Compute Fibonacci Numbers with Python

fibonacci.py

def fib(n):
    """ Compute nth element of a Fibonacci sequence:
    1, 2, 3, 5, 8, 13, 21, ...
    
    f(n) = f(n-1) + f(n-2)
    
    f(0) = 0
    f(1) = 1
    f(2) = 1
    f(3) = 2
    
    Parameters
    ----------
    n: uint
        nth element to compute
    Returns
    -------
    uint
    Computed value of a nth element of a Fibonacci sequence.
    
    Algorithm
    ---------
    
    Algo#1: simple 2 recursive calls f(n-1), f(n-2). Not efficient - creates a tree of depth n, with 2*n elements
    Algo#2: no explicit recursion, just operating on array of two elements!
        0 -> [0]
        1 -> [0, 1]
        2 -> [1, 1]
        3 -> [1, 2]
        4 -> [2, 3]
        ....
    
    """
    
    if n==0:
        return 0
    if n==1:
        return 1
    
    two_last = [0, 1]
    
    for i in range(2, n+1):
        curr = two_last[0] + two_last[1]
        two_last[0] = two_last[1]
        two_last[1] = curr
    
    return two_last[1]

for i in range(0, 100):
    print(fib(i))