CS 2C: Adv Data Structures & Algorithms in C++

Project 36.1

Complete an AVL tree Nth largest operation as described below, based on the partially completed files provided below.

Step 1: Inspect the BSTNode.h and BinarySearchTree.h files

Inspect the BSTNode class declaration for a binary search tree node in BSTNode.h. The BSTNode class has private member variables for the key, parent pointer, left child pointer, and right child pointer. Accessor functions exist for each.

Inspect the BinarySearchTree class declaration for a binary search tree node in BinarySearchTree.h. The GetNthKey() function is the only pure virtual function that exists.

Step 2: Inspect other classes related to the inheritance hierarchy

Classes AVLNode and AVLTree inherit from BSTNode and BinarySearchTree, respectively. Each class is implemented in a read only header.

Classes ExtendedAVLNode and ExtendedAVLTree are declared, but implementations are incomplete. Both classes must be implemented in this lab.

Step 3: Understand the purpose of the subtreeKeyCount variable

The ExtendedAVLNode class inherits from AVLNode and adds one integer member variable, subtreeKeyCount. Each node's subtree key count is the number of keys in the subtree rooted at that node. Example:

ExtendedAVLNode's constructor and GetSubtreeKeyCount() member functions are already implemented and should not be changed. Additional member functions are needed to ensure that subtreeKeyCount remains accurate.

Step 4: Implement ExtendedAVLTree and ExtendedAVLNode

Each node in an ExtendedAVLTree must have a correct subtreeKeyCount after an insertion or removal operation. Determine which member functions in AVLTree and AVLNode must be overridden in ExtendedAVLTree and ExtendedAVLNode to keep each node's subtreeKeyCount correct. New functions can be added along with overridden functions, if desired.

Hint: Consider an UpdateSubtreeKeyCount() member function for the ExtendedAVLNode class. The function requires each child node's subtreeKeyCount to be correct, and updates the node's subtreeKeyCount appropriately. Overridden functions in both ExtendedAVLNode and ExtendedAVLTree can call a node's UpdateSubtreeKeyCount() function as needed.

Once determinations are made, complete the implementation of both the ExtendedAVLTree and ExtendedAVLNode classes. Do not implement ExtendedAVLTree's GetNthKey() in this step. GetNthKey() requires correct subtree counts at each node.

Step 5: Run tests

TreeTestCommand is an abstract base class defined in TreeCommands.h. A TreeTestCommand object is an executable command that operates on a binary search tree. Classes inheriting from TreeTestCommand are also declared in TreeCommands.h:

  • TreeInsertCommand inserts keys into the tree
  • TreeRemoveCommand removes keys from the tree
  • TreeVerifyKeysCommand verifies the tree's keys using an inorder traversal
  • TreeVerifySubtreeCountsCommand verifies that each node in the tree has the expected subtree key count
  • TreeGetNthCommand verifies that GetNthKey() returns an expected value

Code in main.cpp contains three automated test cases. Each test executes a vector of TreeTestCommand objects in sequence. The third test includes TreeGetNthCommands and will not pass until the completion of Step 6. The first two tests should pass after completion of step 4.

Before proceeding to Step 6, ensure that the first two tests in main.cpp pass.

Step 6: Implement ExtendedAVLTree's GetNthKey() member function (worst case O(log n))

GetNthKey() must return the tree's nth-largest key. The parameter n starts at 0 for the smallest key in the tree. Ex: Suppose a tree has keys: 

10, 19, 20, 30, 42, 55, 77

Then GetNthKey(0) returns 10, GetNthKey(1) returns 19, ..., GetNthKey(5) returns 55, and GetNthKey(6) returns 77.

Determine an algorithm that uses the subtree key counts so that GetNthKey() operates in worst case O(log n) time.

Here are the files you'll need. You should not need to examine the contents of the last three. They are for testing purposes only.

Here are some hints that a former student provided that seem pretty helpful to me. Feel free to give me some feedback if you don't find them to be all that helpful.

  • UpdateSubtreeCount might seem more complex than it really is, just follow the UpdateHeight format so you don't try referencing fields of nullptrs.
  • GetNthKey required some writing down to find relationships between subtreecounts and indices. I'd recommend figuring out the relationship between leftchild's subtree count and the index of the current node.

No documentation is required.