Eloquent fibonacci sequences in python

Table of Contents

“If by chance I have omitted anything more or less proper or necessary, I beg forgiveness, since there is no one who is without fault and circumspect in all matters.”

― Leonardo Bonacci - italian mathematician

Leonardo Bonacci

Quick introduction

The idea of this article to collect eloquent python patterns using well-known Fibonacci sequence.

Recursive approach

cat fibonacci1.py

def fibonacci1(n):
    if n < 2:
        return n
    return fibonacci1(n - 2) + fibonacci1(n - 1)
    
if __name__ == '__main__':
    from timeit import timeit
    print(timeit("fibonacci1(5)", setup="from __main__ import fibonacci1"))

$ python3 fibonacci1_bench.py # On my MacBook Pro (Mid 2015) 2.5 GHz Intel Core i7, 16 GB 1600 MHz DDR3
2.0335577040023054

Recursive approach using caching

My favorite advice: you should know you language standard library. You can find lot’s of info under functools module docs. Default maxsize is 128 for lru_cache decorator.

$ cat fibonacci2.py

import functools


@functools.lru_cache()
def fibonacci2(n):
    if n < 2:
        return n
    return fibonacci2(n - 2) + fibonacci2(n - 1)

    
if __name__ == '__main__':
    from timeit import timeit
    print(timeit("fibonacci2(5)", setup="from __main__ import fibonacci2"))

$ python3 fibonacci2_bench.py # On my MacBook Pro (Mid 2015) 2.5 GHz Intel Core i7, 16 GB 1600 MHz DDR3
0.09731649799505249

$ cat fibonacci_generator.py

Generator approach for using yield

def fibonacci_generator():
    a, b = 0, 1
    while True:
        yield a
        a, b = b, a + b

if __name__ == '__main__':
    from timeit import timeit
    print(timeit("list(itertools.islice(fibonacci_generator(), 5))",
                 setup="from __main__ import fibonacci_generator"))

$ python3 fibonacci_generator.py # On my MacBook Pro (Mid 2015) 2.5 GHz Intel Core i7, 16 GB 1600 MHz DDR3
1.1730475709991879

About timeit instead of conclusion.

Also keep in mind:

Note By default, timeit() temporarily turns off garbage collection during the timing. The advantage of this approach is that it makes independent timings more comparable. This disadvantage is that GC may be an important component of the performance of the function being measured. If so, GC can be re-enabled as the first statement in the setup string.

More info about timeit Lib/timeit.py