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Challenge: Write the recursive Fibonacci algorithm in a different language.

andreanidouglas profile image Douglas R Andreani ・1 min read

Hellow DEV community, how are you?

Can we challenge ourselves in this fun "game"?

Let's see how many languages we can enumerate by writing the Fibonacci recursive algorithm on the comments. Are you in?

EDIT: this is not about having the fast/better code, just to have some fun

Discussion

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avalander profile image
Avalander

I'll continue with javascript.

const fibonacci = (n, i=0, curr=1, prev=0) =>
    (i >= n ? curr : fibonacci(n, i + 1, curr + prev, curr))

(Look mum, with a single expression function!)

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gypsydave5 profile image
David Wickes

To be absolutely pedantic, this code is valid and will work with large numbers because it is written in EcmaScript 6. Part of the ES6 standard is for the language interpreter to implement tail call optimization (TCO). EcmaScript is a language defined by a standard, not by an implementation.

Now, at present, barely any interpreters implement TCO - here's a fun comparison table to see which do or don't. This makes me sad, but there we are.

But, as I say, the function above will work just fine according to the language standard. Whether this code blows the call stack of your interpreter is dependent on whether your interpreter implements the full ES6 standard. Which it probably doesn't.

To put it strongly, complaining that this code doesn't run on an JS interpreter without TCO is like complaining that it can't run by a Ruby interpreter. The fault is with the interpreter, not the code.

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gypsydave5 profile image
David Wickes

I like this! Don't think you need the outer parens though :D

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avalander profile image
Avalander

Should work without, I'm just used to wrapping ternary expressions between them for some reason and I find it weird without :)

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hoelzro profile image
Rob Hoelz

I haven't seen a SQL implementation yet, so here's one:

with recursive fib(a, b) as
    (select 1 as a, 0 as b

     union

     select a + b as a, a as b from fib)

select a from fib limit 10;
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slavius profile image
Slavius

Here's interesting one for SQL Server with maximum value before arithmetic overflow due to data type limit:

SET STATISTICS TIME,PROFILE ON

DECLARE @MAX SMALLINT
SET @MAX = 1474

SELECT TOP 1 s.Fib FROM (
SELECT
    FLOOR(POWER(( 1 + SQRT(5) ) / 2.0, number) / SQRT(5) + 0.5) AS Fib
FROM master..spt_values
WHERE TYPE = 'p' AND number BETWEEN 1 AND @MAX
) AS s
ORDER BY s.Fib DESC

Execution plan

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scottishross profile image
Ross Henderson

Here it is in Oracle SQL:

with FIBONACCI (i, SPIRAL, PREV) as 
(
   select 
      1 i, 0 SPIRAL, cast(null as number) PREV 
   from 
      DUAL
   union all
   select 
      f1.i + 1 i, f1.SPIRAL + nvl(f1.PREV,1) SPIRAL, f1.SPIRAL PREV
    from 
       FIBONACCI f1
    where 
   f1.i < 605
)

select SPIRAL from FIBONACCI order by i;

The limit of 605 is the limit before numeric overflow.

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avalander profile image
Avalander

👏👏 I never thought you could do that with SQL!

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alephnaught2tog profile image
M. Shemayev

Fuck yes SQL!

I feel like every time someone responds to one of these with a SQL implementation that a) my heart grows a few sizes and b) they earn extra special bonus points in my head because hell yeah.

⭐️

(nonironic gold star, fwiw)

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slavius profile image
Slavius

I'll follow up in C# (and LINQ):

Console.WriteLine(
  Enumerable.Range(1, 10)
  .Skip(2)
  .Aggregate(
    new { Current = 1, Prev = 1 }, (x, index) => new { 
      Current = x.Prev + x.Current, Prev = x.Current }
  ).Current
);

(Look ma', single expression lambda without recursion!)

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avalander profile image
Avalander

Imaginative, I like it (even if it's not recursive :P)!

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slavius profile image
Slavius

I lied a bit. The recursion is there, hidden in the Aggregate function. It's the framework abstraction that masks it.

Otherwise it wouldn't qualify as an answer to OP challenge, or would it? ;)

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avalander profile image
Avalander

I know nothing about C#, but I thought that the Aggregate function was somehow invoking an anonymous function here that given current and previous values returns the next element. If that's the case, and it's a function calling another function multiple times instead of the function invoking itself, can we still call it recursion?

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slavius profile image
Slavius

The Aggregate function is member of the Enumerable type and applies an anonymous accumulator function looping all elements in that "array/set". Hard to tell if we can treat it as a recursion. I would have to look at the stack if there are pointers left to the originating caller.

Fibonacci's sequence is strictly sequential so it works well but for more parallel calculations, like SUM, AVG, MAX, MIN accumulator functions you can do:

var result = Enumerable.Range(1,100000)
  .AsParallel()
  .Aggregate(0, (sum, i) => { sum += i } );

And it will multithread across many OS threads to achieve the best efficiency.

Edit: This is however not plain C# .Net anymore but LINQ ;)

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avalander profile image
Avalander

Since I doubt anybody else is going to do it, here is an implementation in Scheme

(define (fib n)
    (define (fib-iter a b count)
        (if (= count n)
            b
            (fib-iter (+ a b) a (+ count 1))))
    (fib-iter 1 0 0))

Tested for values of n up to 10001.

citizen428 profile image
Michael Kohl

Tail-recursive or not, no function accepts any input. Infinity is rather big, I can always find a number that not longer fits in the working memory of your computer. Does that make your solution incorrect?

Excuse the silly hyperbole, but on a site that also attracts a lot of new(ish) developers your self-indulgent overcorrectness on what OP explicitly called a fun "game" is a bit off-putting to be honest.

slavius profile image
Slavius

Please do not feed this troll.

He picked fib(10000) because it blows Int64 and now he's trying to victoriously convince everyone their programming language of choice is crap.

The same as if I would say I can compute and save a file containing Pi to 1e+13 numbers and don't tell anyone I have 12TB NAS storage attached...

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avalander profile image
Avalander

Aleksei, if you try to work with very large numbers in Javascript, at some point (before the 10000th element in the fibonacci series) it just returns Infinity because it can't deal with them.

avalander profile image
Avalander

If you think it's important enough for a code challenge to have a Javascript implementation that returns Infinity instead of blowing the stack for large values, be my guest and suggest an alternative implementation.

Just posting the console output of calling my function with an arbitrarily long value seems rather pointless. I agree my solution is not perfect but I'd appreciate a better solution more than an error message.

andreanidouglas profile image
Douglas R Andreani Author

man, just sit down and relax. there is no point for all this harassement.

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fxedel profile image
Felix Edelmann

I did this some time ago in Rust.

My first approach (the naive one) is very similar to @rapidnerd 's (George Marr's) solution in R and @andreanidouglas ' (Douglas R Andreani's) solution in Python:

fn fib(n: u64) -> u64 {
  match n {
    0 => 0,
    1 => 1,
    _ => fib(n-1) + fib(n-2),
  }
}

I realized that this solution quickly exceeded in execution time for n > 40, so I optimized it using a mathematical theorem:

Given that n and p are integers, and that n = 2p + 1, i. e. n is odd, the n-th fibonacci number is then

fib(n) = fib(p + (p+1)) = fib(p)² + fib(p+1)²

This means, we can break down numbers with odd indices into to numbers with about the half of the index – and do this again and again and again. This dramatically reduces execution time:

fn fib_fast(n: u64) -> u64 {
  match n {
    0 => 0,
    1 => 1,

    // even
    _ if n % 2 == 0 => fib_fast(n-1) + fib_fast(n-2),

    // odd
    _ => {
      let a = (n-1)/2;
      let b = n-a;
      let fib_a = fib_fast(a);
      let fib_b = fib_fast(b);
      return fib_a*fib_a + fib_b*fib_b;
    },
  }
}

Inspired by @avalander 's answer, I also added this even faster algorithm:

fn fib_super_fast(n: u64, i: u64, curr: u64, prev: u64) -> u64 {
  if i >= n {
    return curr;
  }

  return fib_super_fast(n, i + 1, curr + prev, curr);
}

fib_fast and fib_super_fast execute within microseconds even for higher indices. However, indices of 94 and higher cause a crash:

thread 'main' panicked at 'attempt to add with overflow', src/main.rs:42:35

Some performance measurements:

Enter n:
5
fib_super_fast(n) = 5 (0µs)
fib_fast(n)       = 5 (0µs)
fib(n)            = 5 (1µs)

Enter n:
20
fib_super_fast(n) = 6765 (1µs)
fib_fast(n)       = 6765 (10µs)
fib(n)            = 6765 (536µs)

Enter n:
40
fib_super_fast(n) = 102334155 (1µs)
fib_fast(n)       = 102334155 (54µs)
fib(n)            = 102334155 (1908011µs)

Enter n:
45
fib_super_fast(n) = 1134903170 (2µs)
fib_fast(n)       = 1134903170 (15µs)
fib(n)            = 1134903170 (21216762µs)

Enter n:
90
fib_super_fast(n) = 2880067194370816120 (2µs)
fib_fast(n)       = 2880067194370816120 (958µs)

Enter n:
93
fib_super_fast(n) = 12200160415121876738 (3µs)
fib_fast(n)       = 12200160415121876738 (152µs)

Enter n:
94
thread 'main' panicked at 'attempt to add with overflow', src/main.rs:42:35
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gypsydave5 profile image
David Wickes

Just for a nice style, you could factor out the returns as if is an expression...

fn fib_super_fast(n: u64, curr: u64, prev: u64) -> u64 {
  if n == 0 {
    curr
  } else {
    fib_super_fast(n - 1, curr + prev, curr)
  }
}
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avalander profile image
Avalander

Nice!

Since writing my implementation I've remembered that the parameter i is unnecessary and you can decrease n instead until it's 0.

fn fib_super_fast(n: u64, curr: u64, prev: u64) -> u64 {
  if n <= 0 {
    return curr;
  }

  return fib_super_fast(n - 1, curr + prev, curr);
}

By the way, you didn't set default values for curr and prev, how does that work, do you need to call it with fib_super_fast(n, 1, 0)?

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fxedel profile image
Felix Edelmann

Yes, I do. But I have to use fib_super_fast(n, 1, 1, 0) as my other implementations also begin with 1. The code for calling the fibonacci methods is:

fn main() {
  loop {
    println!("Enter n:");

    let mut n_str = String::new();
    io::stdin().read_line(&mut n_str).expect("Failed to read line");
    let n = user_input_to_int(n_str);

    let t0 = SystemTime::now();
    let fib_super_fast_n = fib_super_fast(n, 1, 1, 0);
    let t1 = SystemTime::now();
    println!("fib_super_fast(n) = {} ({}µs)", fib_super_fast_n, time_difference(t0, t1));

    let t0 = SystemTime::now();
    let fib_fast_n = fib_fast(n);
    let t1 = SystemTime::now();
    println!("fib_fast(n)       = {} ({}µs)", fib_fast_n, time_difference(t0, t1));

    let t0 = SystemTime::now();
    let fib_n = fib(n);
    let t1 = SystemTime::now();
    println!("fib(n)            = {} ({}µs)", fib_n, time_difference(t0, t1));
  }
}
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marvodor profile image
Marvodor

Here's a Python variant for quite large numbers. Alas, due to recursion depth restrictions, any new calculated Fibonacci number should not have a larger sequence position than about 500 more than that of the highest already calculated.

def fib(a, F={}):
    if a in F:
        return F[a]
    if a < 2:
        return 1
    f = fib(a-1)
    F[a-1] = f
    return f + fib(a-2)

for i in range(0,50001,500):
    print("fib(%i) = %i"%(i,fib(i)))
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fnh profile image
Fabian

Technically lazy evaluation of a endless stream is iterative, not recursive, but anyway, here is a solution in Haskell:

fibonnaciNums = 0 : 1 : zipWith (+) fibonnaciNums (tail fibonnaciNums)

fibonnaci n        = last $ take n fibonnaciNums 
-- or even shorter:  fibonnaciNums !! n
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dwd profile image
Dave Cridland
#include <iostream>

template<long long i> long long fibonacci() {
    return fibonacci<i-1>() + fibonacci<i-2>();
}

template<> long long fibonacci<1>() {
    return 1;
}

template<> long long fibonacci<2>() {
    return 1;
}

int main() {
    std::cout << "Fibonacci of 27 is " << fibonacci<27>() << std::endl;
    return 0;
}

C++ can, of course, do it at build time with a bit of templates.

Here, we're definitely recursing - twice, because it's simpler. At runtime, it's just printing the value out that's been calculated by the compiler during the build.

slavius profile image
Slavius

I see what you did there. Trying to troll languages that you think may not have Int128 support :D. Nice try!

using System;
using System.Linq;
using System.Numerics;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            var start = DateTime.Now;
            Console.WriteLine(
              Enumerable.Range(1, 10000)
              .Skip(2)
              .Aggregate(
                new { Current = (BigInteger)1, Prev = (BigInteger)1 }, (x, index) => new {
                    Current = x.Prev + x.Current,
                    Prev = x.Current
                }
              ).Current
            );
            Console.WriteLine(DateTime.Now - start);
            Console.ReadLine();
        }
    }
}
33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875
00:00:00.0245407
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sam_ferree profile image
Sam Ferree

Funge++:

v   >:1-\2-101O\101O+B
 :1`|
    >$1B
>&:!#v_101O.55+,
     @
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gypsydave5 profile image
David Wickes

Common Lisp!

(defun fib (n &optional (curr 0) (next 1)) 
  (if (zerop n) 
      curr 
      (fib (1- n) next (+ curr next))))

(and for the TCO crowd... it's implementation dependent, so YMMV)

citizen428 profile image
Michael Kohl

Thanks for taking the time to type out this response!

Like you I'm not a native English speaker, and my native language (and culture) generally is also much more direct and — for lack of a better word — "confrontational" than English. That said I moved a lot over the last 16 years and spent almost half of that time in East and Southeast Asia, where communication tends to be very indirect and high context, and overall culture is extremely non-confrontational. This definitely had some influence on how I communicate nowadays.

I don't doubt that you have only the best intentions, and will keep that in mind for future occasions where I may feel tempted to butt in.

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manzanit0 profile image
Javier Manzano

Read The Culture Map? :)

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citizen428 profile image
Michael Kohl

Yes. I guess the choice of words gave it away, though it’s not unique to that book. Also “The Geography Of Thought” and quite a few other books on (intercultural) communication.

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avalander profile image
Avalander

And your point is...?

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stereobooster profile image
stereobooster

No worries @avalander . You all did right, it is just JS doesn't support TCO there were some attempts (as far as I remember it is hold back by Microsoft member or committee or something like that). There is still way around - you can use trampoline

const trampoline = (fn) => {
  let newFn = eval(fn.toString().replace(new RegExp(fn.name + '\\(([^\\)]*)\\)'), '[$1]'))
  return function() {
    let result = newFn.apply(null, arguments)
    while (result instanceof Array) result = newFn.apply(null, result)
    return result
  }
};

const _fibonacciIter = (n, i, curr, prev) =>
    (i >= n ? curr : _fibonacciIter(n, i + 1, curr + prev, curr));

const fibonacciIter = trampoline(_fibonacciIter);

const fibonacci = n => fibonacciIter(n, 0, 1, 0);

I doubt you would want to use this in production, but just to make a point.

TCO - stands for tail call optimisation, to prevent Maximum call stack error
Trampoline is the way how some compilers implement TCO, they convert recursion to a loop

UPD: read about TCO status in Chrome here stackoverflow.com/questions/427881...

Thread Thread
avalander profile image
Avalander

Wow, that's great, I didn't know this trick, thank you!

slavius profile image
Slavius

I'm just letting everyone (else) know I'm not reacting to his childish unsuccessfull trolling attempts anymore... I'm not his mother to raise him to his adulthood.

I know my shit, anyone who writes C# can see it as well. I will now just silently laugh...

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citizen428 profile image
Michael Kohl

Also since your answers in this entire thread are a bit nitpicky, the non-recursive solutions are not incorrect per se, they just work on a smaller domain than ℕ.

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dwd profile image
Dave Cridland
def fib(arg):
  curr, prev = 1, 1
  n = int(arg)
  if n != arg or n <= 0:
    raise ValueError("Argument must be positive integer")
  if n <= 2:
    return 1
  for count in range(n - 2):
    curr, prev = curr + prev, curr
  return curr

Quick bit of Python. The error handling probably isn't complete, but Python has the useful benefit here that it has native, transparent, Big Number support - you can do fib(10000) if you want (or much higher if you have the memory).

But yeah, I just noticed Douglas wanted a recusrive algorithm, whereas I've done it iteratively without thinking. In general, iterative solutions will execute faster - though this isn't always the case.

citizen428 profile image
Michael Kohl

For people to grow from mistakes they need to listen to the person who points them out. To be that person, I'd reconsider my communication style.

There's nothing wrong with posting your own answer and discussing the merits of tail recursion and the problems with other solutions there. Posting a comment under every single answer seems a bit...too much.

Anyway, it's not my site, you're of course free to post whatever you want. But that may also invite people to comment on the limits of your communication style, so as long as you're cool with that ¯\(ツ)

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jvanbruegge profile image
Jan van Brügge

I have haskell here with the best form of recursion: Self-recursion!

fibs = 1:1:zipWith (+) fibs (tail fibs)
fib n = fibs !! n

Here fibs is an infinite List of all fibonacci numbers, the !! function returns the nth element of the list.

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jvanbruegge profile image
Jan van Brügge

I also have the boring tail recursive version here:

fib n = fibHelper n 1 1
    where fibHelper  0 a  _ = a
          fibHelper !n a !b = fibHelper (n-1) b (a+b)
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slavius profile image
Slavius
> #reset
Resetting execution engine.
Loading context from 'CSharpInteractive.rsp'.
> var start = DateTime.Now;
. Console.WriteLine(
.   Enumerable.Range(1, 10000)
.   .Skip(2)
.   .Aggregate(
.     new { Current = 1, Prev = 1 }, (x, index) => new {
.         Current = x.Prev + x.Current,
.         Prev = x.Current
.     }
.   ).Current
. );
. Console.WriteLine(DateTime.Now - start);
1242044891
00:00:00.0025070
> 
avalander profile image
Avalander

Language limitations are the worst excuse for the developer, aren’t they?

It's also rather convenient to claim that other people's proposal is incorrect because they have to implement things that your language of choice gives you for free (or, in the case of Ruby, you need to enable a runtime option; still beats Javascript's strategy of not having it at all).

According to you I should not only hack tail-call optimisation into Javascript somehow (most current runtimes don't do any kind of tail-call optimisation, ever), but roll my own custom system to handle arbitrarily large numbers. I don't really think this was the point of the challenge.

Also, let's keep in mind that my solution blows when the stack isn't big enough to keep track of all the function calls, and yours blow when the number is too large to be kept in memory. So, while in practice my solution blows much, much earlier than yours, both are, technically, incorrect if the definition of correct is that it works for all natural numbers, and they are both incorrect for the same reason: computer limitations apply.

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stereobooster profile image
stereobooster

So, while in practice my solution blows much, much earlier than yours, both are, technically, incorrect if the definition of correct is that it works for all natural numbers, and they are both incorrect for the same reason: computer limitations apply.

The word you are looking for is "totality". Function is total if it returns a value for each input in the domain

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yorodm profile image
Yoandy Rodriguez Martinez

An Emacs Lisp version. Warning!! This will likely freeze your Emacs!!

(defun fib(n)
         (cond
          ((= n 0) 0)
          ((= n 1) 1)
          (t (+ (fib (- n 1)) (fib (- n 2))))))

UPDATE
Just realized it counts as a Common Lisp version too

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rapidnerd profile image
George Marr

I'll continue with it in R

fibR <- function(n) {
    if ((n == 0) | (n == 1)) 
        return(1)
    else
        return(fibR(n-1) + fibR(n-2))
}

fibR(20)
nestedsoftware profile image
Nested Software

Respectfully, if you want to help newbies on a general issue such as recursion, just make a top-level comment addressing this problem. Show an example of the problem and suggest ways it can be fixed. That way, if the community deems the comment to be helpful, it will bubble up near the top of the discussion and it will be one of the first comments that newbies encounter.

In this manner, you won't be repeating the same comment all over the place, and you will have something clear that novices can wrap their minds around. In my opinion, making grumpy statements to the effect of "this crashes when the input reaches X" doesn't really help the very novices you say you most want to reach.

Edit: Added "in my opinion" :)

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citizen428 profile image
Michael Kohl

Because different language runtimes have different execution models, so doing it automatically might not always be possible/feasible. Given that Scala — another JVM language — also has a @tailrec annotation I'd guess it's hard to efficiently detect tail recursion in the generated byte code, probably because the JVM was originally built without support for proper tail calls (unlike for example Scheme where tail call elimination is part of the standard since R5RS).

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dwd profile image
Dave Cridland
#include <iostream>

constexpr long long fibonacci(long long i) {
    if (i <= 2) {
        return 1LL;
    }
    return fibonacci(i - 1) + fibonacci(i - 2);
}

int main() {
    std::cout << "Fibonacci of 27 is " << fibonacci(27) << std::endl;
    return 0;
}

Modern C++ can do it more simply, though - this uses constexpr to tell the compiler that it can calculate these at build time if it wants. Using a constexpr arg (here a literal), it probably will do, but we could also pass in a variable to make it calculate it at runtime.