For the last couple weeks we have been building an AVL class its time to put all the pieces together. The assignment is to create a templated avltree<TKey, TValue> class in the file avl.h which properly balances trees as part of the insert function. When completed, search and insert must be O(lgN) operations; size and height must be O(1) operations. Recall that we began modifying insert in HW #07 to compute the heights; in HW #08 you were asked to implement the left and right rotate functions. Your test cases were created as part of lab week #07.

The major change to make now is to modify insert so that as you walk up the tree updating heights, you also check to see if the AVL condition is broken. If so then rotate to fix either one rotation for AVL cases 1 and 4, or 2 rotations for AVL cases 2 and 3. Recall that in class (day 20) we discussed a _RotateToFix function that insert could call to fix the tree; this function in turn calls _LeftRotate and _RightRotate.

You will need to implement the following public functions in your avltree class, exactly as shown here. You cannot add nor remove parameters, or change types:

template<typename TKey, typename TValue> class avltree

{ private:

.

.

. public:

avltree()

avltree(avltree& other)

virtual ~avltree() // destructor: int size() int height()

void clear() // clear:

TValue* search(TKey key)

void insert(TKey key, TValue value)

int distance(TKey k1, TKey k2) // distance:

void inorder() std::vector<TKey> inorder_keys() std::vector<TValue> inorder_values() std::vector<int> inorder_heights()

};

Note that three functions have been added for the purposes of project #03: a destructor to free memory, a clear function to empty a given tree, and a distance function that returns the path length between 2 keys. Your avltree class must now free all allocated memory; more details in the next section.

Assignment details

Your avlclass must now contain a destructor that properly frees all memory allocated by the avltree class. On submission well check using valgrind, so you should do the same as part of your testing; recall that destructors and valgrind were introduced in lab during week 05.

Your avlclass must also contain a clear function that empties the tree of all nodes, properly freeing the memory. Note that you *cannot* call the destructor to do this; destructors in C++ are special functions that should only be called by the compiler. Instead, what you should do is create a private helper function that both the destructor and clear call. When clear returns, the root should be nullptr and the size 0.

Finally, add a function distance(k1, k2) that returns the distance between the keys k1 and k2. The distance is defined as the length of the minimum path between k1 and k2. For example, consider the following tree > The distance(5, 100) = 6. The distance from 31 to 12 is 3. And the distance from 46 to 12 = 3. The reverse are also true, e.g. the distance(100, 5) = 6.

If k1 or k2 is not in the tree, then the distance is defined as -1. If k1 = k2, then the distance is 0.

Programming Environment

You are free to program in any environment you want; final submissions will be collected using Gradescope. If you want to use Codio, a project has been created named cs251-project03-avl. The environment will contain catch and valgrind for testing purposes.

In Codio, use make catch to build your Catch-based test.cpp program. Then make run to run. If you want to run your program with valgrind to check for memory leaks / pointer errors, do make valgrind.

Requirements

Your avltree class must be templated, and follow the approach we have been discussing in class (and building in the HW and Labs). Rebalancing must occur during insert, both search and insert must be O(lgN), and size and height must be O(1). This implies your private NODE structure must contain a height field that is properly maintained by the insert and the rotate functions.

Additional program requirements:

1. No other data structures may be used to implement the AVL tree itself i.e. build your tree using a Struct NODE with Key, Value, Height, Left and Right pointers. You can add a Parent pointer if you want, but nothing else should be needed nor added. You can use a stack to walk up the tree and update the heights, etc., but the tree itself must be built using NODEs and pointers.

2. Use std::vector to capture and return the data needed by the inorder testing functions. Likewise, if you need an additional data structure to implement your distance function, by all means use one.