Warmup: Fibonacci
The Fibonacci Sequence, which sums each number with the one before it, is a great example of a problem that can be solved recursively.
Assignment 1
- Using iteration, write a method
#fibswhich takes a number and returns an array containing that many numbers from the fibonacci sequence. Using an example input of8, this method should return the array[0, 1, 1, 2, 3, 5, 8, 13]. - Now write another method
#fibs_recwhich solves the same problem recursively. This can be done in just 3 lines (or 1 if you’re crazy, but don’t consider either of these lengths a requirement… just get it done).
Understanding recursive Fibonacci
Did you figure it out? Congratulations! But do you really understand what is taking place? If you need some help understanding what’s going on with this method, give Khan Academy’s Stepping Through Recursive Fibonacci Function video a watch. If you prefer to read, Recursive Fibonnaci Explained is also very helpful!
Project: merge sort
We spent some time early on dealing with sorting (e.g. bubble sort). Now it’s time to take another look at sorting with Merge Sort, a type of sort that lends itself well to recursion and can be much faster than bubble sort on the right data sets. You’ll build a method which sorts a given array but uses a “merge sort” method for doing so.
It can be a bit strange to wrap your head around, but just remember you’re “dividing and conquering” the problem.
Background viewing
The first step is to actually understand what the merge sort algorithm is doing:
- Check out this introductory video from Harvard’s CS50x course.
- Check out this more detailed video explanation by David J. Malan (watch only until 1:14:00).
- Merge Sort – How it Works part 1 and Merge Sort – How it Works part II on YouTube give you a more formal look at this problem if you’re still unclear.
- (Optional) Play with this Merge Sort Visualizer to get a better feel for exactly what is happening during a Merge Sort.
Assignment 2
- Build a method
#merge_sortthat takes in an array and returns a sorted array, using a recursive merge sort methodology. - Tips:
- Think about what the base case is and what behavior is happening again and again and can actually be delegated to someone else (e.g. that same method!).
- It may be helpful to check out the background videos again if you don’t quite understand what should be going on.
Additional resources
This section contains helpful links to other content. It isn’t required, so consider it supplemental.
- Another look at merge sort
- For more attempts at recursion try the first 5 problems in Project Euler