#  Fibonacci sequence calculations

# n:      0  1  2  3  4  5  6  7  8  9
# fib(n): 0  1  1  2  3  5  8  13 21 34

# A non-recursive function for calculating the nth Fibonacci number:
def fib(n):
    if n < 2:
        return n
    prev = 0
    curr = 1
    for i in range(2,n+1):
        new_curr = prev + curr
        prev = curr
        curr = new_curr
    return curr

# Calculating the ratios of pairs of Fibonacci numbers -- like fib(6)/fib(5)
def CalcFibRatios(low,high):
    for i in range(low,high+1):
        print(fib(i)/fib(i-1))
        
# The recursive function for Fibonacci
def fib_r(n):
    if n < 2:
        return n
    return fib_r(n-1) + fib_r(n-2)

# Timing how long it takes to calculate fib_r(n)
def timeit(n):
    import time
    start = time.time()
    fib_r(n)
    end = time.time()
    return end - start