Once again, I thought it would be fun to kick off one of these challenges in as many programming languages as possible. Last time, we tried our hand at Fizz Buzz in Every Language. If you haven't gotten a chance to share a solution in your favorite language, go for it! Otherwise, we're going to tackle Fibonacci in Every Language today.

## The Challenge

As many of you are probably aware, Fibonacci is a term often associated with a particular sequence of numbers where the nth term is the sum of the previous two terms—or more formally: F_{n} = F_{n-1} + F_{n-2}. For our purposes, we'll start the sequence with a pair of ones:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

The goal in this challenge is to write a program in a language of your choice to output the sequence up to the nth term. In other words, the program should be able to be executed like:

```
./fib 5
```

and, output the sequence above up to the fifth term:

```
1, 1, 2, 3, 5
```

If you're feeling adventurous, you could try making your program conform to the requirements outlined in the Sample Programs repo. In addition to outputting the sequence, you should also output the index of each term:

```
1: 1
2: 1
3: 2
4: 3
5: 5
```

Either style is fine for the purposes of this challenge. That said, if you follow the second convention, it'll be much easier to transition into the repo!

## The Solution

As always, I'll kick off the fun with a solution in Haskell brought to you by a couple of our contributors (Parker Johansen and Panagiotis Georgiadis):

```
module Main where
import System.Environment
import Text.Read
fibonacci :: Int -> [Integer]
fibonacci = flip (take) fibs
fibs :: [Integer]
fibs = 1 : 1 : zipWith (+) fibs (tail fibs)
headMaybe :: [a] -> Maybe a
headMaybe [] = Nothing
headMaybe (x:xs) = Just x
-- Takes a list of values and returns a list of strings in the format "ONE_BASED_INDEX: VALUE"
printWithIndex :: (Show a) => [a] -> [[Char]]
printWithIndex = zipWith (\i x -> (show i) ++ ": " ++ (show x)) [1..]
-- Prints out the first N numbers from the fibonacci sequence
-- where N equals to the first command line argument.
main :: IO ()
main = do
args <- getArgs
let n = headMaybe args
case n >>= readMaybe of
Nothing -> putStrLn "Usage: please input the count of fibonacci numbers to output"
Just n -> mapM_ (putStrLn) $ (printWithIndex . fibonacci) n
```

For those of you that maybe haven't seen functional programming before, this solution probably looks pretty wild. That said, I think Haskell is far more readable than anything Lisp-based, so you can probably get the gist of how this works.

Unfortunately, we don't currently have this solution documented in our collection, so maybe one of you can help out. We'd appreciate the support!

## Discussion

Python: (constant time solution)

Edit:This is accurate until F_{4767}with the given precision.Clever! I didn't realize there was an equation that could so closely approximate the series.

It turns out also in DSP, it is a classical example of use of z-trasform for beginners. Actually, the exact form has two terms: phi above and 1/phi and the n-th term is something like C*(phi

^{n}+1/phi^{n}) (more or less, I am going by memory and I am too lazy now to do the computation... ;-)). Of course, since 1/phi is smaller than one, 1/phi^{n}goes rapidly to zero and you get a wonderful approximation with only phi^{n}already for small n.I only know it because my Theory of Computability professor used the “one trillionth Fibonacci number” as a limit to our newfound power understanding recursive solutions. (To find the F

_{n}, you need to find F_{n-1}+ F_{n-2}. To find those two numbers, you need to find F_{n-2}+ 2*F_{n-3}+F_{n-4}. This gets towards heat death of the universe level amount of instructions fairly quickly. The loop with saved state gets you down to hours IIRC.)Then he dropped that this equation existed and my mind kinda exploded.

It wasn’t until trying to get that Project Euler question 2 to complete in under 30 seconds that I ever implemented this. It’s simpler than I expected going in.

Yeah, it’s not too hard to put together an inefficient solution using recursion (since that’s how the equation is written). If you’re clever, you might save computations in a list. Or, maybe you write an iterative solution which only needs two variables at any give time.

That said, an equation like this is next level. Haha

Solution in Go language:

Ada (unfortunately seems that no syntax highlighting is available for Ada)

This is my first post here. I am intrigued by such kinds of problems. this is a simple enough JS code, I hope, to achieve the goal.

It is a recursive function, hence I am not expecting very match in terms of performance.

You may try this on chrome dev tools for quick tests.

Racket:

As much as I like Haskell in general, monadic IO really isn't my cup of tea and one of the reasons I always go back to less pure FP languages.

haskell

For anyone interested, this challenge is also available here in 257 languages : rosettacode.org/wiki/Fibonacci_seq...

Also related, Project Euler problem #2

Love that the example solution for this challenge was implemented in Haskell. Even being a beginner, I appreciate all that functional goodness.