#
# Sep 16 homework 
# chap 3 exercise 16
# Jim Mahoney's example solution.
#
# Find n'th Fibonnaci number, where n is entered by the user.
#
# I choose to number the sequence this way.
#   F[0] = 0
#   F[1] = 1
#   F[n+2] = F[n] + F[n+1]   for  n >= 0.
# See for example http://en.wikipedia.org/wiki/Fibonacci_number
# That gives for the first few these numbers.
#     n    F[n]
#     --   ----
#     0    0  definition
#     1    1  definition
#     2    1  = sum of two previous ones = 0 + 1
#     3    2  = 1 + 1
#     4    3  = 1 + 2
#     5    5  = 2 + 3
#     6    8  = 3 + 5
#     7   13  = 5 + 8
#

print("-- chap3ex16.py --")
print("Find the n'th Fibonnaci number.")

def fib():
    n = int(input("What is n? "))
    F_n = 0    
    F_n_plus_1 = 1 
    for i in range(n):
        F_n_plus_2 = F_n + F_n_plus_1  # Calculate F[n+2] = F[n] + F[n+1]
        F_n = F_n_plus_1               # Slide up to the next value of n.
        F_n_plus_1 = F_n_plus_2
        ##
        ## -- implementation remarks --
        ##
        ## Another way to do the last two lines would be with tuples:
        # (F_n, F_n_plus_1) = (F_n_plus_1, F_n_plus_2)
        ##
        ## Or all three lines could be done in at once:
        # (F_n, F_n_plus_1) = (F_n_plus_1, F_n + F_n_plus_1)
        ##
    print("F[", n, "] = ", F_n)

fib()