Description
Getting motivated
In this lab, you will gain familiarity with the binary search tree data structure and the iterator abstraction. The first is a core data structure. The latter is a core C++/STL concept.
Lab submission and due date
Submit your work via Canvas as usual. The BST.h header file that statisfies BST1 and drawings that illustrate the support functions needed by BST2 and BST3 are due 11.59pm Tuesday Apr 2, 2019; scan the drawings mentioned below to PDF or take photos and submit JPG or PNG files (make sure they are readable). The BST.h file that statisfies BST2 and BST3 is due 11.59pm Tuesday Apr 9, 2019. Do not submit any cpp files. Your task is to update the binary search tree template code which goes in the BST.h header file.
Programs you need to write
Write the following code. See the TAs well in advance of the deadline to get your problems sorted out. This assignment may be more difficult than you first think. Base your code on the bst1 handout, which uses left and right pointers, not the bst2 handout, which uses a link array of pointers.

Run the /home/cs140/labs/lab6/copy script to obtain a skeleton header file called bst.h, source code driver programs called bst1_usage.cpp, bst2_usage.cpp, and bst3_usage.cpp, x86Linux executables called bst1, bst2 and bst3, as well as data files called test1_int.txt and test2_int.txt for development purposes. The executables showcase the functionality described next. When in doubt about what to do, run these executables and study the output. Make sure your programs work on other data than the two files given to you.

For 40 points, create the BST.h file needed to compile and run the BST1 program which is based on bst1_usage.cpp. Here is how you do it.
Copy bst.h to BST.h. Strip out comments as well as any code not needed like the iterator subclass and all undefined bst member functions. Add a node ID (int) and a parent pointer (node *) to the bst::node subclass. Define define and implement the bst::node() constructor. Have the constructor take a node ID argument which is set to 0 if absent, and use this argument to initialize the node ID. Set the parent pointer to NULL.
The node ID is a unique integer assigned to nodes as they are created. Add a node ID to the bst class which is initialized in the bst constructor and updated everytime a new node is added to the binary search tree. Update bst::insert to do the latter and to pass the updated value along to the bst::node constructor.
With respect to the parent pointer (or link), be aware that bst::insert() is a recursive function which does not have access to the parent when processing a node. You must therefore set the parent pointer as you ascend out of the recursion (when you reach the parent, you have access to the root of the subtree just processed).
Update bst::node::print() to output the node key, its ID, the parent ID, and the left and right subtree IDs (if they exist). See an output example below.

For 25 points, make simple drawings that illustrate how the following three functions described below are meant to work, namely, bst::iterator::operator++() which implements a single step for an inorder traversal, and bst::lower_bound(key) and bst::upper_bound(key) which find nodes that bracket a search range for a given key, i.e., lower_bound ≤ key < upper_bound. Add a few sentences to explain your drawings but be succinct. These drawings are meant for you to think about functionality before you think about code. That is, you can’t code what you don’t understand, and you don’t understand what you can’t explain. This makes you explain.

For 90 points, modify BST.h as necessary to compile and run the BST2 program which is based on bst2_usage.cpp. A quick look at the latter should convince you that this is a matter of adding an iterator subclass to the bst class. Here is how you do it.
Add public member functions bst::begin() and bst::end() which respectively return an iterator that points to the node which holds the smallest key and an iterator that contains a NULL pointer which indicates the binary search tree has been exhausted (analogous to the first node and the end of a singlelinked list). Recall that the smallest key is found in the leftmost node. You find it by iteratively searching thru the sequence of left children starting at the root of the tree.
The bst.h file lists a number of iterator operators that must be included, namely: ++ PRE increment for an inorder move to the next node, * for dereferencing and thus accessing the node key, == and != for comparing iterators. Base your code for these operators on the list::iterator code covered in class. This might be a good time to read and understand the corresponding code handout which available from Canvas.
The ++ PRE increment operator is by far the most complicated code you will write in this lab assignment. Before you even think about programming it, make sure you know how to carry out an inorder traversal with focus on how to advance from one node to the next. Be aware that you will NOT be using recursion. Each call to bst::iterator::operator++ must explicitly update the underlying node pointer to the next node.
Hint: The bst::begin() function sets the node pointer to the leftmost node in the binary search tree. The next node is the parent thereof. The next node after that is the leftmost node in the parent’s right subtree (if it has any). You then return to that node’s parent before you process it’s right subtree. Eventually, you return to the root of the tree whereafter you descend into the main right subtree. See the pattern? Be very careful when you ascend out of the tree when the last node has been processed. That is, you must detect and handle an attempt to access the parent of the root node since it doesn’t exist. If you forget to this, your code will seg fault. Guaranteed.
When the bst::iterator subclass has been implemented, the print() function in bst2_usage.cpp will output the content of the binary search tree in a lexicographically sorted order. See an output example below.

For 45 points, modify BST.h as necessary to compile and run the BST3 program which is based on bst3_usage.cpp. A quick look at the latter should convince you that this is a matter of adding two public member functions to the bst class, namely, bst::lower_bound() and bst::upper_bound() which both take a key as input and return an iterator corresponding to node in the binary search tree. Here is how these functions are suppposed to work.
The bst::lower_bound(key) function must return an iterator to the first node in the binary search tree whose key is not less than the given key, i.e., lower_bound ≤ key. If the key exists, the returned iterator points to that node. If the key does not exist, the returned iterator points to the first node whose key value is greater. Your search must be based on explicitly traversing the appropriate path from the root to the target node. That is, do not use an iterator based inorder traversal.
The bst::upper_bound() function must return an iterator to the first node in the binary search tree whose key is strictly greater than the given key, i.e., key < upper_bound. If the key exists, the returned iterator points to the next node when performing an inorder traversal. If the max key does not exist, the returned iterator should represent a NULL pointer. Your search must be based on explicitly traversing the appropriate path from the root to the target node. That is, do not use an iterator based inorder traversal.
Hint: bst::lower_bound() and bst::upper_bound() are nearly identical; their only difference is the comparison operator used.
The iterators returned from bst::lower_bound() and bst::upper_bound() are passed to the global print() function which outputs the corresponding sequence of data stored in the binary search tree. See an output example below.
Executable output examples
Note: Extra white space has been added for ease of reading.
bst1
user> cat test1_int.txt 4 2 1 3 2 6 5 7 user> ./bst1 test1_int.txt 4 1 : ROOT L= 2 R= 5 2 2 : P= 1 L= 3 R= 4 6 5 : P= 1 L= 6 R= 7 1 3 : P= 2 3 4 : P= 2 5 6 : P= 5 7 7 : P= 5
bst2
user> ./bst2 test1_int.txt
1 2 3 4 5 6 7
bst3
user> ./bst3 test1_int.txt 1 2 3 4 5 6 7 Print [key0:key1]: 5 8 *** lower bound 5 *** upper bound INF 5 6 7 Print [key0:key1]: 0 2 *** lower bound 1 *** upper bound 3 1 2 Print [key0:key1]: 3 3 *** lower bound 3 *** upper bound 4 3 Print [key0:key1]: 10 20 *** lower bound INF *** upper bound INF Print [key0:key1]: CtrlD
Grade Rubric
BST1 code (30 points)
*15: Definition and use of bst::node::ID information *15: Definition and use bst::node::parent information
BST2 understanding (15 points)
*15: Drawing that illustrates bst::iterator++() mode of operation
BST2 code (90 points)
*20: Definition of bst::iterator subclass, implementation of all
member functions and operator overloads except operator++().
*50: Implementation of bst::iterator::operator++()
*10: Implementation of bst::begin and bst::end member functions
*10: Code structure and comments
BST3 understanding (20 points)
*10: Drawing of bst::lower_bound() computation *10: Drawing of bst::upper_bound() computation
BST3 code (45 points)
*20: Implementation of bst::lower_bound member function *20: Implementation of bst::upper_bound member function *5: Code structure and comments