CODEWITHSUNDEEP
pythonpython-3.xmemoizationtimeit
jnooree
jnooree

Reputation: 65

Why python fibonacci sequence loop is slower than recursion?

Below is the well-known example of fibonacci sequence

# test.py
import sys
sys.setrecursionlimit(20000)

def fib_loop(n):
    if n <= 1:
        return n
    fn, fnm1 = 1, 0
    for _ in range(2, n+1):
        fn, fnm1 = fn + fnm1, fn
    return fn

def fib_recursion(n, memo={}):
    if n <= 1:
        return n
    if n not in memo:
        memo[n] = fib_recursion(n-1, memo) + fib_recursion(n-2, memo)
    return memo[n]

As everybody does, I used to think that the loop variant will be much faster than the recursive one. However, the actual result is quite surprising.

$ python3 -m timeit "import test; test.fib_loop(10000)"
100 loops, best of 5: 1.93 msec per loop
$ python3 -m timeit "import test; test.fib_recursion(10000)"
500000 loops, best of 5: 471 nsec per loop

I have no idea why. Could anybody help me?

Upvotes: 3

Views: 247

Answers (1)

juanpa.arrivillaga
juanpa.arrivillaga

Reputation: 95948

Because you are memoizing your result. And you are re-using that memo dict on every iteration. So the first time it runs it is slow. On every other invoctation, it is a simple dict-lookup.

If you use number=1 so it only runs just once, you'll see the first call is actually slower

>>> import sys
>>> sys.setrecursionlimit(20000)
>>>
>>> def fib_loop(n):
...     if n <= 1:
...         return n
...     fn, fnm1 = 1, 0
...     for _ in range(2, n+1):
...         fn, fnm1 = fn + fnm1, fn
...     return fn
...
>>> def fib_recursion(n, memo={}):
...     if n <= 1:
...         return n
...     if n not in memo:
...         memo[n] = fib_recursion(n-1, memo) + fib_recursion(n-2, memo)
...     return memo[n]
...
>>> import timeit
>>> timeit.timeit("fib_loop(1000)", setup="from __main__ import fib_loop", number=1)
9.027599999456015e-05
>>> timeit.timeit("fib_recursion(1000)", setup="from __main__ import fib_recursion", number=1)
0.0016194200000114733

Alternatively, if you pass a new memo dict for each outer call, you get the same behavior:

>>> timeit.timeit("fib_recursion(1000, {})", setup="from __main__ import fib_recursion", number=1000)
0.38679519899999093
>>> timeit.timeit("fib_loop(1000)", setup="from __main__ import fib_loop", number=1000)
0.07079556799999409

Upvotes: 3

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