Fibonnacci_numbers.ipynb

Kernel: T - Python 3 (Ubuntu Linux)

The Task - create a program that prints the fibonacci numbers

Fibonacci numbers are a set of numbers where each sequential number is the sum of the previous two numbers... i.e. 1, 1, 2, 3, 5, 8, 13, etc.

I explore three different ways to code a solution. The first solution shown below takes an input x, and generates all fibonacci numbers between 1 and x.

First solution - switching the values around

"""
My first solution was to use two variables: a and b, in order to shuffle values around, and
then update a third value: 'result' which is the actual fibonacci number printed with each iteration.
"""
def fibo(x):
    a, b, result = 0, 1, 1  # a : current fibo iteration, b : previous fibo iteration
    while result <= x:  # runs u
        print result,
        b = result  # b stores the previous fibo number
        result = result + a # result updated to next fibo number
        a = b  # increment a ready for next calculation

fibo(1000)

1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987

Streamlined version:

"""
Here I have removed the result variable, moved a and b into the function definition as default values,
and consolidated the juggling of figures onto one line.
"""
def fibo(x, a = 0, b = 1):
    while b <= x:
        print b,
        a, b = b, a + b

fibo(1000)

1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987

What if we wanted to produce a set number of fibonacci numbers, as opposed to all the fibo numbers up to a particular value?

Second solution - set number of iterations:

def fibo(x):
    nums = [0,1]  # a list to hold the fibonacci numbers
    for i in range(1, x):  # append the next fibonacci number to the list for the defined number of iterations 'x'
        nums.append(nums[-1] + nums[-2])  # by summing the two previous numbers
    print(" ".join(str(i) for i in nums[1:])) # print a string of the numbers from the list, avoiding the starting '0'

fibo(20)

1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

Third solution - recursive:

"""Returns the nth fibonacci number via recursion."""
def fibo(n):
    if n == 1 or n == 2:  # first two fibbo no.'s are 1. These end the recursion
        return 1
    return fibo(n - 1) + fibo(n - 2)  # recursively sum the two previous numbers

fibo(20)

6765

I would like to use the above recursive function to print x iterations, so I will define a separate function to do so:

def fiboPrint(x):
    for i in range(1, x + 1):
        print fibo(i),

fiboPrint(20)

1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

And finally...

I wish to make the output slightly more practical for the user. To clarify what the nth value is, I have slightly altered the FiboPrint function:

def fiboPrint(x):
    for i in range(1, x + 1):
        print "Iteration " + str(i) + " is: " + str(fibo(i))

fiboPrint(10)

Iteration 1 is: 1
Iteration 2 is: 1
Iteration 3 is: 2
Iteration 4 is: 3
Iteration 5 is: 5
Iteration 6 is: 8
Iteration 7 is: 13
Iteration 8 is: 21
Iteration 9 is: 34
Iteration 10 is: 55