped functions rather than global, that they would need to be forward declared:
<lang lua> local m,n function m(n) return n > 0 and n - f(m(n-1)) or 0 end function f(n) return n > 0 and n - m(f(n-1)) or 1 end</lang>
M4
<lang m4>define(`female',`ifelse(0,$1,1,`eval($1 - male(female(decr($1))))')')dnl define(`male',`ifelse(0,$1,0,`eval($1 - female(male(decr($1))))')')dnl define(`loop',`ifelse($1,$2,,`$3($1) loop(incr($1),$2,`$3')')')dnl loop(0,20,`female') loop(0,20,`male')</lang>
Mathematica
Without caching: <lang Mathematica>f[0]:=1 m[0]:=0 f[n_]:=n-m[f[n-1]] m[n_]:=n-f[m[n-1]]</lang> With caching: <lang Mathematica>f[0]:=1 m[0]:=0 f[n_]:=f[n]=n-m[f[n-1]] m[n_]:=m[n]=n-f[m[n-1]]</lang> Example finding f(1) to f(30) and m(1) to m(30): <lang Mathematica>m /@ Range[30] f /@ Range[30]</lang> gives back: <lang Mathematica>{0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12,12,13,14,14,15,16,16,17,17,18,19} {1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12,13,13,14,14,15,16,16,17,17,18,19}</lang>
MATLAB
female.m: <lang MATLAB>function Fn = female(n)
if n == 0 Fn = 1; return end Fn = n - male(female(n-1));
end</lang>
male.m: <lang MATLAB>function Mn = male(n)
if n == 0 Mn = 0; return end Mn = n - female(male(n-1));
end</lang>
- Output:
<lang MATLAB>>> n = (0:10); >> arrayfun(@female,n)
ans =
1 1 2 2 3 3 4 5 5 6 6
>> arrayfun(@male,n)
ans =
0 0 1 2 2 3 4 4 5 6 6</lang>
Maxima
<lang maxima>f[0]: 1$ m[0]: 0$ f[n] := n - m[f[n - 1]]$ m[n] := n - f[m[n - 1]]$
makelist(f[i], i, 0, 10); [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6]
makelist(m[i], i, 0, 10); [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6]
remarray(m, f)$
f(n) := if n = 0 then 1 else n - m(f(n - 1))$ m(n) := if n = 0 then 0 else n - f(m(n - 1))$
makelist(f(i), i, 0, 10); [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6]
makelist(m(i), i, 0, 10); [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6]
remfunction(f, m)$</lang>
Mercury
<lang>
- - module mutual_recursion.
- - interface.
- - import_module io.
- - pred main(io::di, io::uo) is det.
- - implementation.
- - import_module int, list.
main(!IO) :-
io.write(list.map(f, 0..19), !IO), io.nl(!IO), io.write(list.map(m, 0..19), !IO), io.nl(!IO).
- - func f(int) = int.
f(N) = ( if N = 0 then 1 else N - m(f(N - 1)) ).
- - func m(int) = int.
m(N) = ( if N = 0 then 0 else N - f(m(N - 1)) ). </lang>
MMIX
<lang mmix> LOC Data_Segment
GREG @ NL BYTE #a,0 GREG @ buf OCTA 0,0
t IS $128 Ja IS $127
LOC #1000
GREG @ // print 2 digits integer with trailing space to StdOut // reg $3 contains int to be printed bp IS $71 0H GREG #0000000000203020 prtInt STO 0B,buf % initialize buffer LDA bp,buf+7 % points after LSD % REPEAT 1H SUB bp,bp,1 % move buffer pointer DIV $3,$3,10 % divmod (x,10) GET t,rR % get remainder INCL t,'0' % make char digit STB t,bp % store digit PBNZ $3,1B % UNTIL no more digits LDA $255,bp TRAP 0,Fputs,StdOut % print integer GO Ja,Ja,0 % 'return'
// Female function F GET $1,rJ % save return addr PBNZ $0,1F % if N != 0 then F N INCL $0,1 % F 0 = 1 PUT rJ,$1 % restore return addr POP 1,0 % return 1 1H SUBU $3,$0,1 % N1 = N - 1 PUSHJ $2,F % do F (N - 1) ADDU $3,$2,0 % place result in arg. reg. PUSHJ $2,M % do M F ( N - 1) PUT rJ,$1 % restore ret addr SUBU $0,$0,$2 POP 1,0 % return N - M F ( N - 1 )
// Male function M GET $1,rJ PBNZ $0,1F PUT rJ,$1 POP 1,0 % return M 0 = 0 1H SUBU $3,$0,1 PUSHJ $2,M ADDU $3,$2,0 PUSHJ $2,F PUT rJ,$1 SUBU $0,$0,$2 POP 1,0 $ return N - F M ( N - 1 )
// do a female run Main SET $1,0 % for (i=0; i<25; i++){ 1H ADDU $4,$1,0 % PUSHJ $3,F % F (i) GO Ja,prtInt % print F (i) INCL $1,1 CMP t,$1,25 PBNZ t,1B % } LDA $255,NL TRAP 0,Fputs,StdOut // do a male run SET $1,0 % for (i=0; i<25; i++){ 1H ADDU $4,$1,0 % PUSHJ $3,M % M (i) GO Ja,prtInt % print M (i) INCL $1,1 CMP t,$1,25 PBNZ t,1B % } LDA $255,NL TRAP 0,Fputs,StdOut TRAP 0,Halt,0</lang>
- Output:
~/MIX/MMIX/Rosetta> mmix mutualrecurs1 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 13 14 14 15 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12 13 14 14 15
Nemerle
<lang Nemerle>using System; using System.Console;
module Hofstadter {
F(n : int) : int { |0 => 1 |_ => n - M(F(n - 1)) } M(n : int) : int { |0 => 0 |_ => n - F(M(n - 1)) } Main() : void { foreach (n in [0 .. 20]) Write("{0} ", F(n)); WriteLine(); foreach (n in [0 .. 20]) Write("{0} ", M(n)); }
}</lang>
Nim
<lang nim>proc m(n): int
proc f(n): int =
if n == 0: 1 else: n - m(f(n-1))
proc m(n): int =
if n == 0: 0 else: n - f(m(n-1))
for i in 1 .. 10:
echo f(i) echo m(i)</lang>
Objective-C
Objective-C has prior declaration rules similar to those stated above for C, for C-like types. In this example we show the use of a two class method; this works since we need an interface block that is like declaration of functions in C code.
<lang objc>#import <Foundation/Foundation.h>
@interface Hofstadter : NSObject + (int)M: (int)n; + (int)F: (int)n; @end
@implementation Hofstadter + (int)M: (int)n {
if ( n == 0 ) return 0; return n - [self F: [self M: (n-1)]];
} + (int)F: (int)n {
if ( n == 0 ) return 1; return n - [self M: [self F: (n-1)]];
} @end
int main() {
int i;
for(i=0; i < 20; i++) { printf("%3d ", [Hofstadter F: i]); } printf("\n"); for(i=0; i < 20; i++) { printf("%3d ", [Hofstadter M: i]); } printf("\n"); return 0;
}</lang>
Objeck
<lang objeck> class MutualRecursion {
function : Main(args : String[]) ~ Nil { for(i := 0; i < 20; i+=1;) { f(i)->PrintLine(); }; "---"->PrintLine(); for (i := 0; i < 20; i+=1;) { m(i)->PrintLine(); }; } function : f(n : Int) ~ Int { return n = 0 ? 1 : n - m(f(n - 1)); } function : m(n : Int) ~ Int { return n = 0 ? 0 : n - f(m(n - 1)); }
} </lang>
OCaml
<lang ocaml>let rec f = function
| 0 -> 1 | n -> n - m(f(n-1))
and m = function
| 0 -> 0 | n -> n - f(m(n-1))
- </lang>
The let rec f ... and m ...
construct indicates that the functions call themselves (rec
) and each other (and
).
Octave
We don't need to pre-declare or specify in some other way a function that will be defined later; but both must be declared before their use.
(The code is written to handle vectors, as the testing part shows)
<lang octave>function r = F(n)
for i = 1:length(n) if (n(i) == 0) r(i) = 1; else r(i) = n(i) - M(F(n(i)-1)); endif endfor
endfunction
function r = M(n)
for i = 1:length(n) if (n(i) == 0) r(i) = 0; else r(i) = n(i) - F(M(n(i)-1)); endif endfor
endfunction</lang>
<lang octave># testing ra = F([0:19]); rb = M([0:19]); disp(ra); disp(rb);</lang>
Oforth
Oforth can declare methods objects without any implementation. This allows to implement mutual recursion. This does not work with functions (declaration and implementation must be together).
<lang Oforth>Method new: M
Integer method: F
self 0 == ifTrue: [ 1 return ] self self 1 - F M - ;
Integer method: M
self 0 == ifTrue: [ 0 return ] self self 1 - M F - ;
0 20 seqFrom map(#F) println 0 20 seqFrom map(#M) println</lang>
- Output:
[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 13] [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12]
Order
Since Order is powered by the C preprocessor, definitions follow the same rule as CPP macros: they can appear in any order relative to each other as long as all are defined before the ORDER_PP block that calls them.
<lang c>#include <order/interpreter.h>
- define ORDER_PP_DEF_8f \
ORDER_PP_FN(8fn(8N, \
8if(8is_0(8N), \ 1, \ 8sub(8N, 8m(8f(8dec(8N)))))))
- define ORDER_PP_DEF_8m \
ORDER_PP_FN(8fn(8N, \
8if(8is_0(8N), \ 0, \ 8sub(8N, 8f(8m(8dec(8N)))))))
//Test ORDER_PP(8for_each_in_range(8fn(8N, 8print(8f(8N))), 0, 19)) ORDER_PP(8for_each_in_range(8fn(8N, 8print(8m(8N))), 0, 19))</lang>
Oz
<lang oz>declare
fun {F N} if N == 0 then 1 elseif N > 0 then N - {M {F N-1}} end end
fun {M N} if N == 0 then 0 elseif N > 0 then N - {F {M N-1}} end end
in
{Show {Map {List.number 0 9 1} F}} {Show {Map {List.number 0 9 1} M}}</lang>
PARI/GP
<lang parigp>F(n)=if(n,n-M(F(n-1)),1) M(n)=if(n,n-F(M(n-1)),0)</lang>
Pascal
In Pascal we need to pre-declare functions/procedures; to do so, the forward statement is used.
<lang pascal>Program MutualRecursion;
{M definition comes after F which uses it} function M(n : Integer) : Integer; forward;
function F(n : Integer) : Integer; begin
if n = 0 then F := 1 else F := n - M(F(n-1));
end;
function M(n : Integer) : Integer; begin
if n = 0 then M := 0 else M := n - F(M(n-1));
end;
var
i : Integer;
begin
for i := 0 to 19 do begin write(F(i) : 4) end; writeln; for i := 0 to 19 do begin write(M(i) : 4) end; writeln;
end.</lang>
Perl
<lang perl>sub F { my $n = shift; $n ? $n - M(F($n-1)) : 1 } sub M { my $n = shift; $n ? $n - F(M($n-1)) : 0 }
- Usage:
foreach my $sequence (\&F, \&M) {
print join(' ', map $sequence->($_), 0 .. 19), "\n";
}</lang>
- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
Perl 6
A direct translation of the definitions of and : <lang perl6>multi F(0) { 1 }; multi M(0) { 0 } multi F(\𝑛) { 𝑛 - M(F(𝑛 - 1)) } multi M(\𝑛) { 𝑛 - F(M(𝑛 - 1)) }
say map &F, ^20; say map &M, ^20;</lang>
- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
Phix
<lang Phix>function F(integer n)
return iff(n?n-M(F(n-1)):1)
end function
function M(integer n)
return iff(n?n-F(M(n-1)):0)
end function
for i=0 to 20 do
printf(1," %d",F(i))
end for printf(1,"\n") for i=0 to 20 do
printf(1," %d",M(i))
end for</lang> You can also explicitly declare forward routines, which may sometimes be necessary for routines with optional or named parameters, or just make something easier to understand. <lang Phix>forward function F(integer n) forward function M(integer n)</lang>
- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12
PHP
<lang php><?php function F($n) {
if ( $n == 0 ) return 1; return $n - M(F($n-1));
}
function M($n) {
if ( $n == 0) return 0; return $n - F(M($n-1));
}
$ra = array(); $rb = array(); for($i=0; $i < 20; $i++) {
array_push($ra, F($i)); array_push($rb, M($i));
} echo implode(" ", $ra) . "\n"; echo implode(" ", $rb) . "\n"; ?></lang>
PicoLisp
<lang PicoLisp>(de f (N)
(if (=0 N) 1 (- N (m (f (dec N)))) ) )
(de m (N)
(if (=0 N) 0 (- N (f (m (dec N)))) ) )</lang>
PL/I
<lang PL/I>test: procedure options (main);
M: procedure (n) returns (fixed) recursive; /* 8/1/2010 */
declare n fixed; if n <= 0 then return (0); else return ( n - F(M(n-1)) );
end M;
F: procedure (n) returns (fixed) recursive;
declare n fixed; if n <= 0 then return (1); else return ( n - M(F(n-1)) );
end F;
declare i fixed;
do i = 1 to 15; put skip list ( F(i), M(i) ); end;
end test;</lang>
PostScript
<lang> /female{ /n exch def n 0 eq {1} { n n 1 sub female male sub }ifelse }def
/male{ /n exch def n 0 eq {0} { n n 1 sub male female sub }ifelse }def </lang>
<lang postscript> /F { {
{0 eq} {pop 1} is? {0 gt} {dup 1 sub F M sub} is?
} cond }.
/M { {
{0 eq} {pop 0} is? {0 gt} {dup 1 sub M F sub} is?
} cond }.
</lang>
PowerShell
<lang powershell>function F($n) {
if ($n -eq 0) { return 1 } return $n - (M (F ($n - 1)))
}
function M($n) {
if ($n -eq 0) { return 0 } return $n - (F (M ($n - 1)))
}</lang>
Prolog
<lang prolog>female(0,1). female(N,F) :- N>0, N1 is N-1, female(N1,R), male(R, R1), F is N-R1.
male(0,0). male(N,F) :- N>0, N1 is N-1, male(N1,R), female(R, R1), F is N-R1.</lang>
<lang prolog>flist(S) :- for(X, 0, S), female(X, R), format('~d ', [R]), fail. mlist(S) :- for(X, 0, S), male(X, R), format('~d ', [R]), fail.</lang>
Testing
| ?- flist(19). 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 no | ?- mlist(19). 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
Pure
The Pure definitions very closely maps to the mathematical definitions.
<lang pure>F 0 = 1; M 0 = 0; F n = n - M(F(n-1)) if n>0; M n = n - F(M(n-1)) if n>0;</lang>
<lang pure>> let females = map F (0..10); females; [1,1,2,2,3,3,4,5,5,6,6] > let males = map M (0..10); males; [0,0,1,2,2,3,4,4,5,6,6]</lang>
PureBasic
<lang PureBasic>Declare M(n)
Procedure F(n)
If n = 0 ProcedureReturn 1 ElseIf n > 0 ProcedureReturn n - M(F(n - 1)) EndIf
EndProcedure
Procedure M(n)
If n = 0 ProcedureReturn 0 ElseIf n > 0 ProcedureReturn n - F(M(n - 1)) EndIf
EndProcedure
Define i If OpenConsole()
For i = 0 To 19 Print(Str(F(i))) If i = 19 Continue EndIf Print(", ") Next PrintN("") For i = 0 To 19 Print(Str(M(i))) If i = 19 Continue EndIf Print(", ") Next Print(#CRLF$ + #CRLF$ + "Press ENTER to exit") Input() CloseConsole()
EndIf</lang>
- Output:
1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12
Python
.
<lang python>def F(n): return 1 if n == 0 else n - M(F(n-1)) def M(n): return 0 if n == 0 else n - F(M(n-1))
print ([ F(n) for n in range(20) ]) print ([ M(n) for n in range(20) ])</lang>
- Output:
[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12] [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12]
In python there is no need to pre-declare M for it to be used in the definition of F. (However M must be defined before F calls it).
R
<lang R>F <- function(n) ifelse(n == 0, 1, n - M(F(n-1))) M <- function(n) ifelse(n == 0, 0, n - F(M(n-1)))</lang>
<lang R>print.table(lapply(0:19, M)) print.table(lapply(0:19, F))</lang>
REBOL
<lang REBOL>REBOL [
Title: "Mutual Recursion" Date: 2009-12-14 Author: oofoe URL: http://rosettacode.org/wiki/Mutual_Recursion
References: [1] ]
f: func [ "Female." n [integer!] "Value." ] [either 0 = n [1][n - m f n - 1]]
m: func [ "Male." n [integer!] "Value." ] [either 0 = n [0][n - f m n - 1]]
fs: [] ms: [] for i 0 19 1 [append fs f i append ms m i] print ["F:" mold fs crlf "M:" mold ms]</lang>
- Output:
F: [1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12] M: [0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12]
Racket
<lang Racket>#lang racket (define (F n)
(if (>= 0 n) 1 (- n (M (F (sub1 n))))))
(define (M n)
(if (>= 0 n) 0 (- n (F (M (sub1 n))))))</lang>
REXX
vanilla
This version uses vertical formatting of the output. <lang rexx>/*REXX program shows mutual recursion (via the Hofstadter Male and Female sequences). */ parse arg lim .; if lim= then lim=40; w=length(lim); pad=left(, 20)
do j=0 to lim; jj=right(j, w); ff=right(F(j), w); mm=right(M(j), w) say pad 'F('jj") =" ff pad 'M('jj") =" mm end /*j*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ F: procedure; parse arg n; if n==0 then return 1; return n - M( F(n-1) ) M: procedure; parse arg n; if n==0 then return 0; return n - F( M(n-1) )</lang> output when using the default input of: 40
F( 0) = 1 M( 0) = 0 F( 1) = 1 M( 1) = 0 F( 2) = 2 M( 2) = 1 F( 3) = 2 M( 3) = 2 F( 4) = 3 M( 4) = 2 F( 5) = 3 M( 5) = 3 F( 6) = 4 M( 6) = 4 F( 7) = 5 M( 7) = 4 F( 8) = 5 M( 8) = 5 F( 9) = 6 M( 9) = 6 F(10) = 6 M(10) = 6 F(11) = 7 M(11) = 7 F(12) = 8 M(12) = 7 F(13) = 8 M(13) = 8 F(14) = 9 M(14) = 9 F(15) = 9 M(15) = 9 F(16) = 10 M(16) = 10 F(17) = 11 M(17) = 11 F(18) = 11 M(18) = 11 F(19) = 12 M(19) = 12 F(20) = 13 M(20) = 12 F(21) = 13 M(21) = 13 F(22) = 14 M(22) = 14 F(23) = 14 M(23) = 14 F(24) = 15 M(24) = 15 F(25) = 16 M(25) = 16 F(26) = 16 M(26) = 16 F(27) = 17 M(27) = 17 F(28) = 17 M(28) = 17 F(29) = 18 M(29) = 18 F(30) = 19 M(30) = 19 F(31) = 19 M(31) = 19 F(32) = 20 M(32) = 20 F(33) = 21 M(33) = 20 F(34) = 21 M(34) = 21 F(35) = 22 M(35) = 22 F(36) = 22 M(36) = 22 F(37) = 23 M(37) = 23 F(38) = 24 M(38) = 24 F(39) = 24 M(39) = 24 F(40) = 25 M(40) = 25
with memoization
This version uses memoization as well as a horizontal (aligned) output format.
The optimization due to memoization is faster by many orders of magnitude.
<lang rexx>/*REXX program shows mutual recursion (via the Hofstadter Male and Female sequences). */
parse arg lim .; if lim== then lim=40 /*assume the default for LIM? */
w=length(lim); $m.=.; $m.0=0; $f.=.; $f.0=1; Js=; Fs=; Ms=
do j=0 to lim Js=Js right(j, w); Fs=Fs right(F(j), w); Ms=Ms right(M(j), w) end /*j*/
say 'Js=' Js /*display the list of Js to the term.*/ say 'Fs=' Fs /* " " " " Fs " " " */ say 'Ms=' Ms /* " " " " Ms " " " */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ F: procedure expose $m. $f.; parse arg n; if $f.n==. then $f.n=n-M(F(n-1)); return $f.n M: procedure expose $m. $f.; parse arg n; if $m.n==. then $m.n=n-F(M(n-1)); return $m.n</lang> output when using the default input of: 99
Js= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Fs= 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 13 14 14 15 16 16 17 17 18 19 19 20 21 21 22 22 23 24 24 25 25 26 27 27 28 29 29 30 30 31 32 32 33 34 34 35 35 36 37 37 38 38 39 40 40 41 42 42 43 43 44 45 45 46 46 47 48 48 49 50 50 51 51 52 53 53 54 55 55 56 56 57 58 58 59 59 60 61 61 Ms= 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12 13 14 14 15 16 16 17 17 18 19 19 20 20 21 22 22 23 24 24 25 25 26 27 27 28 29 29 30 30 31 32 32 33 33 34 35 35 36 37 37 38 38 39 40 40 41 42 42 43 43 44 45 45 46 46 47 48 48 49 50 50 51 51 52 53 53 54 54 55 56 56 57 58 58 59 59 60 61 61
with memoization, specific entry
This version is identical in function to the previous example, but it also can compute and
display a specific request (indicated by a negative number for the argument).
<lang rexx>/*REXX program shows mutual recursion (via the Hofstadter Male and Female sequences). */
/*───────────────── If LIM is negative, a single result is shown for the abs(lim) entry.*/
parse arg lim .; if lim== then lim=99; aLim=abs(lim) w=length(aLim); $m.=.; $m.0=0; $f.=.; $f.0=1; Js=; Fs=; Ms=
do j=0 to Alim Js=Js right(j, w); Fs=Fs right(F(j), w); Ms=Ms right(M(j), w) end /*j*/
if lim>0 then say 'Js=' Js; else say 'J('aLim")=" word(Js, aLim+1) if lim>0 then say 'Fs=' Fs; else say 'F('aLim")=" word(Fs, aLim+1) if lim>0 then say 'Ms=' Ms; else say 'M('aLim")=" word(Ms, aLim+1) exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ F: procedure expose $m. $f.; parse arg n; if $f.n==. then $f.n=n-M(F(n-1)); return $f.n M: procedure expose $m. $f.; parse arg n; if $m.n==. then $m.n=n-F(M(n-1)); return $m.n</lang> output when using the input of: -70000
J(70000)= 70000 F(70000)= 43262 M(70000)= 43262
output when using the input of a negative ¼ million: -250000
J(250000)= 250000 F(250000)= 154509 M(250000)= 154509
Ring
<lang ring> see "F sequence : " for i = 0 to 20
see "" + f(i) + " "
next see nl see "M sequence : " for i = 0 to 20
see "" + m(i) + " "
next
func f n
fr = 1 if n != 0 fr = n - m(f(n - 1)) ok return fr
func m n
mr = 0 if n != 0 mr = n - f(m(n - 1)) ok return mr
</lang>
Ruby
<lang ruby>def F(n)
n == 0 ? 1 : n - M(F(n-1))
end def M(n)
n == 0 ? 0 : n - F(M(n-1))
end
p (Array.new(20) {|n| F(n) }) p (Array.new(20) {|n| M(n) })</lang>
- Output:
[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12] [0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12]
In ruby there is no need to pre-declare M for it to be used in the definition of F. (However M must be defined before F calls it).
Run BASIC
<lang Runbasic>print "F sequence:"; for i = 0 to 20
print f(i);" ";
next i print :print "M sequence:"; for i = 0 to 20
print m(i);" ";
next i end
function f(n)
f = 1 if n <> 0 then f = n - m(f(n - 1))
end function
function m(n)
m = 0 if n <> 0 then m = n - f(m(n - 1))
end function</lang>
- Output:
F sequence:1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 M sequence:0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12
Rust
<lang rust>fn f(n: u32) -> u32 {
match n { 0 => 1, _ => n - m(f(n - 1)) }
}
fn m(n: u32) -> u32 {
match n { 0 => 0, _ => n - f(m(n - 1)) }
}
fn main() {
for i in (0..20).map(f) { print!("{} ", i); } println!("");
for i in (0..20).map(m) { print!("{} ", i); } println!("")
}</lang>
- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
S-lang
<lang S-lang>% Forward definitions: [also deletes any existing definition] define f(); define m();
define f(n) {
if (n == 0) return 1; else if (n < 0) error("oops"); return n - m(f(n - 1));
}
define m(n) {
if (n == 0) return 0; else if (n < 0) error("oops"); return n - f(m(n - 1));
}
foreach $1 ([0:19])
() = printf("%d ", f($1));
() = printf("\n"); foreach $1 ([0:19])
() = printf("%d ", m($1));
() = printf("\n");</lang>
- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
Sather
<lang sather>class MAIN is
f(n:INT):INT pre n >= 0 is if n = 0 then return 1; end; return n - m(f(n-1)); end;
m(n:INT):INT pre n >= 0 is if n = 0 then return 0; end; return n - f(m(n-1)); end;
main is loop i ::= 0.upto!(19); #OUT + #FMT("%2d ", f(i)); end; #OUT + "\n"; loop i ::= 0.upto!(19); #OUT + #FMT("%2d ", m(i)); end; end;
end;</lang>
There's no need to pre-declare F or M.
Scala
<lang scala>def F(n:Int):Int =
if (n == 0) 1 else n - M(F(n-1))
def M(n:Int):Int =
if (n == 0) 0 else n - F(M(n-1))
println((0 until 20).map(F).mkString(", ")) println((0 until 20).map(M).mkString(", "))</lang>
- Output:
1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12
Scheme
define
declarations are automatically mutually recursive:
<lang scheme>(define (F n)
(if (= n 0) 1 (- n (M (F (- n 1))))))
(define (M n)
(if (= n 0) 0 (- n (F (M (- n 1))))))</lang>
If you wanted to use a let
-like construct to create local bindings, you would do the following. The define
construct above is just a syntactic sugar for the following where the entire rest of the scope is used as the body.
<lang scheme>(letrec ((F (lambda (n)
(if (= n 0) 1 (- n (M (F (- n 1))))))) (M (lambda (n) (if (= n 0) 0 (- n (F (M (- n 1)))))))) (F 19)) # evaluates to 12</lang>
The letrec
indicates that the definitions can be recursive, and fact that we placed these two in the same letrec
block makes them mutually recursive.
Seed7
<lang seed7>$ include "seed7_05.s7i";
const func integer: m (in integer: n) is forward;
const func integer: f (in integer: n) is func
result var integer: res is 0; begin if n = 0 then res := 1; else res := n - m(f(n - 1)); end if; end func;
const func integer: m (in integer: n) is func
result var integer: res is 0; begin if n = 0 then res := 0; else res := n - f(m(n - 1)); end if; end func;
const proc: main is func
local var integer: i is 0; begin for i range 0 to 19 do write(f(i) lpad 3); end for; writeln; for i range 0 to 19 do write(m(i) lpad 3); end for; writeln; end func;</lang>
- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
Sidef
<lang ruby>func F(){} func M(){} F = func(n) { n > 0 ? (n - M(F(n-1))) : 1 } M = func(n) { n > 0 ? (n - F(M(n-1))) : 0 } [F, M].each { |seq|
}</lang>- Output:
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12
Smalltalk
Using block closure.
<lang smalltalk>|F M ra rb|
F := [ :n |
(n == 0) ifTrue: [ 1 ] ifFalse: [ n - (M value: (F value: (n-1))) ]
].
M := [ :n |
(n == 0) ifTrue: [ 0 ] ifFalse: [ n - (F value: (M value: (n-1))) ]
].
ra := OrderedCollection new. rb := OrderedCollection new. 0 to: 19 do: [ :i |
ra add: (F value: i). rb add: (M value: i)
].
ra displayNl. rb displayNl.</lang>
SNOBOL4
<lang SNOBOL4> define('f(n)') :(f_end) f f = eq(n,0) 1 :s(return)
f = n - m(f(n - 1)) :(return)
f_end
define('m(n)') :(m_end)
m m = eq(n,0) 0 :s(return)
m = n - f(m(n - 1)) :(return)
m_end
- # Test and display
L1 s1 = s1 m(i) ' ' ; s2 = s2 f(i) ' '
i = le(i,25) i + 1 :s(L1) output = 'M: ' s1; output = 'F: ' s2
end</lang>
- Output:
M: 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12 13 14 14 15 16 16 F: 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 13 14 14 15 16 16
SNUSP
The program shown calculates F(3) and demonstrates simple and mutual recursion. <lang SNUSP> /======\ F==!/=!\?\+# | />-<-\
\@\-@/@\===?/<# | |
$+++/======|====/ |
/=/ /+<<-\ | \!/======?\>>=?/<# dup | \<<+>+>-/ | !
\======|====\ |
| | ==\ |
M==!\=!\?\#| | | \@/-@/@/===?\<# ^ \>-<-/ |
^ ^ ^ ^ | | | subtract from n | | mutual recursion | recursion | n-1
check for zero</lang> Standard ML<lang sml>fun f 0 = 1 |
f n = n - m (f (n-1))
and m 0 = 0 |
m n = n - f (m (n-1))
The <lang sml>val rec f = fn 0 => 1 |
n => n - m (f (n-1))
and m = fn 0 => 0 |
n => n - f (m (n-1))
which indicates that the functions call themselves ( SwiftIt just works. No special pre-declaration is necessary. <lang swift>func F(n: Int) -> Int { return n == 0 ? 1 : n - M(F(n-1)) } func M(n: Int) -> Int { return n == 0 ? 0 : n - F(M(n-1)) } for i in 0..20 { print("\(F(i)) ") } println() for i in 0..20 { print("\(M(i)) ") } println()</lang> Tcl<lang tcl>proc m {n} { if { $n == 0 } { expr 0; } else { expr {$n - [f [m [expr {$n-1}] ]]}; } } proc f {n} { if { $n == 0 } { expr 1; } else { expr {$n - [m [f [expr {$n-1}] ]]}; } } for {set i 0} {$i < 20} {incr i} { puts -nonewline [f $i]; puts -nonewline " "; } puts "" for {set i 0} {$i < 20} {incr i} { puts -nonewline [m $i]; puts -nonewline " "; } puts ""</lang> TI-89 BASIC<lang ti89b>Define F(n) = when(n=0, 1, n - M(F(n - 1))) Define M(n) = when(n=0, 0, n - F(M(n - 1)))</lang> TXR<lang txrlisp>(defun f (n) (if (>= 0 n) 1 (- n (m (f (- n 1)))))) (defun m (n) (if (>= 0 n) 0 (- n (f (m (- n 1)))))) (each ((n (range 0 15))) (format t "f(~s) = ~s; m(~s) = ~s\n" n (f n) n (m n)))</lang> $ txr mutual-recursion.txr f(0) = 1; m(0) = 0 f(1) = 1; m(1) = 0 f(2) = 2; m(2) = 1 f(3) = 2; m(3) = 2 f(4) = 3; m(4) = 2 f(5) = 3; m(5) = 3 f(6) = 4; m(6) = 4 f(7) = 5; m(7) = 4 f(8) = 5; m(8) = 5 f(9) = 6; m(9) = 6 f(10) = 6; m(10) = 6 f(11) = 7; m(11) = 7 f(12) = 8; m(12) = 7 f(13) = 8; m(13) = 8 f(14) = 9; m(14) = 9 f(15) = 9; m(15) = 9 uBasic/4tHuBasic/4tH supports mutual recursion. However, the underlying system can't support the stress this puts on the stack - at least not for the full sequence. This version uses memoization to alleviate the stress and speed up execution. <lang>LOCAL(1) ' main uses locals as well FOR a@ = 0 TO 200 ' set the array @(a@) = -1 NEXT PRINT "F sequence:" ' print the F-sequence FOR a@ = 0 TO 20 PRINT FUNC(_f(a@));" "; NEXT PRINT PRINT "M sequence:" ' print the M-sequence FOR a@ = 0 TO 20 PRINT FUNC(_m(a@));" "; NEXT PRINT END
IF a@ = 0 THEN RETURN (1) ' memoize the solution IF @(a@) < 0 THEN @(a@) = a@ - FUNC(_m(FUNC(_f(a@ - 1)))) RETURN (@(a@)) ' return array element
IF a@ = 0 THEN RETURN (0) ' memoize the solution IF @(a@+100) < 0 THEN @(a@+100) = a@ - FUNC(_f(FUNC(_m(a@ - 1)))) RETURN (@(a@+100)) ' return array element</lang>
F sequence: 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 M sequence: 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12 0 OK, 0:199 UNIX Shell<lang bash>M() { local n n=$1 if $n -eq 0 ; then echo -n 0 else echo -n $(( n - $(F $(M $((n-1)) ) ) )) fi } F() { local n n=$1 if $n -eq 0 ; then echo -n 1 else echo -n $(( n - $(M $(F $((n-1)) ) ) )) fi } for((i=0; i < 20; i++)); do F $i echo -n " " done echo for((i=0; i < 20; i++)); do M $i echo -n " " done echo</lang> UrsalaForward declarations are not an issue in Ursala, which allows any
definition to depend on any symbol declared within the same
scope. However, cyclic dependences are not accepted unless the
programmer explicitly accounts for their semantics. If the recurrence
can be solved using a fixed point combinator, the compiler can be
directed to use one by the <lang Ursala>#import std
F = ~&?\1! difference^/~& M+ F+ predecessor M = ~&?\0! difference^/~& F+ M+ predecessor</lang> This test program applies both functions to the first twenty natural numbers. <lang Ursala>#cast %nLW test = ^(F*,M*) iota 20</lang>
( <1,1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12>, <0,0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12>) x86 AssemblySince all "labels" (symbols), if not local, can be seen by the whole code in the same source unit, we don't need special care to let the subroutine func_f call func_m. If the function would have been in another source unit, we should have declared it extern (the linker will resolve the symbol), as done for printf. section .text func_f mov eax, [esp+4] cmp eax, 0 jz f_ret dec eax push eax call func_f mov [esp+0], eax call func_m add esp, 4 mov ebx, [esp+4] sub ebx, eax mov eax, ebx ret f_ret mov eax, 1 ret func_m mov eax, [esp+4] cmp eax, 0 jz m_ret dec eax push eax call func_m mov [esp+0], eax call func_f add esp, 4 mov ebx, [esp+4] sub ebx, eax mov eax, ebx ret m_ret xor eax, eax ret main mov edx, func_f call output_res mov edx, func_m call output_res ret output_res xor ecx, ecx loop0 push ecx call edx push edx push eax push form call printf add esp, 8 pop edx pop ecx inc ecx cmp ecx, 20 jnz loop0 push newline call printf add esp, 4 ret
end</lang> XPL0<lang XPL0>code ChOut=8, CrLf=9, IntOut=11; ffunc M; \forward-referenced function declaration func F(N); int N; return if N=0 then 1 else N - M(F(N-1)); func M(N); int N; return if N=0 then 0 else N - F(M(N-1)); int I; [for I:= 0 to 19 do [IntOut(0, F(I)); ChOut(0, ^ )]; CrLf(0); for I:= 0 to 19 do [IntOut(0, M(I)); ChOut(0, ^ )]; CrLf(0); ]</lang>
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 zklThis works if the functions are in a file or on one line (in the REPL) as zkl doesn't like referencing undefined objects. You could also pass/close the other function. <lang zkl>fcn f(n){ if(n==0)return(1); n-m(f(n-1,m),f) } fcn m(n){ if(n==0)return(0); n-f(m(n-1,f),m) } [0..19].apply(f).println(); // or foreach n in ([0..19]){ print(f(n)," ") } [0..19].apply(m).println(); // or foreach n in ([0..19]){ print(m(n)," ") }</lang>
L(1,1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12) L(0,0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12) |
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