CS35 Lab 8B: AVL Trees

Due by 11:59 p.m., Sunday, November 8, 2015
Your work for this lab consists of two parts:
  1. Complete and test a templated implementation of an AVL tree, AVLTree.
  2. Extend your plagiarism detector for Part A to use your AVLTree to build an index of essays and detect plagiarised documents.
While implementing AVLTree sounds lengthy, 95% was already done in last week's lab. All non-insert and remove methods work the same when comparing a LinkedBST to AVLTree, and we've seen pseudocode for most of the other functions. Below, I will detail the modifications needed to maintain the balanced AVL property. At a high level, you will need to accomplish the following:
  1. Initial setup - get and set up files to for your AVLTree implementation
  2. Modify insert/remove - modify insertInSubtree and removeFromSubtree to balance
  3. Implement balancing and rotations - store node heights, detect imbalances, and implement rotations
  4. Test your AVL Tree - add tests for balancing to testBST
  5. Extend cheatDetector - add AVLTree option to your main program; run benchmark tests.


The AVLTree is very similar to the LinkedBST from Lab 7, except it maintains the AVL balance property to guarantee that the tree is balanced. The AVL balance property is that, for each node in the tree, the height of that node's left and right subtrees differs by at most one.

To efficiently maintain the AVL property, each AVLTreeNode stores its current height in addition to the other data stored by a LinkedBSTNode. In sum, each AVLTreeNode contains:

Our algorithms define an empty child node to have a height of 0 for simplicity, but an empty child node is not an actual node. It is the pointer NULL. You will need to be careful to check that children nodes are not NULL before attempting to access information such as a child node's height or children.

To maintain a roughly O(lg n) tree height, you will extend your LinkedBST implementation to detect imbalances after insertions and removes and then use one of four tree rotation methods to fix the imbalance.

Getting started


Your repo will start with the following files:

Neither of these files needs modifications. Instead, all of you work will be done in AVLTree-private-inl.h. Since the vast majority of methods will be the same as your LinkedBST private methods, you'll use your linkedBST-private-inl.h file as a starting point. To do so, do the following:
  1. Copy your linkedBST-private-inl.h file:
    $ cp linkedBST-private-inl.h AVLTree-private-inl.h
  2. Replace all instances of BSTNode with AVLTreeNode and LinkedBST with AVLTree. This is done using search and replace. Each editor has a built in way of doing this, and you are free to do it by hand. We can do it from the command line with a linux program called sed:
    $ sed -i 's/BSTNode/AVLTreeNode/g' AVLTree-private-inl.h 
    $ sed -i 's/LinkedBST/AVLTree/g' AVLTree-private-inl.h 

You're free to start from your own implementation, or from the one provided. Note that the testAVL make option won't work until you copy this over.

Inserts/Removes in AVLTree


To insert in an element an AVL Tree, we follow the normal protocol. As we saw in class, the insertInSubtree method should handle the 4 cases (i.e., base case, duplicate key, smaller key, larger key) for recursion the same as LinkedBST. Once that work is complete, current is the root of a sub-tree that may now be unbalanced and require a rotation. This check must be done at every call since the imbalance could be detected at any step back up the tree. Your overall method should follow this protocol:

  1. Handle the 4 cases the same as LinkedBST
  2. Before returning:
    1. Calculate height of node
    2. Check for imbalances
    3. Fix imbalances with rotations
  3. Step 2 may have resulted in a new root for the sub-tree. Return the root of the sub-tree to the calling function
Implementing this should take 1 to 2 lines of code at most. You completed #1 already from Lab 8. #2 should be handled by another function (balance()) specified below. #3 should take the value returned by balance and return it.

removeFromSubtree follows the same outline. Before every return statement, you should call balance to handle all of the work of updating heights and checking for imbalances.

Balancing and rotations


To complete the AVLTree, you should complete each of the rotation functions discussed in class. Their prototypes can be found in AVLTree.h file. There is one rotation function for each of the four cases discussed in class, and each returns the new root of the sub-tree to the calling function:

Each rotation should do the following:

These functions are called by the balance function (which is in turn called by insertInSubtree and removeFromSubtree). balance does much of the book-keeping to maintain the AVL property. To complete this method, you should take the following steps:

  1. If current is NULL, return current. There is no work to do.
  2. Update current's height. You should implement this routine in computeHeightFromChildren. Remember to account for potential empty children (NULL).
  3. Check for a left imbalance (left child is 2 taller than right)
    • If so, check which of left's children is taller. Call either rightRotate (left grandchild is bigger) or leftRightRotate (right grandchild is bigger)
  4. Check for a right imbalance (right child is 2 taller than left)
    • If so, check which of right's children is taller. Call either leftRotate (right grandchild is bigger) or rightLeftRotate (left grandchild is bigger)
  5. Return the root of the sub-tree. Note that it may have changed.

Unit-testing the AVLTree

You should test the AVLTree implementation using the testBST program from last week. This should stress test the AVLTree implementation for a large number of random insertions and deletions. In addition, your tests should confirm that each of your rotation functions behaves as expected for known examples of the tree. While you cannot access private methods, you can come up with specific examples that guarantee certain rotations will occur and then use public methods such getHeight() or getPreOrder() to inspect the contents of the tree.

Extending cheatDetector

Return to the write-up for Part A and ensure that your cheatDetector can work with either LinkedBSTs or AVLTrees. The details are found in that write-up. Once that is complete, run your program with both and pay attention to the performance. How do the heights of trees change by using balancing? You will need to answer a few questions for the README.

Submitting your work

Submit your solution along with Part A by pushing to Github as usual.