Project Euler Problem 25 Solution

Question

The Fibonacci sequence is defined by the recurrence relation:

Fn=Fn1+Fn2 where F1=1 and F2=1\displaystyle F_n = F_{n-1} + F_{n-2} \text{ where } F_1 = 1 \text{ and } F_2 = 1

Hence the first 12 terms will be:

F1=1F2=1F3=2F4=3F5=5F6=8F7=13F8=21F9=34F10=55F11=89F12=144\displaystyle \begin{aligned} F_1 &= 1 \\ F_2 &= 1 \\ F_3 &= 2 \\ F_4 &= 3 \\ F_5 &= 5 \\ F_6 &= 8 \\ F_7 &= 13 \\ F_8 &= 21 \\ F_9 &= 34 \\ F_{10} &= 55 \\ F_{11} &= 89 \\ F_{12} &= 144 \end{aligned}

The 12th term, F12F_{12}, is the first term to contain three digits.

What is the first term in the Fibonacci sequence to contain 1000 digits?

Clojure

#!/usr/bin/env clojure
(def fibs
  (lazy-cat [(BigInteger/ZERO) (BigInteger/ONE)] (map + fibs (rest fibs))))

(println (count (take-while #(< % (.pow (BigInteger/TEN) 999)) fibs)))
$ time clojure fibonacci.clj
real   0m0.751s
user   0m1.388s
sys    0m0.060s

Haskell

fibs ::  [Integer]
fibs = 0 : 1 : zipWith (+) fibs (tail fibs)

main ::  IO ()
main = print $ head [i | i <- [1..], (==1000) . length . show $ fibs !! i]
$ ghc -O2 -o fibonacci fibonacci.hs
$ time ./fibonacci
real   0m0.125s
user   0m0.120s
sys    0m0.000s

Ruby

#!/usr/bin/env ruby
i = 1
t1, t2 = 0, 1
while t2.to_s.length < 1000
  t1, t2 = t2, t1 + t2
  i += 1
end
puts i
$ time ruby fibonacci.rb
real   0m0.069s
user   0m0.060s
sys    0m0.008s

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