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MP5: Lists and Recursion
Recursion is an important and powerful programming technique. Sometimes it is the best way to solve a problem, and sometimes it is almost the only way to solve a problem.
Recursion can be tricky to wrap your head around at first, but as usual the best way to get comfortable with this technique is to practice. For MP5 you’ll complete several programming tasks that encourage you to consider both recursive and iterative solutions.
MP5 is due Monday 4/2/2018 @ 5PM. To receive full credit, you must submit by this deadline. In addition, 10% of your grade on MP5 is for submitting code that earns at least 30 points by Monday 3/26/2018 @ 5PM. Note that this is the day after Spring Break, so we encourage you to get started the week that MP5 is released.
As usual, late submissions will be subject to the MP late submission policy.
1. Learning Objectives
MP5 introduces the concept of recursive programming and to working with linked lists and object references. You’ll learn how to complete simple recursive methods to accomplish common programming tasks. We also introduce you to binary trees, an important computer science data structure and one very amenable to recursive approaches. Finally, MP5 provides practice at working with linked lists, another important computer science data structure.
2. Assignment Structure
MP5 consists of three programming tasks:

SingleLL.java
: here you must extend complete several methods on a linked list class that storesint
s, including inserting, removing, and swapping values. Consider this task a warm up. 
Tree.java
: here you must create and complete a binary search tree class, including adding constructors and insertion methods, along with methods that search and perform computations on your tree. This tasks contains the bulk of the points for the MP, so work on it once you’ve finishedSingleLL.java
. 
DNA.java
: for the final task you must complete a class that stores a DNA sequence and a static method that computes the longest common subsequence of two DNA instances. Longest common subsequence is the hardest algorithmic challenge on this MP, so leave this for the end. It’s only worth 10 points and you can consider it a challenge problem.
Like MP4, MP5 provides a bit less scaffolding than previous MPs. The official specification is our MP5 online documentation. It should precisely define what each public method in each class should do. Private methods are left for you to design in any way that allows the tests to pass. If you believe that the documentation is unclear, please post on the forum and we’ll offer clarification as needed.
2.1. Obtaining MP5
Use this GitHub Classroom invitation link to fork your copy of MP5. Once your repository has been created, import it into IntelliJ following our assignment Git workflow guide.
2.2. Your Goal
At this point you should be familiar with the requirements from previous MPs. See the grading description below.
3. Approaching MP5
Completing MP5 requires writing fewer lines of code than MP3 and MP4. But some of it is recursive code, so it will take you longer. Don’t expect to make as much progress writing recursive code when you are getting started. It’s tricky, and takes practice. Slow down and focus on applying the recursive design principles that we’ve taught in lecture and in lab.
3.1. Understand The Requirements
To complete MP5 you must understand the specification. Read that first. And then read it again.
3.2. Designing Recursive Functions
Recall the guidelines for designing recursive functions that we presented in lab and lecture:

Every recursive function must have a base case. If you don’t stop recursing, you will eventually run out of memory and your program will crash. So there must be some case where you do not call yourself again.

The base case must be reached. As a corollary to the above, every set of recursive calls must eventually reach the base case, otherwise (again) your program will recurse infinitely, run out of memory and crash.

The problem should get smaller each time. Each recursive step should reduce the size of the problem somehow. This can happen in several ways. In Fibonacci, for example, we reduce the size of the problem by reduction toward known staring values. When processing trees, we reduce the size of the problem by splitting the tree into several subtrees which are considered separately. How this happens depends on the problem, but it does need to happen somehow.
It can also be helpful to consider simple cases. How do you reverse a list with only one element? Now, extend that to a list with two elements, then three. You may begin to see a pattern emerge that helps you understand how to design your recursive approach.
3.3. Binary Search Trees
MP5 also introduces you to binary search trees, an important computer science data structure. Binary search trees are also recursive data structures, in that each tree node refers to other tree nodes, including a parent (moving up the tree) and two children (down the tree).
Like other data structures, binary search trees are useful because of the algorithms that we can run on them. As the name implies, searching can be particularly efficient on binary search trees due to the way that they structure data.
3.3.1. Insertion algorithm
There are many great online resources to help you learn about binary search trees. But let’s consider one of the more basic tree operations: insertion. Storing data in my tree requires that I be able to insert values. And being able to efficiently search for values later requires that I perform insertions in a particular way.

Start at the root of the tree.

Compare the value that is being inserted with the value of the current node.

If it is larger, try to move to the right.

If it is smaller, try to move to the left.

If the current node has a left or right child (depending on the choice above), make that the current node and continue.

Otherwise set the left or right child (depending on the choice above) of the current node to a new node with the new inserted value.

Continue until the node is inserted.
Note that the binary search trees you implement for MP5 can reject duplicate values. So if you reach a node that has the same value as the one you are trying to insert, the insertion can fail. However, this is an implementation decision, and you should think about how you might store duplicate values if needed.
If you maintain the sorted structure during your insertions as described above, the other algorithms that we ask you to complete on trees will be straightforward.
3.4. Getting Help
The course staff is ready and willing to help you every step of the way! Please come to office hours, or post on the forum when you need help. You should also feel free to help each other, as long as you do not violate the academic integrity requirements.
4. Grading
MP5 is worth 100 points total, broken down as follows:

20 points:
SingleLL.java
:
5 points for insertion

5 points for removal

10 points for swaps 1


50 points:
Tree.java
:
10 points for constructors and insertion

10 points for minimum and maximum

10 points for search

10 points for depth counting

10 points for descendant counting


10 points:
DNA.java

10 points for no
checkstyle
violations 
10 points for committing code that earns at least 30 points before Monday 3/26/2018 @ 5PM.
4.1. Test Cases
As in previous MPs, we have provided exhaustive test cases for each part of MP5. Please review the MP0 testing instructions.
4.2. Autograding
Like previous MPs we have provided you with an autograding script that you can use to estimate your current grade as often as you want. Please review the MP0 autograding instructions.
5. Submitting Your Work
Follow the instructions from the submitting portion of the CS 125 workflow instructions.
And remember, you must submit something that earns 30 points before Monday 3/26/2018 @ 5PM to earn 10 points on the assignment.
5.1. Academic Integrity
Please review the MP0 academic integrity guidelines.
Nothing makes Chuchu sadder than cheaters!