Fibonacci Series Exercise
Computing the Fibonacci and Lucas Series
Some nifty uses of recursion
Goal:
The Fibonacci Series is a numeric series starting with the integers 0 and 1.
In this series, the next integer is determined by summing the previous two
This gives us:
0, 1, 1, 2, 3, 5, 8, 13, ...
We will write a function that computes this series – then generalize it.
Step 1
Create a new file
series.pyin the exercise repo.In it, add a function called
fibonacci.The function should have one parameter
n.The function should return the
nthvalue in the Fibonacci series (starting with zero index).
Ensure that your function has a well-formed “docstring”
Note that the Fibonacci series is naturally recursive – the value is defined by previous values:
fib(n) = fib(n-2) + fib(n-1)
Lucas Numbers
The Lucas Numbers are a related series of integers that start with the values 2 and 1 rather than 0 and 1. The resulting series looks like this:
2, 1, 3, 4, 7, 11, 18, 29, ...
In your series.py file, add a new function lucas that returns the
nth value in the Lucas numbers series (starting with zero index).
Ensure that your function has a well-formed “docstring”
You should find it’s very similar to the fibonacci() function.
Generalizing
Both the fibonacci series and the lucas numbers are based on an identical formula:
f(n) = f(n-2) + f(n-1)
That’s why the code is so similar.
This formula creates a class of series that are all related – each with a different two starting numbers.
Add a third function called sum_series that can compute all of these related series.
It should have one required parameter and two optional parameters. The required parameter will determine which element in the series to print. The two optional parameters will have default values of 0 and 1 and will determine the first two values for the series to be produced.
Calling this function with no optional parameters will produce numbers from the Fibonacci series (because 0 and 1 are the defaults).
Calling it with the optional arguments 2 and 1 will produce values from the Lucas numbers.
Other values for the optional parameters will produce other series.
Note: While you could check the input arguments, and then call one of the functions you wrote, the idea of this exercise is to make a general function, rather than one specialized. So you should re-implement the code in this function.
In fact, you could go back and re-implement your Fibonacci and Lucas
functions to call sum-series with particular arguments.
Ensure that your function has a well-formed “docstring”
Tests…
Add a block of code to the end of your series.py module.
Use the block to write a series of assert statements that
demonstrate that your three functions work properly.
Use comments in this block to inform the observer what your tests do.
We have created a template for you to use to clarify what we mean by these asserts:
Add your new module to your personal git repo and commit frequently while working on your implementation. Include good commit messages that explain concisely both what you are doing and why.
When you are finished, push your changes to your fork of exercise repository in GitHub and make a pull request to submit it.