Assignment Description
In this lab we’ll explore some cool helper functions for binary trees, learn about creating helper functions and thinking both iteratively and recursively, and hopefully see some fancy ascii trees on the terminal!
Lab Insight
Trees are a very powerful structure for lookups and finding data quickly. Examples of use cases for this data structure includes search engine optimization and fast sorted data retrieval. CS 410, Text Information Systems, is a course that delves into topics involving text manipulation such as test search lookups. Trees can even be used for syntax and language grammar analysis which relates a lot with CS 421, Programming Languages and Compilers.
A new C++ thing
We’ll be using templates again in this lab, and unfortunately, this means we have to walk into a dark scary corner of C++. But hopefully we can take our lantern and cast some light here before any compiler errors bite.
The following function definitions won’t compile:
template <typename T>
Node * BinaryTree<T>::myHelperFunction(Node * node)
// The compiler doesn't know what a Node is, since the return type isn't scoped
// with the function.
So we have to scope it:
template <typename T>
BinaryTree<T>::Node * BinaryTree<T>::myHelperFunction(Node * node)
Using g++, the latter will show an error such as:
error: expected constructor, destructor, or type conversion before '*' token
Clang gives a more helpful error message:
fatal error: missing 'typename' prior to dependent type name 'BinaryTree<T>::Node'
Without going into the ugly details of it, this is happening because your
compiler thinks Node is a member variable of the BinaryTree<T> class (since
it’s a template). We can resolve this issue simply by adding a nice, friendly,
typename keyword before our BinaryTree<T>::Node type. This lets the
compiler know that Node really is a type, not a variable:
template <typename T>
typename BinaryTree<T>::Node * BinaryTree<T>::myHelperFunction(Node * node)
The above, fixed, definition compiles correctly. Since you’ll probably want to create your own helper functions for this lab, this is important to remember when you see the strange error above. You won’t be responsible for this nuance of templates on any exam in this class.
Getting Set Up
From your CS 225 git directory, run the following on EWS:
git pull
git fetch release
git merge release/lab_trees -m "Merging initial lab_trees files"
If you’re on your own machine, you may need to run:
git pull
git fetch release
git merge --allow-unrelated-histories release/lab_trees -m "Merging initial lab_trees files"
Part of good “git hygiene” is to run git pull before you do anything else.
Upon a successful merge, your lab_trees files are now in your lab_trees directory.
The code for this activity resides in the lab_trees/ directory. Get
there by typing this in your working directory:
cd lab_trees/
A reference for the lab is provided for you in Doxygen form.
Testing Your Code
To test your code, compile using make:
make
Then run it with:
./treefun color
You will see that the output is colored — green means correct output, red means incorrect output, and underlined red means expected output that was not present. This mode is a bit experimental, and it might cause problems with your own debugging output (or other problems in general). To turn it off, simply leave off the “color” argument:
./treefun
Helper Functions and Recursion
You’ll want to be thinking about the following problems recursively. To do
this, though, you’ll have to make your own helper functions to help implement
the functions, so that you can recursively act differently on different nodes.
There is room in the .h file for you to declare these extra functions. A
helper function stub for height() has been provided for you.
The height() Function
There is a function called height() that returns the height of the binary
tree. Recall that the height of a binary tree is just the length of the longest
path from the root to a leaf, and that the height of an empty tree is -1.
We have implemented height() for you (see binarytree.cpp) to help you get a
sense of recursive functions. Please read through the code, and ask questions
if you are unsure of how it finds the height of a tree.
The printLeftToRight() Function
There is a function called printLeftToRight() that prints out the values of
the nodes of a binary tree in order. That is, everything to the left of a node
will be printed out before that node itself, and everything to the right of a
node will be printed out after that node.
We have implemented printLeftToRight() for you (see binarytree.cpp). Please
read through the code, and ask questions if you are unsure of how it works.
Note that printLeftToRight() uses an in-order-traversal to print out the
nodes of a tree. You will need to use one of the three traversals covered in
lecture for some of the following functions.
The mirror() Function
The mirror() function should flip our tree over a vertical axis, modifying
the tree itself (not creating a flipped copy).
For example, if our original tree was
______ 8 ______
______/ \______
__ 5 __ 9 __
__/ \__ \__
2 7 10
/ \ /
1 4 6
/
3
Our mirrored tree would be
______ 8 ______
______/ \______
__ 9 __ 5 __
__/ __/ \__
10 7 2
\ / \
6 4 1
\
3
The TreeTraversals Family
Class Hierarchy for TreeTraversals family:
We’ve already implemented PreorderTraversal class for you (see TreeTraversals/PreorderTraversal.h). Read the constructor and operator++ of TreeTraversal::Iterator to understand how they interact with TreeTraversals. Notice that TreeTraversal and TreeTraversal::Iterator are two separate classes. You can read more about iterators here. Your task is to implement the the following constructors and functions for InorderTraversal class:
InorderTraversal(typename BinaryTree<T>::Node* root)void add(typename BinaryTree<T>::Node *& treeNode)
Test your InorderTraversal class:
clang++ -std=c++1y -stdlib=libc++ -lc++abi main.cpp -o main #run these commands INSIDE TreeTraversals folder
./main
The isOrdered() Family
The isOrdered() family includes two functions, one should be implemented
iteratively, the other should be implemented recursively.
Both functions return true if an in-order traversal of the tree
would produce a nondecreasing list output values, and false otherwise. (This is
also the criterion for a binary tree to be a binary search tree.)
For example, isOrdered() should return true on the following tree:
__ 5 __
__/ \__
1 8
\
2
\
4
but false for
__ 5 __
__/ \__
1 8
\
2
\
11
You’ll need to implement the following functions:
bool isOrderedIterative() constbool isOrderedRecursive() const
Hint: What conditions need to be true for a tree to be in order (as defined above)? How can we check this iteratively? (Your Iterator class might help) How can we check this recursively? You might want to write your own helper functions for this exercise.
Testing Your Code with Catch
Run the Catch tests as follows (this requires your code to compile when run simply as make):
make test
./test
Submitting Your Work
The following files are used in grading:
binarytree.hbinarytree.cppTreeTraversals\InorderTraversal.h
All other files including any testing files you have added will not be used for grading.
Good luck!
Thanks to Nick Parlante/Stanford, Princeton’s CS 126, and CS 473 Spring 2011 for the exercises and inspiration.