SPOILER ALERT: Don't look at this if you are trying to solve Project Euler's problem #2 on your own w/o looking at the answer.
I've already completed problem #2 of Project Euler (computing the sum of all even Fibonacci(n) numbers less than or equal to 4 million) - I'm using these problems to practice my C/Ada skills, to revisit my Common Lisp and to learn Haskell.
When I'm trying to re-implement my solution in Haskell, I'm running into a problem. In classical fashion, it is calculating the wrong answer. However, I think my Haskell implementation resembles my Common Lisp one (which does produce the correct result.)
The algorithm only computes the Fibonacci number for n where n % 3 == 0. This is because
- We need to sum only the even-valued Fibonacci numbers F(n) <= 4M, and
- (n % 3 == 0) <--> (F(n) % 2 == 0)
Here is the Haskell implementation:
uber_bound = 40000000 -- Upper bound (exclusive) for fibonacci values
expected = 4613732 -- the correct answer
-- The implementation amenable for tail-recursion optimization
fibonacci :: Int -> Int
fibonacci n = __fibs (abs n) 0 1
where
-- The auxiliary, tail-recursive fibs function
__fibs :: Int -> Int -> Int -> Int
__fibs 0 f1 f2 = f1 -- the stopping case
__fibs n f1 f2 = __fibs (n - 1) f2 (f1 + f2)
-- NOT working. It computes 19544084 when it should compute 4613732
find_solution :: Int
find_solution = sum_fibs 0
where
sum_fibs :: Int -> Int
sum_fibs n =
if fibs > uber_bound
then
0 -- stopping condition
else
-- remember, (n % 3 == 0) <--> (fib(n) % 2 == 0)
-- so, seek the next even fibs by looking at the
-- the next n = n@pre + 3
fibs + sum_fibs (n + 3)
where
fibs = fibonacci n
actual = find_solution
problem_2 = (expected == actual)
The thing is printing 19544084 when the correct answer is 4613732. My Common Lisp solution (which does work) is below.
I thought my Haskell implementation would resemble it, but I'm missing something.
(set `expected 4613732) ;; the correct answer
;; tail-recursive fibonacci
(defun fibonacci (n)
(labels
( ;; define an auxiliary fibs for tail recursion optimization
(__fibs (n f1 f2)
(if (<= n 0)
f1 ;; the stopping condition
(__fibs
(- n 1) ;; decrement to ensure a stopping condition
f2
(+ f1 f2))))
) ;; end tail_rec_fibs auxiliary
(__fibs n 0 1)
);; end labels
) ;; end fibonacci
(defun sum_fibs(seed)
(let*
((f (fibonacci seed)))
(if (> f 4000000)
0
;; else
(+ f (sum_fibs (+ 3 seed)))
);; end if
);; end of let
);; end of sum-fibs
(defun solution () (sum_fibs 0))
(defun problem_2 ()
(let
(
(actual (solution))
)
(format t "expected:~d actual:~d" expected actual)
(= expected actual)
)
) ;; end of problem_2 defun
What on Earth am I doing wrong? Granted that I'm using a Neanderthal approach to learning Haskell (I'm currently just re-implementing my Lisp on Haskell as opposed to learning idiomatic Haskell, the coding/problem solving approach that goes with the language.)
I'm not looking for somebody to just give me the solution (this is not a can i haz the codez?). I'm looking more, but much more for an explanation of what I'm missing in my Haskell program. Where is the bug, or am I missing a very specific Haskell idiosyncratic evaluation/pattern matching thing? Thanks.
